Question: a bag consists of 30 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?

<gadget id="calculator">5 + 9</gadget>
<output>14</output>

<gadget id="calculator">30 - 14</gadget>
<output>16</output>

<gadget id="calculator">16 + 9</gadget>
<output>25</output>

<gadget id="calculator">25 / 30</gadget>
<output>5/6 = around 0.833333</output>
<result>5/6 = around 0.833333</result>

Choices:
A. 5 / 6
B. 2 / 4
C. 1 / 4
D. 1 / 8
E. 1 / 16

divide(add(subtract(30, add(5, 9)), 9), 30)

Explanation: "bag consists of 20 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 30 - 5 - 9 = 16 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 30 + 16 / 30 = 25 / 30 = 5 / 6 hence , answer will be a ."


Question: a present value of a machine is $ 1000 . its value depletiation rate is 10 % per annum then find the machine value after 2 years ?

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">(9/10) ** 2</gadget>
<output>81/100 = around 0.81</output>

<gadget id="calculator">1_000 * (81/100)</gadget>
<output>810</output>
<result>810</result>

Choices:
A. $ 900
B. $ 810
C. $ 915
D. $ 715
E. $ 795

multiply(1000, power(subtract(const_1, divide(10, const_100)), 2))

Explanation: "p = $ 1000 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 1000 * 9 / 10 * 9 / 10 = $ 810 answer is b"


Question: in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 48 . what is the total number of students in the school ?

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">48 * (2/3)</gadget>
<output>32</output>

<gadget id="calculator">48 + 32</gadget>
<output>80</output>

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">80 / (4/5)</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 72
B. 80
C. 120
D. 100
E. 150

divide(add(48, multiply(48, divide(2, 3))), subtract(const_1, divide(20, const_100)))

Explanation: "let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 48 + 2 / 3 of 48 ( 80 / 100 ) x = 80 x = 100 . answer d"


Question: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 756 find the share of a .

<gadget id="calculator">3_000 * 8</gadget>
<output>24_000</output>

<gadget id="calculator">3_000 - 1_000</gadget>
<output>2_000</output>

<gadget id="calculator">12 - 8</gadget>
<output>4</output>

<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>

<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>

<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>

<gadget id="calculator">4_000 + 1_000</gadget>
<output>5_000</output>

<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>

<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>

<gadget id="calculator">32_000 + 52_000</gadget>
<output>84_000</output>

<gadget id="calculator">756 / 84_000</gadget>
<output>9/1_000 = around 0.009</output>

<gadget id="calculator">(9/1_000) * 32_000</gadget>
<output>288</output>
<result>288</result>

Choices:
A. 240
B. 388
C. 288
D. 277
E. 122

multiply(divide(756, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

Explanation: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 756 = 288 answer : c"


Question: 100 people are attending a newspaper conference . 35 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?

<gadget id="calculator">38 + 1</gadget>
<output>39</output>

<gadget id="calculator">39 + 35</gadget>
<output>74</output>

<gadget id="calculator">100 - 74</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 21
B. 26
C. 28
D. 30
E. 32

subtract(100, add(add(38, const_1), 35))

Explanation: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 35 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 35 + { editors } - x + 2 x - - > x = 65 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 65 - 39 = 26 . answer : b ."


Question: there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 78 . how tall is the fourth person ?

<gadget id="calculator">78 * 4</gadget>
<output>312</output>

<gadget id="calculator">4 + 6</gadget>
<output>10</output>

<gadget id="calculator">6 + 10</gadget>
<output>16</output>

<gadget id="calculator">312 - 16</gadget>
<output>296</output>

<gadget id="calculator">296 / 4</gadget>
<output>74</output>

<gadget id="calculator">74 + 10</gadget>
<output>84</output>
<result>84</result>

Choices:
A. 82
B. 84
C. 86
D. 88
E. 90

add(divide(subtract(multiply(78, 4), add(6, add(4, 6))), 4), add(4, 6))

Explanation: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 78 ) = 312 x = 74 and the fourth person has a height of 74 + 10 = 84 inches the answer is b ."


Question: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability w that this product will be a multiple of 45 ?

<gadget id="calculator">20 + 4</gadget>
<output>24</output>

<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<result>1/24 = around 0.041667</result>

Choices:
A. 1 / 32
B. 1 / 28
C. 1 / 24
D. 1 / 16
E. 1 / 14

Explanation: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability w = 1 / 24 . answer c ."


Question: during a pizza buffet where a eats more times 1.8 than b , and b eats 8 times less than c . find the leat number of times all the 3 has to eat

<gadget id="calculator">1.8 * 10</gadget>
<output>18</output>

<gadget id="calculator">18 / 3</gadget>
<output>6</output>

<gadget id="calculator">6 * 6</gadget>
<output>36</output>

<gadget id="calculator">36 * 10</gadget>
<output>360</output>
<result>360</result>

Choices:
A. 350
B. 260
C. 360
D. 380
E. 285

multiply(multiply(divide(multiply(1.8, const_10), 3), divide(multiply(1.8, const_10), 3)), const_10)

Explanation: a eats more than b if b eats 1 times than the ratio of a and b is a : b is 1.8 : 1 or 9 : 5 and as b eat 8 times less the c the the ratio of b : c is 5 : 40 the the least number of times all three has eat is the lcm of a , b , c that is 360 . . answer : c


Question: ashok secured average of 72 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?

<gadget id="calculator">72 * 6</gadget>
<output>432</output>

<gadget id="calculator">74 * 5</gadget>
<output>370</output>

<gadget id="calculator">432 - 370</gadget>
<output>62</output>
<result>62</result>

Choices:
A. 62
B. 74
C. 78
D. 80
E. none of these

subtract(multiply(72, 6), multiply(74, 5))

Explanation: explanation : number of subjects = 6 average of marks in 6 subjects = 72 therefore total marks in 6 subjects = 72 * 6 = 432 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 432 – 370 = 62 answer a


Question: at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 85 . if the restaurant serves 120 customers today , raising the average to 90 customers per day , what is the value of x ?

<gadget id="calculator">120 - 90</gadget>
<output>30</output>

<gadget id="calculator">90 - 85</gadget>
<output>5</output>

<gadget id="calculator">30 / 5</gadget>
<output>6</output>

<gadget id="calculator">120 - 100</gadget>
<output>20</output>

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">6 - (1/5)</gadget>
<output>29/5 = around 5.8</output>
<result>29/5 = around 5.8</result>

Choices:
A. 2
B. 5
C. 6
D. 15
E. 30

subtract(divide(subtract(120, 90), subtract(90, 85)), divide(subtract(120, const_100), const_100))

Explanation: "withoutusing the formula , we can see that today the restaurant served 30 customers above the average . the total amount above the average must equal total amount below the average . this additional 30 customers must offset the “ deficit ” below the average of 90 created on the x days the restaurant served only 85 customers per day . 30 / 5 = 6 days . choice ( a ) . withthe formula , we can set up the following : 90 = ( 85 x + 120 ) / ( x + 1 ) 90 x + 90 = 85 x + 120 5 x = 30 x = 6 answer choice ( c )"


Question: two boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction . what time will they take to be 20 km apart ?

<gadget id="calculator">7.5 - 5.5</gadget>
<output>2</output>

<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 10
B. 11
C. 14
D. 15
E. 20

Explanation: "explanation : relative speed = 7.5 - 5.5 = 2 kmph ( because they walk in the same direction ) distance = 20 km time = distance / speed = 20 / 2 = 10 hr answer : a"


Question: a man can row 6 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

<gadget id="calculator">6 + 2</gadget>
<output>8</output>

<gadget id="calculator">6 - 2</gadget>
<output>4</output>

<gadget id="calculator">8 * 4</gadget>
<output>32</output>

<gadget id="calculator">8 + 4</gadget>
<output>12</output>

<gadget id="calculator">32 / 12</gadget>
<output>8/3 = around 2.666667</output>

<gadget id="calculator">(8/3) * 2</gadget>
<output>16/3 = around 5.333333</output>
<result>16/3 = around 5.333333</result>

Choices:
A. 5.32
B. 5.7
C. 5.76
D. 5.74
E. 5.71

multiply(divide(multiply(add(6, 2), subtract(6, 2)), add(add(6, 2), subtract(6, 2))), const_2)

Explanation: "m = 6 s = 2 ds = 8 us = 4 x / 8 + x / 4 = 1 x = 2.66 d = 2.66 * 2 = 5.32 answer : a"


Question: if 8 workers can build 8 cars in 8 days , then how many days would it take 6 workers to build 6 cars ?

<gadget id="calculator">8 * 8</gadget>
<output>64</output>

<gadget id="calculator">64 / 8</gadget>
<output>8</output>

<gadget id="calculator">6 / 6</gadget>
<output>1</output>

<gadget id="calculator">8 * 1</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 2
B. 4
C. 6
D. 8
E. 12

multiply(divide(multiply(8, 8), 8), divide(6, 6))

Explanation: "8 workers can build 1 car per day on average . 1 worker can build 1 / 8 of a car per day . 6 workers can build 6 / 8 car per day . the time required to build 6 cars is 6 / ( 6 / 8 ) = 8 days the answer is d ."


Question: a person can swim in still water at 12 km / h . if the speed of water 10 km / h , how many hours will the man take to swim back against the current for 8 km ?

<gadget id="calculator">12 - 10</gadget>
<output>2</output>

<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 4
B. 7
C. 5
D. 9
E. 6

Explanation: "m = 12 s = 10 us = 12 - 10 = 2 d = 8 t = 8 / 2 = 4 answer : a"


Question: the moon revolves around the earth at a speed of approximately 0.2 kilometers per second . this approximate speed is how many kilometers per hour ?

<gadget id="calculator">0.2 * 3_600</gadget>
<output>720</output>
<result>720</result>

Choices:
A. 60
B. 720
C. 62.5
D. 3,600
E. 3,672

Explanation: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 0.2 * 3600 = 720 kilometers per hour . option b is correct"


Question: if 1.5 cm of a pencil is purple , 0.5 cm of the remaining is black and the remaining 2 cm is blue , what is the total length of the pencil ?

<gadget id="calculator">1.5 + 0.5</gadget>
<output>2</output>

<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 5 cm
B. 3 cm
C. 1 cm
D. 4 cm
E. 2 cm

Explanation: purple is 1.5 cm black is 0.5 cm blue is 2 cm 1.5 + 0.5 + 2 = 4 cm answer is d ) 4 cm


Question: of the 130 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?

<gadget id="calculator">130 - 80</gadget>
<output>50</output>

<gadget id="calculator">50 - 20</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 20
B. 30
C. 50
D. 80
E. 100

Explanation: full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 30 answer : option b


Question: what is the rate percent when the simple interest on rs . 810 amount to rs . 155 in 4 years ?

<gadget id="calculator">100 * 155</gadget>
<output>15_500</output>

<gadget id="calculator">810 * 4</gadget>
<output>3_240</output>

<gadget id="calculator">15_500 / 3_240</gadget>
<output>775/162 = around 4.783951</output>
<result>775/162 = around 4.783951</result>

Choices:
A. 4.78
B. 4.68
C. 4.58
D. 4.48
E. 4.38

divide(multiply(const_100, 155), multiply(810, 4))

Explanation: "155 = ( 810 * 4 * r ) / 100 r = 4.78 % answer : a"


Question: a pharmaceutical company received $ 4 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?

<gadget id="calculator">4 / 20</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>

<gadget id="calculator">9 / 108</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/12) * 100</gadget>
<output>25/3 = around 8.333333</output>

<gadget id="calculator">20 - (25/3)</gadget>
<output>35/3 = around 11.666667</output>

<gadget id="calculator">(35/3) / 20</gadget>
<output>7/12 = around 0.583333</output>

<gadget id="calculator">(7/12) * 100</gadget>
<output>175/3 = around 58.333333</output>
<result>175/3 = around 58.333333</result>

Choices:
A. 8 %
B. 15 %
C. 45 %
D. 52 %
E. 58 %

multiply(divide(subtract(multiply(divide(4, 20), const_100), multiply(divide(9, 108), const_100)), multiply(divide(4, 20), const_100)), const_100)

Explanation: "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 4 / 20 = 1 / 5 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 4 / 20 ) x 60 = 12 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 12 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 12 ) / 12 ] x 100 - 175 / 3 x 100 at this point we can stop and consider the answer choices . since we know that 175 / 3 is just a bit less than ½ , we know that - 175 / 3 x 100 is about a 58 % decrease . answer e ."


Question: a father said to his son , ` ` i was as old as you are at the present at the time of your birth ' ' . if the father ' s age is 52 years now , the son ' s age 5 years back was :

<gadget id="calculator">52 / 2</gadget>
<output>26</output>

<gadget id="calculator">26 - 5</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 14
B. 67
C. 56
D. 21
E. 34

Explanation: let the son ' s present age be x years . then , ( 52 - x ) = x 2 x = 52 . x = 26 . son ' s age 5 years back ( 26 - 5 ) = 21 years . answer : d


Question: at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 20 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 20 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?

<gadget id="calculator">56 * 20</gadget>
<output>1_120</output>

<gadget id="calculator">52 * 20</gadget>
<output>1_040</output>

<gadget id="calculator">1_120 - 1_040</gadget>
<output>80</output>

<gadget id="calculator">60 - 52</gadget>
<output>8</output>

<gadget id="calculator">80 / 8</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 6
B. 7
C. 8
D. 9
E. 10

divide(subtract(multiply(56, 20), multiply(52, 20)), subtract(60, 52))

Explanation: "let number of apples = a number of oranges = b a + b = 20 - - - 1 . 56 = ( . 4 a + . 6 b ) / 20 = > 56 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 4 b = 16 let the number of oranges put back = c 52 * ( 20 - c ) = 40 * 4 + 60 ( 16 - c ) = > c = 10 answer e"


Question: there are 20 cm , 21 cm , 22 cm , 23 cm , 24 cm , 25 cm rods of quantities 23 , 64 , 32 respectively . find average of this data .

<gadget id="calculator">20 * 23</gadget>
<output>460</output>

<gadget id="calculator">21 * 23</gadget>
<output>483</output>

<gadget id="calculator">460 + 483</gadget>
<output>943</output>

<gadget id="calculator">22 * 64</gadget>
<output>1_408</output>

<gadget id="calculator">943 + 1_408</gadget>
<output>2_351</output>

<gadget id="calculator">23 * 64</gadget>
<output>1_472</output>

<gadget id="calculator">2_351 + 1_472</gadget>
<output>3_823</output>

<gadget id="calculator">24 * 32</gadget>
<output>768</output>

<gadget id="calculator">3_823 + 768</gadget>
<output>4_591</output>

<gadget id="calculator">25 * 32</gadget>
<output>800</output>

<gadget id="calculator">4_591 + 800</gadget>
<output>5_391</output>

<gadget id="calculator">23 + 64</gadget>
<output>87</output>

<gadget id="calculator">87 + 32</gadget>
<output>119</output>

<gadget id="calculator">119 * 2</gadget>
<output>238</output>

<gadget id="calculator">5_391 / 238</gadget>
<output>5_391/238 = around 22.651261</output>
<result>5_391/238 = around 22.651261</result>

Choices:
A. 32.25
B. 21.45
C. 45
D. 22.45
E. 22

divide(add(add(add(add(add(multiply(20, 23), multiply(21, 23)), multiply(22, 64)), multiply(23, 64)), multiply(24, 32)), multiply(25, 32)), multiply(add(add(23, 64), 32), const_2))

Explanation: average = ( 20 * 2 + 21 * 3 + 22 * 6 + 23 * 4 + 24 * 3 + 25 * 2 ) / 20 = 22.45 answer : d


Question: a can finish a work in 18 days and b can do the same work in half the time taken by a . then , working together what part of the same work they can finish in a day ?

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>

<gadget id="calculator">18 / 2</gadget>
<output>9</output>

<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>

<gadget id="calculator">(1/18) + (1/9)</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>

Choices:
A. 1 / 2
B. 1 / 3
C. 1 / 6
D. 2 / 5
E. 2 / 9

add(divide(const_1, 18), divide(const_1, divide(18, const_2)))

Explanation: 1 days work of a + b = ( 18 + 9 ) / 18 * 9 = 1 / 6 answer is c


Question: if n is a positive integer and n ^ 2 is divisible by 18 , then what is the largest positive integer that must divide n ?

<gadget id="calculator">18 / 2</gadget>
<output>9</output>

<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 3
B. 4
C. 6
D. 8
E. 9

Explanation: "18 = 2 * 3 ^ 2 if 18 divides n ^ 2 , then n must be divisible by 2 * 3 = 6 the answer is c ."


Question: an employee ’ s annual salary was increased $ 25000 . if her new annual salary now equals $ 90000 , what was the percent increase ?

<gadget id="calculator">90_000 - 25_000</gadget>
<output>65_000</output>

<gadget id="calculator">25_000 / 65_000</gadget>
<output>5/13 = around 0.384615</output>

<gadget id="calculator">(5/13) * 100</gadget>
<output>500/13 = around 38.461538</output>
<result>500/13 = around 38.461538</result>

Choices:
A. 15 %
B. 162 ⁄ 3 %
C. 20 %
D. 38.46 %
E. 24 %

Explanation: new annual salary = $ 90,000 salary increase = $ 25,000 . original salary = $ 90,000 - $ 25,000 . = $ 75,000 % increase = ( $ 25,000 / $ 65,000 ) * 100 = 38.46 % hence d .


Question: in a class of 45 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?

<gadget id="calculator">45 + 12</gadget>
<output>57</output>

<gadget id="calculator">57 - 22</gadget>
<output>35</output>

<gadget id="calculator">35 - 12</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 30
B. 10
C. 18
D. 23
E. 32

Explanation: "total = english + german - both + neither - - > 45 = english + 22 - 12 + 0 - - > english = 35 - - > only english = english - both = 35 - 12 = 23 . answer : d ."


Question: mr . parkin invested in fund z and fund b . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund z paid 23 % and fund b paid 17 % . the interest earned in fund b was exactly $ 200 greater than the interest earned in fund z . how much did ms . morris invest in fund z ?

<gadget id="calculator">23 + 17</gadget>
<output>40</output>

<gadget id="calculator">40 * 100_000</gadget>
<output>4_000_000</output>

<gadget id="calculator">4_000_000 / 100</gadget>
<output>40_000</output>
<result>40_000</result>

Choices:
A. $ 32000
B. $ 36000
C. $ 40000
D. $ 42000
E. $ 45000

Explanation: 0.17 b - 0.23 z = 200 | * 100 17 b - 23 z = 20000 z + b = 100000 b = 100000 - z 17 ( 100000 - z ) - 23 z = 20000 1 , 700000 - 17 z - 23 z = 20000 1 , 680000 = 40 z divide by 40 first two digits : 42 . . . so answer is d .


Question: a train 100 meters long completely crosses a 300 meters long bridge in 36 seconds . what is the speed of the train is ?

<gadget id="calculator">100 + 300</gadget>
<output>400</output>

<gadget id="calculator">400 / 1_000</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">36 / 3_600</gadget>
<output>1/100 = around 0.01</output>

<gadget id="calculator">(2/5) / (1/100)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 32 kmph
B. 76 kmph
C. 34 kmph
D. 43 kmph
E. 40 kmph

divide(divide(add(100, 300), const_1000), divide(36, const_3600))

Explanation: "s = ( 100 + 300 ) / 36 = 400 / 36 * 18 / 5 = 40 answer : e"


Question: a school has 11 maths 8 physics and 5 chemistry teachers each teacher can teach 3 subjects max what is he minimum number of teachers required

<gadget id="calculator">11 + 8</gadget>
<output>19</output>

<gadget id="calculator">19 + 5</gadget>
<output>24</output>

<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 2
B. 4
C. 6
D. 8
E. 9

Explanation: "total subjects = 11 + 8 + 5 = 24 max subjects by 1 teacher = 3 so , min of teachers required = 24 / 3 = 8 answer : d"


Question: trapezoid jklm in the x - y plane has coordinates j = ( – 3 , – 4 ) , k = ( – 3 , 1 ) , l = ( 5 , 7 ) , and m = ( 5 , – 4 ) . what is its perimeter ?

<gadget id="calculator">1 + 4</gadget>
<output>5</output>

<gadget id="calculator">10 + 5</gadget>
<output>15</output>

<gadget id="calculator">3 + 5</gadget>
<output>8</output>

<gadget id="calculator">15 + 8</gadget>
<output>23</output>

<gadget id="calculator">7 + 4</gadget>
<output>11</output>

<gadget id="calculator">23 + 11</gadget>
<output>34</output>
<result>34</result>

Choices:
A. 34
B. 36
C. 38
D. 40
E. ( f ) 42

Explanation: jk = 5 lm = 11 kl = using distance formula 10 jm = using distance formula 8 sum of all is 34 a


Question: | - 2 | ( | - 25 | - | 5 | ) = ? ? source : preparation material mba center

<gadget id="calculator">25 - 5</gadget>
<output>20</output>

<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 40
B. – 60
C. 60
D. 75
E. 100

Explanation: absolute value will turn negatives into their positive ' equivalents ' , and will leave positives unchanged , so | - 2 | = 2 , | - 25 | = 25 , and | 5 | = 5 . getting rid of our absolute values we have : | - 2 | ( | - 25 | - | 5 | ) = ( 2 ) ( 25 - 5 ) = 2 * 20 = 40


Question: at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 30 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 30 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?

<gadget id="calculator">56 * 30</gadget>
<output>1_680</output>

<gadget id="calculator">52 * 30</gadget>
<output>1_560</output>

<gadget id="calculator">1_680 - 1_560</gadget>
<output>120</output>

<gadget id="calculator">60 - 52</gadget>
<output>8</output>

<gadget id="calculator">120 / 8</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 10
B. 11
C. 13
D. 14
E. 15

divide(subtract(multiply(56, 30), multiply(52, 30)), subtract(60, 52))

Explanation: "let number of apples = a number of oranges = b a + b = 30 - - - 1 . 56 = ( . 4 a + . 6 b ) / 30 = > 56 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 6 b = 24 let the number of oranges put back = c 52 * ( 30 - c ) = 40 * 6 + 60 ( 24 - c ) = > c = 15 answer e"


Question: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 12 % while buying and by 30 % while selling . what is his percentage profit ?

<gadget id="calculator">100 + 12</gadget>
<output>112</output>

<gadget id="calculator">100 - 30</gadget>
<output>70</output>

<gadget id="calculator">112 - 70</gadget>
<output>42</output>

<gadget id="calculator">42 * 100</gadget>
<output>4_200</output>

<gadget id="calculator">4_200 / 70</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 10.22 %
B. 20.22 %
C. 21.22 %
D. 60 %
E. ca n ' t be calculated

divide(multiply(subtract(add(const_100, 12), subtract(const_100, 30)), const_100), subtract(const_100, 30))

Explanation: "the owner buys 100 kg but actually gets 112 kg ; the owner sells 100 kg but actually gives 70 kg ; profit : ( 112 - 70 ) / 70 * 100 = ~ 60 % answer : d ."


Question: a statue is being carved by a sculptor . the original piece of marble weighed 180 kg . in the first week 28 percent is cut away . in the second week 18 percent of the remainder is cut away . in the third week the statue is completed when 20 percent of the remainder is cut away . what is the weight of the final statue ?

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>

<gadget id="calculator">1 - (9/50)</gadget>
<output>41/50 = around 0.82</output>

<gadget id="calculator">28 / 100</gadget>
<output>7/25 = around 0.28</output>

<gadget id="calculator">1 - (7/25)</gadget>
<output>18/25 = around 0.72</output>

<gadget id="calculator">180 * (18/25)</gadget>
<output>648/5 = around 129.6</output>

<gadget id="calculator">(41/50) * (648/5)</gadget>
<output>13_284/125 = around 106.272</output>

<gadget id="calculator">(4/5) * (13_284/125)</gadget>
<output>53_136/625 = around 85.0176</output>
<result>53_136/625 = around 85.0176</result>

Choices:
A. 105 kg
B. 85 kg
C. 108 kg
D. 125 kg
E. 117 kg

multiply(subtract(const_1, divide(20, const_100)), multiply(subtract(const_1, divide(18, const_100)), multiply(180, subtract(const_1, divide(28, const_100)))))

Explanation: "b 85 kg 180 ã — 0.72 ã — 0.82 ã — 0.8 = 85 kg ."


Question: there are 22 kids in a classroom . 12 kids are wearing socks and 8 are wearing shoes . 6 kids are wearing both . how many are bare feet ?

<gadget id="calculator">12 - 6</gadget>
<output>6</output>

<gadget id="calculator">8 - 6</gadget>
<output>2</output>

<gadget id="calculator">6 + 2</gadget>
<output>8</output>

<gadget id="calculator">8 + 6</gadget>
<output>14</output>

<gadget id="calculator">22 - 14</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 10
B. 2
C. 4
D. 5
E. 8

subtract(22, add(add(subtract(12, 6), subtract(8, 6)), 6))

Explanation: 12 kids wear socks 8 kids wear shoes 6 wear both . 12 â € “ 6 = 6 ( wear only socks ) 8 â € “ 6 = 2 ( wear only shoes ) 6 ( wear both ) hence , 22 - 14 = 8 8 kids are with bare feet . e


Question: a and b together can do a piece of work in 6 days and a alone can do it in 13 days . in how many days can b alone can do it ?

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">1 / 13</gadget>
<output>1/13 = around 0.076923</output>

<gadget id="calculator">(1/6) - (1/13)</gadget>
<output>7/78 = around 0.089744</output>

<gadget id="calculator">1 / (7/78)</gadget>
<output>78/7 = around 11.142857</output>
<result>78/7 = around 11.142857</result>

Choices:
A. 12 days
B. 15 days
C. 78 / 7 days
D. 21 days
E. 22 / 7 days

Explanation: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 13 work in 1 day b alone can do ( 1 / 6 - 1 / 13 ) = 7 / 78 work in 1 day = > complete work can be done in 78 / 7 days by b answer : option c"


Question: the length of a side of a hexagon is 4 inches . what is the perimeter ?

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">4 * 6</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 22
B. 23
C. 24
D. 25
E. 26

Explanation: hexagon . it means 6 equal sides . p = 6 ( 4 ) = 24 inches answer c


Question: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 112 m length ?

<gadget id="calculator">110 + 112</gadget>
<output>222</output>

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>

<gadget id="calculator">222 / 20</gadget>
<output>111/10 = around 11.1</output>
<result>111/10 = around 11.1</result>

Choices:
A. 82.1 sec
B. 12.1 sec
C. 16.1 sec
D. 11.1 sec
E. 12.15 sec

Explanation: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 112 = 222 m . required time = 222 / 20 = 11.1 sec . answer : d"


Question: ketchup , mustard and mayo bottles at a hot dog stand are in the ratio of 3 : 3 : 2 . if there are 6 ketchup bottles , the number of mayo bottles at the hot dog stand is :

<gadget id="calculator">6 / 3</gadget>
<output>2</output>

<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 12
B. 6
C. 3
D. 1
E. 4

Explanation: explanation : let ketchup = 3 x , mustard = 3 x & mayo = 2 x . now , 3 x = 6 hence x = 2 . number of mayo bottles = 2 x which is 4 . answer : e


Question: at a certain university , 65 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?

<gadget id="calculator">100 - 65</gadget>
<output>35</output>

<gadget id="calculator">90 - 65</gadget>
<output>25</output>

<gadget id="calculator">35 + 25</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 25
B. 37.5
C. 50
D. 62.5
E. 75

add(subtract(const_100, 65), subtract(90, 65))

Explanation: "total women = 65 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 25 % but question wants to know the percent of men that are tenured 25 % / 40 % = 62.5 % d"


Question: a can do a work in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>

<gadget id="calculator">(7/60) * 5</gadget>
<output>7/12 = around 0.583333</output>

<gadget id="calculator">1 - (7/12)</gadget>
<output>5/12 = around 0.416667</output>
<result>5/12 = around 0.416667</result>

Choices:
A. 8 / 17
B. 7 / 15
C. 3 / 15
D. 5 / 12
E. 1 / 4

subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 5))

Explanation: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 5 days they work 35 * 5 = 175 remaining work is 300 - 175 = 125 remaining fraction of work is = 125 / 300 = 5 / 12 answer d"


Question: of the 200 stamps in a collection , 90 are foreign and 80 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?

<gadget id="calculator">90 + 80</gadget>
<output>170</output>

<gadget id="calculator">170 - 20</gadget>
<output>150</output>

<gadget id="calculator">200 - 150</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 50
B. 80
C. 100
D. 130
E. 150

subtract(200, subtract(add(90, 80), 20))

Explanation: "20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 60 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 60 ) = 50 the answer is a ."


Question: find the volume & curved surface area of a cylinder with diameter of base 14 cm and height 60 cm .

<gadget id="calculator">14 / 2</gadget>
<output>7</output>

<gadget id="calculator">2 * pi * 7</gadget>
<output>14*pi = around 43.982297</output>

<gadget id="calculator">(14*pi) * 60</gadget>
<output>840*pi = around 2_638.937829</output>
<result>840*pi = around 2_638.937829</result>

Choices:
A. 260 cm 2
B. 2610 cm 2
C. 2600 cm 2
D. 2640 cm 2
E. 264 cm 2

Explanation: volume = pier 2 h = pie x 72 x 60 = 9240 cm 3 curved surface area = 2 pierh = ( 2 x 3.14 x 7 x 60 ) cm 2 = 2640 cm 2 answer : d


Question: a car traveled 560 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?

<gadget id="calculator">560 - 336</gadget>
<output>224</output>

<gadget id="calculator">224 / 6</gadget>
<output>112/3 = around 37.333333</output>

<gadget id="calculator">336 / (112/3)</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 9
B. 16
C. 21
D. 22
E. 27

divide(336, divide(subtract(560, 336), 6))

Explanation: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 462 miles will be covered in 462 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 560 / h = > 336 / c = 560 / ( c + 6 ) = > 336 c + 336 * 6 = 560 c = > c = 336 * 6 / 224 = 9 answer a ."


Question: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 2 dm by 5 dm . the number of stones required is :

<gadget id="calculator">36 * 15</gadget>
<output>540</output>

<gadget id="calculator">2 * 5</gadget>
<output>10</output>

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">540 / (1/10)</gadget>
<output>5_400</output>
<result>5_400</result>

Choices:
A. 180
B. 1800
C. 5400
D. 18000
E. 1.8

divide(multiply(36, 15), divide(multiply(2, 5), const_100))

Explanation: area of the hall = 3600 * 1500 area of each stone = ( 20 * 50 ) therefore , number of stones = ( 3600 * 1500 / 20 * 50 ) = 5400 answer : c


Question: by selling an article at rs . 900 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?

<gadget id="calculator">900 * 100</gadget>
<output>90_000</output>

<gadget id="calculator">25 + 100</gadget>
<output>125</output>

<gadget id="calculator">90_000 / 125</gadget>
<output>720</output>

<gadget id="calculator">720 * 25</gadget>
<output>18_000</output>

<gadget id="calculator">18_000 / 100</gadget>
<output>180</output>

<gadget id="calculator">720 - 180</gadget>
<output>540</output>
<result>540</result>

Choices:
A. s . 600
B. s . 480
C. s . 500
D. s . 540
E. s . 550

subtract(divide(multiply(900, const_100), add(25, const_100)), divide(multiply(divide(multiply(900, const_100), add(25, const_100)), 25), const_100))

Explanation: "sp = 900 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 900 * [ 100 / 125 ] = 720 loss = 25 % = 25 % of 720 = rs . 180 sp = cp - loss = 720 - 180 = rs . 540 answer : d"


Question: a train 220 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?

<gadget id="calculator">220 / 1_000</gadget>
<output>11/50 = around 0.22</output>

<gadget id="calculator">60 + 6</gadget>
<output>66</output>

<gadget id="calculator">(11/50) / 66</gadget>
<output>1/300 = around 0.003333</output>

<gadget id="calculator">3_600 * (1/300)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 5
B. 6
C. 7
D. 12
E. 9

multiply(const_3600, divide(divide(220, const_1000), add(60, 6)))

Explanation: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 220 * 3 / 55 ] sec = 12 sec answer : option d"


Question: assume that f ( 1 ) = 0 and f ( m + n ) = f ( m ) + f ( n ) + 4 ( 9 mn - 1 ) . for all natural numbers ( integers > 0 ) m and n . what is the value of f ( 17 ) ?

<gadget id="calculator">4 * 2</gadget>
<output>8</output>

<gadget id="calculator">4 * 8</gadget>
<output>32</output>

<gadget id="calculator">32 + 32</gadget>
<output>64</output>

<gadget id="calculator">32 + 3</gadget>
<output>35</output>

<gadget id="calculator">35 * 4</gadget>
<output>140</output>

<gadget id="calculator">64 + 140</gadget>
<output>204</output>

<gadget id="calculator">204 + 204</gadget>
<output>408</output>

<gadget id="calculator">4 * 10</gadget>
<output>40</output>

<gadget id="calculator">40 + 3</gadget>
<output>43</output>

<gadget id="calculator">100 + 43</gadget>
<output>143</output>

<gadget id="calculator">143 * 4</gadget>
<output>572</output>

<gadget id="calculator">408 + 572</gadget>
<output>980</output>

<gadget id="calculator">980 + 980</gadget>
<output>1_960</output>

<gadget id="calculator">4 + 1</gadget>
<output>5</output>

<gadget id="calculator">5 * 100</gadget>
<output>500</output>

<gadget id="calculator">17 * 4</gadget>
<output>68</output>

<gadget id="calculator">68 + 9</gadget>
<output>77</output>

<gadget id="calculator">77 - 2</gadget>
<output>75</output>

<gadget id="calculator">500 + 75</gadget>
<output>575</output>

<gadget id="calculator">575 * 4</gadget>
<output>2_300</output>

<gadget id="calculator">1_960 + 2_300</gadget>
<output>4_260</output>

<gadget id="calculator">4_260 + 572</gadget>
<output>4_832</output>
<result>4_832</result>

Choices:
A. 4832
B. 4855
C. 4825
D. 4895
E. 4862

add(add(add(add(add(add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4)), add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4))), multiply(add(const_100, add(multiply(4, const_10), const_3)), 4)), add(add(add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4)), add(add(multiply(4, multiply(const_4, const_2)), multiply(4, multiply(const_4, const_2))), multiply(add(multiply(4, multiply(const_4, const_2)), const_3), 4))), multiply(add(const_100, add(multiply(4, const_10), const_3)), 4))), multiply(add(multiply(add(const_4, const_1), const_100), subtract(add(multiply(17, const_4), 9), const_2)), const_4)), multiply(add(const_100, add(multiply(4, const_10), const_3)), 4))

Explanation: explanation : f ( 1 ) = 0 f ( 2 ) = f ( 1 + 1 ) = f ( 1 ) + f ( 1 ) + 4 ( 9 × 1 × 1 – 1 ) = 0 + 0 + 4 × 8 = 32 f ( 4 ) = f ( 2 + 2 ) = f ( 2 ) + f ( 2 ) + 4 ( 9 × 2 × 2 – 1 ) = 32 + 32 + 4 × 35 = 204 f ( 8 ) = f ( 4 + 4 ) = f ( 4 ) + f ( 4 ) + 4 ( 9 × 4 × 4 – 1 ) = 204 + 204 + 4 × 143 = 980 f ( 16 ) = f ( 8 + 8 ) = f ( 8 ) + f ( 8 ) + 4 ( 9 × 8 × 8 – 1 ) = 980 + 980 + 4 × 575 = 4260 f ( 17 ) = f ( 1 + 16 ) = f ( 16 ) + f ( 1 ) + 4 ( 9 × 16 × 1 – 1 ) = 4260 + 0 + 4 × 143 = 4832 answer : a


Question: allay ' s internet provider offers unlimited traffic which costs $ 0.5 per day charged off at 12 a . m . the service is discontinued when client ' s debt exceeds $ 5 . if today in the morning allay makes a payment of $ 7 , for how many days , including today , will she be connected to the internet without any additional payments , given her initial balance was $ 0 ?

<gadget id="calculator">5 + 7</gadget>
<output>12</output>

<gadget id="calculator">12 / 0.5</gadget>
<output>24</output>

<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 15
B. 24
C. 25
D. 26
E. 13

Explanation: day 0 - payment of $ 7 is made in the morning ( after 12 am midnight ) day 1 onwards ( after 12 am midnight ) internet service will begin and will run for 7 * 2 = 14 days i . e . at the end of day 15 balance will be zero . now allay can still use the internet till her debt reaches $ 5 which means total of 5 * 2 = 10 days . now the question states for how many days , including today , will she be connected to the internet without any additional paymentsi . e . we will have to include day 0 also in our final answer . therefore total no . of days = 1 + 14 + 10 = 25 = c


Question: if ( 2 ^ 16 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?

<gadget id="calculator">10 / 5</gadget>
<output>2</output>

<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 7
B. 8
C. 15
D. 16
E. 23

Explanation: given 2 ^ 16 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 16 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans d on comparing the power of 2 = > m = 16


Question: 90 + 5 * 12 / ( 180 / 3 ) = ?

<gadget id="calculator">5 * 12</gadget>
<output>60</output>

<gadget id="calculator">180 / 3</gadget>
<output>60</output>

<gadget id="calculator">60 / 60</gadget>
<output>1</output>

<gadget id="calculator">90 + 1</gadget>
<output>91</output>
<result>91</result>

Choices:
A. 23
B. 78
C. 27
D. 91
E. 81

add(90, divide(multiply(5, 12), divide(180, 3)))

Explanation: "explanation : 90 + 5 * 12 / ( 180 / 3 ) = 90 + 5 * 12 / ( 60 ) = 90 + ( 5 * 12 ) / 60 = 90 + 1 = 91 . answer : d"


Question: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is

<gadget id="calculator">350 - 340</gadget>
<output>10</output>

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">10 / (1/20)</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 289
B. 231
C. 200
D. 288
E. 111

divide(subtract(350, 340), divide(5, const_100))

Explanation: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"


Question: a welder received an order to make a 1 million liter cube - shaped tank . if he has only 2 x 3 meter sheets of metal that can be cut , how many metal sheets will be required for this order ? ( 1 cubic meter = 1000 liters )

<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">6 * 100</gadget>
<output>600</output>

<gadget id="calculator">600 / 6</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 92
B. 90
C. 82
D. 78
E. 100

divide(multiply(multiply(2, 3), const_100), multiply(2, 3))

Explanation: the question say : a welder received an order to make a 1 million liter cube - shaped tank . ( 1 cubic meter = 1,000 liters ) in other words , the tank is going to have a volume of 1000 cubic meters . that would equal 1 million liters . a cube with a volume of 1000 cubic meters must be ( 10 meters ) x ( 10 meters ) x ( 10 meters ) . the question does n ' t specify whether this tank should have a closed top or an open top . ( the real gmat is good about specifying things like that . ) here , we are going to assume a closed top , only because if the top is open , we do n ' t use enough metal - - - we get an answer smaller than any of the answer choices . a closed - top cube , a full cube , has 6 sides , each of which is ( 10 meters ) x ( 10 meters ) . that ' s a total surface area of 600 sq m . the question tells us : he has only 2 x 3 meter sheets of metal that can be cut . each sheet has an area of 6 sq m . how many of these need to fill up 600 sq m ? 600 / 6 = 100 . he needs 100 sheets . answer = e


Question: if 18 persons can build a wall 140 m long in 42 days , the number of days that 30 persons will take to complete a similar wall 100 m long , is .

<gadget id="calculator">18 * 100</gadget>
<output>1_800</output>

<gadget id="calculator">1_800 * 42</gadget>
<output>75_600</output>

<gadget id="calculator">140 * 30</gadget>
<output>4_200</output>

<gadget id="calculator">75_600 / 4_200</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 18
B. 21
C. 24
D. 28
E. 30

divide(multiply(multiply(18, 100), 42), multiply(140, 30))

Explanation: explanation : ( length 140 : 100 ) : ( persons 30 : 18 ) : : 42 : x = > 140 * 30 * x = 100 * 18 * 42 = > or x = 18 answer : a


Question: when x is multiplied by 3 , the result is 10 more than the result of subtracting x from 26 . what is the value of x ?

<gadget id="calculator">26 + 10</gadget>
<output>36</output>

<gadget id="calculator">3 + 1</gadget>
<output>4</output>

<gadget id="calculator">36 / 4</gadget>
<output>9</output>
<result>9</result>

Choices:
A. - 4
B. 9
C. 11
D. 13
E. 22

Explanation: "the equation that can be formed is : 3 x - 10 = 26 - x or , 4 x = 36 or , x = 9 . b answer ."


Question: if the l . c . m of two numbers is 560 and their product is 42000 , find the h . c . f of the numbers .

<gadget id="calculator">42_000 / 560</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 50
B. 30
C. 75
D. 25
E. none of these

Explanation: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 42000 / 560 = 75 . answer : c"


Question: 1,000 ^ 2 + 1,001 ^ 2 + 1,002 ^ 2 + 1,003 ^ 2 + 1,004 ^ 2 =

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6 , 030,053
B. 6 , 030,054
C. 6 , 030,055
D. 6 , 020,030
E. 6 , 030,057

Explanation: interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 . . . 1004 ^ 2 - > 16 total - > * 30 answer d .


Question: in a room filled with 6 people , all 6 people have exactly 1 sibling in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?

<gadget id="calculator">6 - 1</gadget>
<output>5</output>

<gadget id="calculator">5 - 1</gadget>
<output>4</output>

<gadget id="calculator">6 * 4</gadget>
<output>24</output>

<gadget id="calculator">6 * 5</gadget>
<output>30</output>

<gadget id="calculator">24 / 30</gadget>
<output>4/5 = around 0.8</output>
<result>4/5 = around 0.8</result>

Choices:
A. 3 / 5
B. 4 / 5
C. 5 / 6
D. 5 / 12
E. 7 / 12

divide(multiply(6, subtract(subtract(6, const_1), const_1)), multiply(6, subtract(6, const_1)))

Explanation: the 6 people consist of three sets of 2 siblings . the number of ways to choose 2 people is 6 c 2 = 15 . the number of ways to choose 2 from the first group of siblings is 2 c 2 = 1 . the number of ways to choose 2 from the second group of siblings is 2 c 2 = 1 . the number of ways to choose 2 from the third group of siblings is 2 c 2 = 1 . the number of ways to choose 2 people who are siblings is 1 + 1 + 1 = 3 . the number of ways to choose 2 people who are not siblings is 15 - 3 = 12 . p ( the two people are not siblings ) = 12 / 15 = 4 / 5 the answer is b .


Question: find the least number of complete years in which a sum of money put out at 50 % compound interest will be more than double of itself ?

<gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">log(3/2)</gadget>
<output>log(3/2) = around 0.405465</output>

<gadget id="calculator">log(2) / log(3/2)</gadget>
<output>log(2)/log(3/2) = around 1.709511</output>

<gadget id="calculator">(log(2)/log(3/2)) + 1</gadget>
<output>1 + log(2)/log(3/2) = around 2.709511</output>

<gadget id="calculator">floor(1 + log(2)/log(3/2))</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 2
B. 3
C. 4
D. 5
E. 6

floor(add(divide(log(const_2), log(add(const_1, divide(50, const_100)))), const_1))

Explanation: 2 years answer : a


Question: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?

<gadget id="calculator">1 * 60</gadget>
<output>60</output>

<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) * 60</gadget>
<output>40</output>

<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 18 min
B. 17 min
C. 19 min
D. 20 min
E. 21 min

subtract(multiply(const_1, const_60), multiply(divide(40, 60), const_60))

Explanation: "in 1 hr , the bus covers 60 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 60 - 40 ) km i . e 20 km at 60 km / hr . stoppage time = 20 / 60 hrs = 20 min . answer : d"


Question: in an office , 50 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">16 / (1/10)</gadget>
<output>160</output>

<gadget id="calculator">160 * 90</gadget>
<output>14_400</output>

<gadget id="calculator">14_400 / 100</gadget>
<output>144</output>

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">160 * (1/2)</gadget>
<output>80</output>

<gadget id="calculator">144 - 80</gadget>
<output>64</output>

<gadget id="calculator">2 * 4</gadget>
<output>8</output>

<gadget id="calculator">64 / 8</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 8
B. 64
C. 50
D. 144
E. 160

divide(subtract(divide(multiply(divide(16, divide(10, const_100)), 90), const_100), multiply(divide(16, divide(10, const_100)), divide(const_1, const_2))), multiply(const_2, const_4))

Explanation: ( 10 / 100 ) workers = 16 = > number of workers = 160 ( 50 / 100 ) * workers = x + 16 = > x = 8 answer a


Question: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many d hours does it currently take anne to clean the house on her own ?

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/3) - (1/4)</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 6
B. 7
C. 8
D. 12
E. 14

inverse(subtract(divide(const_1, 3), divide(const_1, 4)))

Explanation: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in d = 3 hours ) solving these 2 equations we can find b as 12 so , d"


Question: the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 8 ?

<gadget id="calculator">20 + 1</gadget>
<output>21</output>

<gadget id="calculator">8 + 32</gadget>
<output>40</output>

<gadget id="calculator">21 * 40</gadget>
<output>840</output>

<gadget id="calculator">20 * 32</gadget>
<output>640</output>

<gadget id="calculator">840 - 640</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 96
B. 200
C. 128
D. 116
E. 122

subtract(multiply(add(20, const_1), add(8, 32)), multiply(20, 32))

Explanation: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 8 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 640 = 200 answer : b"


Question: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 17 , the how old is b ? a . 7 b . 8 c . 9 d . 10 explanation :

<gadget id="calculator">17 - 2</gadget>
<output>15</output>

<gadget id="calculator">4 + 1</gadget>
<output>5</output>

<gadget id="calculator">15 / 5</gadget>
<output>3</output>

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6
B. 7
C. 9
D. 10
E. 11

multiply(divide(subtract(17, const_2), add(const_4, const_1)), const_2)

Explanation: let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 17 5 x = 15 x = 3 . hence , b ' s age = 2 x = 6 years . answer : option a


Question: two pipes can fill a tank in 12 minutes and 20 minutes respectively . both pipes are opened together and after some time the first pipe is closed and the tank is full in totally 10 minutes . for how many minutes was first pipe open ?

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/12) + (1/20)</gadget>
<output>2/15 = around 0.133333</output>

<gadget id="calculator">(2/15) * 10</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">(4/3) - 1</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) / (1/12)</gadget>
<output>4</output>

<gadget id="calculator">10 - 4</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 8 minutes
B. 6 minutes
C. 7 minutes
D. 10 minutes
E. 9 minutes

subtract(10, divide(subtract(multiply(add(inverse(12), inverse(20)), 10), const_1), inverse(12)))

Explanation: second pipe is opened for 10 minutes . so , part of tank filled by the second pipe = 10 / 20 = 1 / 2 . so , 1 - 1 / 2 = 1 / 2 tank is filled by first pipe . first pipe can fill 1 / 2 of tank in 1 * 12 / 2 = 6 minutes . so , the first pipe is opened for 6 minutes . answer : b


Question: the average of 50 numbers id 20 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :

<gadget id="calculator">50 * 20</gadget>
<output>1_000</output>

<gadget id="calculator">45 + 55</gadget>
<output>100</output>

<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>

<gadget id="calculator">50 - 2</gadget>
<output>48</output>

<gadget id="calculator">900 / 48</gadget>
<output>75/4 = around 18.75</output>
<result>75/4 = around 18.75</result>

Choices:
A. 22.75
B. 33.25
C. 22.25
D. 11.75
E. 18.75

divide(subtract(multiply(50, 20), add(45, 55)), subtract(50, const_2))

Explanation: "explanation : total of 50 numbers = ( 50 × 20 ) = 1000 total of 48 numbers = ( 1000 - ( 45 + 55 ) ] = 900 required average = 900 / 48 = 18.75 answer : e"


Question: the area of a triangle is with base 10 m and height 10 m ?

<gadget id="calculator">(10 * 10) / 2</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 11
B. 10
C. 50
D. 122
E. 12

Explanation: "1 / 2 * 10 * 10 = 50 m 2 answer : c"


Question: in what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way ?

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>

<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 3 sec
B. 4 sec
C. 5 sec
D. 6 sec
E. 7 sec

Explanation: "t = 40 / 36 * 18 / 5 = 4 sec answer : b"


Question: find remainder if ( 67 ^ 67 + 67 ) is divided by 68

<gadget id="calculator">67 - 1</gadget>
<output>66</output>
<result>66</result>

Choices:
A. 60
B. 62
C. 66
D. 72
E. 78

Explanation: = > ( 6767 + 1 ) is divisible by ( 67 + 1 ) = > ( 6767 + 1 ) is divisible by 68 = > ( 6767 + 1 ) ÷ 68 gives a remainder of 0 = > [ ( 6767 + 1 ) + 66 ] ÷ 68 gives a remainder of 66 = > ( 6767 + 67 ) ÷ 68 gives a remainder of 66 c


Question: last year a worker saved 6 % of her annual salary . this year , she made 20 % more money than last year and she saved 5 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?

<gadget id="calculator">20 + 100</gadget>
<output>120</output>

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">120 * (1/20)</gadget>
<output>6</output>

<gadget id="calculator">6 / 6</gadget>
<output>1</output>

<gadget id="calculator">100 * 1</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 90 %
B. 100 %
C. 110 %
D. 120 %
E. 130 %

multiply(const_100, divide(6, multiply(add(20, const_100), divide(5, const_100))))

Explanation: let x be the worker ' s salary last year . last year , she saved 0.06 x . this year , she saved 0.05 ( 1.2 x ) = 0.06 x 0.06 x / 0.06 x = 100 % the answer is b .


Question: a walks at 10 kmph and 4 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?

<gadget id="calculator">4 * 20</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 100 km
B. 150 km
C. 80 km
D. 120 km
E. 200 km

Explanation: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 4 hours . x / 10 - x / 20 = 4 x = 80 km answer is c"


Question: a man can swim in still water at 12 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?

<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 1.7
B. 2.67
C. 1.2
D. 1.5
E. 4

Explanation: "m = 12 s = x ds = 12 + x us = 12 + x 12 + x = ( 12 - x ) 2 12 + x = 24 - 2 x 3 x = 12 x = 4 answer : e"


Question: nitin ranks 24 th in a class of 58 students . what is rank from the last ?

<gadget id="calculator">58 - 24</gadget>
<output>34</output>
<result>34</result>

Choices:
A. 33
B. 34
C. 32
D. 28
E. 19

Explanation: "explanation : number students behind the nitin in rank = ( 58 - 24 ) = 34 nitin is 34 nd from the last answer : b ) 34"


Question: a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 4 volts , what was the smallest possible recording in volts ?

<gadget id="calculator">3 * 4</gadget>
<output>12</output>

<gadget id="calculator">12 - 10</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 2
B. 3
C. 4
D. 5
E. 6

Explanation: if average of 3 is 4 so sum of 3 should be 12 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 5 and 5 so a has to be 2 a


Question: 5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 12 days . how many additional pipes q , each draining water at the same constant rate , will be needed to drain the pool in 4 days ?

<gadget id="calculator">12 * 5</gadget>
<output>60</output>

<gadget id="calculator">60 / 4</gadget>
<output>15</output>

<gadget id="calculator">15 - 5</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 6
B. 9
C. 10
D. 12
E. 15

Explanation: this is an inverse proportional problem . . . . . . 5 pipes in 12 days ; so for 4 days , it will be = 12 x 5 / 4 = 15 so , q = 15 - 5 = 10 . c


Question: set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 3 ?

<gadget id="calculator">3 * 1</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 1
B. 2
C. 4
D. 3
E. 16

Explanation: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d"


Question: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 45 % . staff are allowed a further 40 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?

<gadget id="calculator">100 - 45</gadget>
<output>55</output>

<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(11/20) * (2/5)</gadget>
<output>11/50 = around 0.22</output>

<gadget id="calculator">(11/20) - (11/50)</gadget>
<output>33/100 = around 0.33</output>
<result>33/100 = around 0.33</result>

Choices:
A. 0.35 d
B. 0.76 d
C. 0.65 d
D. 0.77 d
E. 0.33 d

subtract(divide(subtract(const_100, 45), const_100), multiply(divide(subtract(const_100, 45), const_100), divide(40, const_100)))

Explanation: effective discount = a + b + ab / 100 = - 45 - 40 + ( - 45 ) ( - 40 ) / 100 = - 67 sale price = d * ( 1 - 67 / 100 ) sale price = . 33 * d answer ( e )


Question: the average weight of 4 person ' s increases by 8.5 kg when a new person comes in place of one of them weighing 95 kg . what might be the weight of the new person ?

<gadget id="calculator">4 * 8.5</gadget>
<output>34</output>

<gadget id="calculator">34 + 95</gadget>
<output>129</output>
<result>129</result>

Choices:
A. 129 kg
B. 134 kg
C. 180 kg
D. 185 kg
E. 190 kg

Explanation: "total weight increased = ( 4 x 8.5 ) kg = 34 kg . weight of new person = ( 95 + 34 ) kg = 129 kg option a"


Question: the s . i . on a certain sum of money for 2 years at 8 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>

<gadget id="calculator">4_000 * (121/100)</gadget>
<output>4_840</output>

<gadget id="calculator">4_840 - 4_000</gadget>
<output>840</output>

<gadget id="calculator">840 / 2</gadget>
<output>420</output>

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">2 * (2/25)</gadget>
<output>4/25 = around 0.16</output>

<gadget id="calculator">420 / (4/25)</gadget>
<output>2_625</output>
<result>2_625</result>

Choices:
A. 2197
B. 1267
C. 1750
D. 2267
E. 2625

divide(divide(subtract(multiply(4000, power(add(const_1, divide(10, const_100)), 2)), 4000), 2), multiply(2, divide(8, const_100)))

Explanation: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 2 * 8 ) = rs . 2625 answer : e"


Question: two trains 120 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?

<gadget id="calculator">120 + 160</gadget>
<output>280</output>

<gadget id="calculator">60 + 40</gadget>
<output>100</output>

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>

<gadget id="calculator">280 / (250/9)</gadget>
<output>252/25 = around 10.08</output>
<result>252/25 = around 10.08</result>

Choices:
A. 10.9
B. 10.7
C. 10.3
D. 10.08
E. 10.2

Explanation: relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 120 + 160 = 280 m . required time = 280 * 9 / 250 = 252 / 25 = 10.08 sec . ' answer : d


Question: in the first 20 overs of a cricket game , the run rate was only 4.6 . what should be the run rate in the remaining 30 overs to reach the target of 396 runs ?

<gadget id="calculator">20 * 4.6</gadget>
<output>92</output>

<gadget id="calculator">396 - 92</gadget>
<output>304</output>

<gadget id="calculator">304 / 30</gadget>
<output>152/15 = around 10.133333</output>
<result>152/15 = around 10.133333</result>

Choices:
A. 10.13
B. 9.13
C. 8.13
D. 11.13
E. 13.13

divide(subtract(396, multiply(20, 4.6)), 30)

Explanation: required run rate = 396 - ( 4.6 x 20 ) / 30 = 304 / 30 = 10.13 option a


Question: a club wants to mix 10 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?

<gadget id="calculator">10 * 8</gadget>
<output>80</output>

<gadget id="calculator">6 * 10</gadget>
<output>60</output>

<gadget id="calculator">80 - 60</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20
B. 30
C. 40
D. 50
E. 60

subtract(multiply(10, 8.00), multiply(6.00, 10))

Explanation: "let number of pounds of 5 $ candy to be used be w 6 = ( 10 * 8 + 5 * w ) / ( 10 + w ) = > 60 + 6 w = 80 + 5 w = > w = 20 answer a"


Question: if the annual increase in the population of a town is 10 % and the present number of people is 15000 , what will the population be in 2 years ?

<gadget id="calculator">10 + 100</gadget>
<output>110</output>

<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">(11/10) * 15_000</gadget>
<output>16_500</output>

<gadget id="calculator">16_500 * (11/10)</gadget>
<output>18_150</output>
<result>18_150</result>

Choices:
A. 12100
B. 15240
C. 18150
D. 18452
E. 19002

multiply(multiply(divide(add(10, const_100), const_100), 15000), divide(add(10, const_100), const_100))

Explanation: "the required population is = 15000 ( 1 + 10 / 100 ) ^ 2 = 15000 * 11 / 10 * 11 / 10 = 18150 answer is c"


Question: a plant manager must assign 8 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ?

<gadget id="calculator">8 / 2</gadget>
<output>4</output>

<gadget id="calculator">factorial(4)</gadget>
<output>24</output>

<gadget id="calculator">24 / 2</gadget>
<output>12</output>

<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>

<gadget id="calculator">8 - 2</gadget>
<output>6</output>

<gadget id="calculator">factorial(6)</gadget>
<output>720</output>

<gadget id="calculator">factorial(2)</gadget>
<output>2</output>

<gadget id="calculator">720 * 2</gadget>
<output>1_440</output>

<gadget id="calculator">40_320 / 1_440</gadget>
<output>28</output>

<gadget id="calculator">12 * 28</gadget>
<output>336</output>
<result>336</result>

Choices:
A. 243
B. 336
C. 350
D. 486
E. 540

multiply(divide(factorial(divide(8, 2)), const_2), divide(factorial(8), multiply(factorial(subtract(8, 2)), factorial(2))))

Explanation: "whatever : my take selecting team of 2 out of 8 to assign to the shifts = 8 c 2 = 28 ways . now 2 out of 8 means total of 4 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 4 * 3 * 2 * 1 = 24 here alt and alt are the same : so 24 / 2 = 12 ways . total ways of selecting = ( selecting 2 out of 8 ) * arranging those teams in shifts = 28 * 12 = 336 ans : b"


Question: 1 = 62 = 363 = 3634 = 3645 = 365 , then 36 = ?

<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 1
B. 2
C. 345
D. 445
E. 235

Explanation: 1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ? 36 = 2 check the second eqn . answer : b


Question: find large number from below question the difference of two numbers is 1000 . on dividing the larger number by the smaller , we get 10 as quotient and the 10 as remainder

<gadget id="calculator">1_000 - 10</gadget>
<output>990</output>

<gadget id="calculator">10 - 1</gadget>
<output>9</output>

<gadget id="calculator">990 / 9</gadget>
<output>110</output>

<gadget id="calculator">110 * 10</gadget>
<output>1_100</output>
<result>1_100</result>

Choices:
A. 1234
B. 1110
C. 1456
D. 1200
E. 1600

multiply(divide(subtract(1000, 10), subtract(10, const_1)), 10)

Explanation: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1000 = 10 x + 10 9 x = 990 x = 110 large number = 110 + 1000 = 1110 b"


Question: the average height of 30 girls out of a class of 40 is 160 cm . and that of the remaining girls is 156 cm . the average height of the whole class is :

<gadget id="calculator">160 * 30</gadget>
<output>4_800</output>

<gadget id="calculator">156 * 10</gadget>
<output>1_560</output>

<gadget id="calculator">4_800 + 1_560</gadget>
<output>6_360</output>

<gadget id="calculator">6_360 / 40</gadget>
<output>159</output>
<result>159</result>

Choices:
A. 158 cms
B. 158.5 cms
C. 159 cms
D. 159.5 cms
E. none

divide(add(multiply(160, 30), multiply(156, const_10)), 40)

Explanation: explanation : average height of the whole class = ( 36 × 160 + 10 × 156 / 40 ) = 159 cms answer c


Question: a man owns 1 / 3 of market reserch beauro buzness , and sells 3 / 5 of his shares for 15000 rs , what is the value of buzness ?

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(1/3) * (3/5)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">15_000 / (1/5)</gadget>
<output>75_000</output>
<result>75_000</result>

Choices:
A. 55000
B. 75000
C. 65000
D. 190000
E. 250000

divide(15000, multiply(divide(1, 3), divide(3, 5)))

Explanation: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 15000 - > x = 75000 answer : b"


Question: jaylen was planning to save all summer for a pair of jordan 12 s . they cost $ 250 . jaylen figured that he could cut grass to help with the cost of the sneakers . how many yards would jaylen have to cut if he charges $ 2.15 per yard ?

<gadget id="calculator">250 / 2.15</gadget>
<output>116.27907</output>
<result>116.27907</result>

Choices:
A. 116 yards
B. 226 yards
C. 97 yards
D. 115.74 yards
E. 1 yard

Explanation: d


Question: at the end of the month , a certain ocean desalination plant ’ s reservoir contained 30 million gallons of water . this amount is twice the normal level . if this amount represents 75 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?

<gadget id="calculator">30 / 2</gadget>
<output>15</output>

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">15 / (3/4)</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 10
B. 15
C. 20
D. 25
E. 30

divide(divide(30, const_2), divide(75, const_100))

Explanation: "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 30 mg = 75 % of total . . total = 30 / . 75 = 40 mg . . normal level = 1 / 2 of 40 = 20 mg . . shortage of normal level = 40 - 20 = 20 mg . . c"


Question: matt gets a $ 1000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 250 , how many sales has matt made ?

<gadget id="calculator">250 - 150</gadget>
<output>100</output>

<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>

<gadget id="calculator">900 / 150</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 3
B. 4
C. 5
D. 6
E. 7

divide(subtract(1000, subtract(250, 150)), 150)

Explanation: let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 250 = 150 + x i . e . x = 100 i . e . y = 5 new sales = y + 1 = 6 answer : option d


Question: the present worth of $ 169 due in 2 years at 4 % per annum compound interest is ?

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">(1/25) + 1</gadget>
<output>26/25 = around 1.04</output>

<gadget id="calculator">(26/25) ** 2</gadget>
<output>676/625 = around 1.0816</output>

<gadget id="calculator">169 / (676/625)</gadget>
<output>625/4 = around 156.25</output>
<result>625/4 = around 156.25</result>

Choices:
A. $ 145.89
B. $ 138.62
C. $ 156.25
D. $ 160.23
E. $ 158.95

divide(169, power(add(divide(4, const_100), const_1), 2))

Explanation: "present worth = 169 / ( 1 + 4 / 100 ) ^ 2 = 169 * 25 / 26 * 25 / 26 = $ 156.25 answer is c"


Question: an urn contains 10 black and 5 white balls . two balls are drawn from the urn one after the other without replacement . what is the probability that both drawn balls are black ?

<gadget id="calculator">10 + 5</gadget>
<output>15</output>

<gadget id="calculator">10 / 15</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">10 - 1</gadget>
<output>9</output>

<gadget id="calculator">15 - 1</gadget>
<output>14</output>

<gadget id="calculator">9 / 14</gadget>
<output>9/14 = around 0.642857</output>

<gadget id="calculator">(2/3) * (9/14)</gadget>
<output>3/7 = around 0.428571</output>
<result>3/7 = around 0.428571</result>

Choices:
A. 1 / 5
B. 3 / 7
C. 2 / 5
D. 3 / 5
E. 2 / 7

multiply(divide(10, add(10, 5)), divide(subtract(10, const_1), subtract(add(10, 5), const_1)))

Explanation: let e and f denote respectively the events that first and second ball drawn are black . we have to find p ( e n f ) or p ( ef ) . now p ( e ) = p ( black ball in first draw ) = 10 / 15 also given that the first ball drawn is black , i . e . , event e has occurred , now there are 9 black balls and five white balls left in the urn . therefore , the probability that the second ball drawn is black , given that the ball in the first draw is black , is nothing but the conditional probability of f given that e has occurred . that is p ( f | e ) = 9 / 14 by multiplication rule of probability , we have p ( e n f ) = p ( e ) p ( f | e ) = 10 / 15 × 9 / 14 = 3 / 7 b


Question: by selling 11 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 20 % ?

<gadget id="calculator">100 + 20</gadget>
<output>120</output>

<gadget id="calculator">100 - 10</gadget>
<output>90</output>

<gadget id="calculator">1 / 90</gadget>
<output>1/90 = around 0.011111</output>

<gadget id="calculator">120 * (1/90)</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">1 / (4/3)</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) * 11</gadget>
<output>33/4 = around 8.25</output>
<result>33/4 = around 8.25</result>

Choices:
A. 8.25
B. 9.25
C. 7.25
D. 10.25
E. 3.25

multiply(divide(const_1, multiply(add(const_100, 20), divide(const_1, subtract(const_100, 10)))), 11)

Explanation: 90 % - - - 11 120 % - - - ? 90 / 120 * 11 = 8.25 answer : a


Question: in the first 10 overs of a cricket game , the run rate was only 4.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?

<gadget id="calculator">10 * 4.2</gadget>
<output>42</output>

<gadget id="calculator">282 - 42</gadget>
<output>240</output>

<gadget id="calculator">240 / 40</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6.25
B. 6.5
C. 6.75
D. 7
E. 6

divide(subtract(282, multiply(10, 4.2)), 40)

Explanation: "10 overs - run rate = 4.2 runs scored in first 10 overs = 42 remaining overs 40 total runs to be scored = 282 42 runs already scored 282 - 42 = 240 240 runs to be scored in 40 overs let required runrate be x 40 * x = 240 x = 240 / 40 x = 6.0 the required runrate is 6.0 answer : e"


Question: average between two sets of numbers is closer to the set withmore numbers ?

<gadget id="calculator">2 * 4</gadget>
<output>8</output>

<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 60
B. 80
C. 98
D. 89
E. 91

Explanation: if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 × 90 + 2 × 805 = 4305 = 86.3 × 90 + 2 × 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b


Question: crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 50 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">50 / (1/2)</gadget>
<output>100</output>

<gadget id="calculator">100 * (1/2)</gadget>
<output>50</output>

<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<result>50</result>

Choices:
A. $ 20
B. $ 40
C. $ 50
D. $ 80
E. $ 100

subtract(divide(50, divide(50, const_100)), multiply(divide(50, divide(50, const_100)), divide(50, const_100)))

Explanation: "deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 50 % , so the manufacturing must have been $ 50 . answer = ( c ) ."


Question: if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2240 less than the principal . what was the principal ?

<gadget id="calculator">4 * 5</gadget>
<output>20</output>

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">2_240 / (4/5)</gadget>
<output>2_800</output>
<result>2_800</result>

Choices:
A. 1500
B. 2500
C. 2507
D. 2800
E. 11500

divide(2240, subtract(const_1, divide(multiply(4, 5), const_100)))

Explanation: "p - 2240 = ( p * 5 * 4 ) / 100 p = 2800 answer : d"


Question: a jeep takes 9 hours to cover a distance of 480 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">(3/2) * 9</gadget>
<output>27/2 = around 13.5</output>

<gadget id="calculator">480 / (27/2)</gadget>
<output>320/9 = around 35.555556</output>
<result>320/9 = around 35.555556</result>

Choices:
A. 48 kmph
B. 52 kmph
C. 35 kmph
D. 63 kmph
E. 65 kmph

Explanation: time = 9 distance = 480 3 / 2 of 9 hours = 9 * 3 / 2 = 13.5 hours required speed = 480 / 13.5 = 35 kmph c )


Question: what is the tens digit of 6 ^ 22 ?

<gadget id="calculator">4 + 1</gadget>
<output>5</output>

<gadget id="calculator">22 % 5</gadget>
<output>2</output>

<gadget id="calculator">6 ** 2</gadget>
<output>36</output>

<gadget id="calculator">36 % 100</gadget>
<output>36</output>

<gadget id="calculator">36 / 10</gadget>
<output>18/5 = around 3.6</output>

<gadget id="calculator">floor(18/5)</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 1
B. 3
C. 5
D. 7
E. 9

floor(divide(reminder(power(6, reminder(22, add(const_4, const_1))), const_100), const_10))

Explanation: "the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 22 has the form 5 n + 2 , so the tens digit of 6 ^ 22 is 3 . the answer is b ."


Question: in one hour , a boat goes 7 km along the steram and 5 km against the stream . the speed of the boat in still waer ( in km / hr ) is :

<gadget id="calculator">7 + 5</gadget>
<output>12</output>

<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 2
B. 4
C. 6
D. 12
E. 15

Explanation: "sol . speed in still water = 1 / 2 ( 7 + 5 ) kmph = 6 kmph . answer c"


Question: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 36 sec . what is the length of the platform ?

<gadget id="calculator">300 / 36</gadget>
<output>25/3 = around 8.333333</output>

<gadget id="calculator">(25/3) * 39</gadget>
<output>325</output>

<gadget id="calculator">325 - 300</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 389 m
B. 350 m
C. 289 m
D. 299 m
E. 25 m

subtract(multiply(speed(300, 36), 39), 300)

Explanation: "speed = 300 / 36 = 25 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 25 / 3 = > x = 25 m . answer : e"


Question: a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 15 more than that received by b , find the total amount shared by a , b and c .

<gadget id="calculator">3 * 15</gadget>
<output>45</output>

<gadget id="calculator">45 * 2</gadget>
<output>90</output>

<gadget id="calculator">2 * 15</gadget>
<output>30</output>

<gadget id="calculator">90 + 30</gadget>
<output>120</output>

<gadget id="calculator">120 + 15</gadget>
<output>135</output>

<gadget id="calculator">120 + 135</gadget>
<output>255</output>

<gadget id="calculator">135 * 3</gadget>
<output>405</output>

<gadget id="calculator">405 - 120</gadget>
<output>285</output>

<gadget id="calculator">255 + 285</gadget>
<output>540</output>
<result>540</result>

Choices:
A. $ 250
B. $ 340
C. $ 640
D. $ 440
E. $ 540

add(add(add(multiply(multiply(const_3, 15), const_2), multiply(const_2, 15)), add(add(multiply(multiply(const_3, 15), const_2), multiply(const_2, 15)), 15)), subtract(multiply(add(add(multiply(multiply(const_3, 15), const_2), multiply(const_2, 15)), 15), const_3), add(multiply(multiply(const_3, 15), const_2), multiply(const_2, 15))))

Explanation: "a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 15 a = 15 + b ( 1 ) = = = > c = 45 + 3 b - b = 2 b + 45 = = > 2 b - c = - 45 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 15 = 2.5 b - 15 = = > 2.5 b - c = 15 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 60 b = $ 120 a = $ 135 c = 405 - 120 = $ 285 total amount = 135 + 120 + 285 = $ 540 answer : e"


Question: williams works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 8 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?

<gadget id="calculator">3 + 4</gadget>
<output>7</output>

<gadget id="calculator">7 - 1</gadget>
<output>6</output>

<gadget id="calculator">8 + 6</gadget>
<output>14</output>

<gadget id="calculator">8 / 14</gadget>
<output>4/7 = around 0.571429</output>
<result>4/7 = around 0.571429</result>

Choices:
A. 3 / 7
B. 5 / 7
C. 6 / 7
D. 1 / 7
E. 4 / 7

divide(8, add(8, subtract(add(const_3, const_4), const_1)))

Explanation: first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 8 x total tips for all months = 6 * x + 8 x = 14 x tips for august / total tips for all months = 8 x / 14 x = 4 / 7 answer : e


Question: ajay can ride 50 km in 1 hour . in how many hours he can ride 1000 km ?

<gadget id="calculator">1_000 / 50</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 10 hrs
B. 15 hrs
C. 20 hrs
D. 25 hrs
E. 18 hrs

Explanation: "1 hour he ride 50 km he ride 1000 km in = 1000 / 50 * 1 = 20 hours answer is c"


Question: a ' s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 80 % of the length of the race ?

<gadget id="calculator">100 - 80</gadget>
<output>20</output>

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">13 / 20</gadget>
<output>13/20 = around 0.65</output>

<gadget id="calculator">(1/5) * (13/20)</gadget>
<output>13/100 = around 0.13</output>

<gadget id="calculator">1 - (13/100)</gadget>
<output>87/100 = around 0.87</output>

<gadget id="calculator">(87/100) * 100</gadget>
<output>87</output>
<result>87</result>

Choices:
A. 44 %
B. 48 %
C. 52 %
D. 42 %
E. 87 %

multiply(subtract(const_1, multiply(divide(subtract(const_100, 80), const_100), divide(13, 20))), const_100)

Explanation: "first calculate the distance , b has covered with his speed in the time , in which a reached 20 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 20 / 13 of b , therefore , b ' s speed is 13 / 20 of a distance covered by b = speed x time = ( 13 / 20 ) x ( 0.2 ) = 0.13 % ( which means b would have covered 0.13 of the race length during the time in which a has covered 0.2 of the race length . therefore to win , b needs a headstart of ( 1 - 0.13 = ) 0.87 of the race length . so the answer is e"


Question: marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 12,000 and the marginal cost is $ 200 , and the total cost is $ 16,000 , what is the value of n ?

<gadget id="calculator">200 / 10</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20
B. 50
C. 60
D. 80
E. 100

Explanation: total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 12,000 + n * $ 200 - - > n = 20 . answer : a .


Question: 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 50 % of the total school population of x students , what is x ?

<gadget id="calculator">90 * 100</gadget>
<output>9_000</output>

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">9_000 / (1/2)</gadget>
<output>18_000</output>

<gadget id="calculator">18_000 ** (1/2)</gadget>
<output>60*sqrt(5) = around 134.164079</output>
<result>60*sqrt(5) = around 134.164079</result>

Choices:
A. 134
B. 150
C. 225
D. 250
E. 500

sqrt(divide(multiply(90, const_100), divide(50, const_100)))

Explanation: "90 = x / 100 * 50 / 100 * x = > x ^ 2 = 9 * 10000 / 5 = > x = 134 a"


Question: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 8 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :

<gadget id="calculator">12_000 - 8_000</gadget>
<output>4_000</output>

<gadget id="calculator">8 * 4_000</gadget>
<output>32_000</output>

<gadget id="calculator">8_000 - 6_000</gadget>
<output>2_000</output>

<gadget id="calculator">32_000 / 2_000</gadget>
<output>16</output>

<gadget id="calculator">8 + 16</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 22
B. 21
C. 88
D. 37
E. 24

Explanation: "explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 8 ) + 6000 ( v - 8 ) < = > 2000 v = 48000 < = > v = 24 answer : e ) 24"


Question: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 7 ?

<gadget id="calculator">1_000 - 3</gadget>
<output>997</output>

<gadget id="calculator">3 * 3</gadget>
<output>9</output>

<gadget id="calculator">9 * 10</gadget>
<output>90</output>

<gadget id="calculator">90 + 9</gadget>
<output>99</output>

<gadget id="calculator">99 + 3</gadget>
<output>102</output>

<gadget id="calculator">997 - 102</gadget>
<output>895</output>

<gadget id="calculator">895 / 7</gadget>
<output>895/7 = around 127.857143</output>

<gadget id="calculator">(895/7) + 1</gadget>
<output>902/7 = around 128.857143</output>

<gadget id="calculator">(902/7) / 2</gadget>
<output>451/7 = around 64.428571</output>

<gadget id="calculator">997 + 102</gadget>
<output>1_099</output>

<gadget id="calculator">(451/7) * 1_099</gadget>
<output>70_807</output>
<result>70_807</result>

Choices:
A. 70,592
B. 64,850
C. 64,749
D. 149,700
E. 156,720

multiply(divide(add(divide(subtract(subtract(const_1000, 3), add(add(multiply(multiply(3, 3), const_10), multiply(3, 3)), 3)), 7), const_1), 2), add(subtract(const_1000, 3), add(add(multiply(multiply(3, 3), const_10), multiply(3, 3)), 3)))

Explanation: "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 7 seeing the options after dividing an finding the reminder of 2 my answer was a"


Question: a tyre has two punctures . the first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes . if air leaks out at a constant rate , how long does it take both the punctures together to make it flat ?

<gadget id="calculator">100 * 3</gadget>
<output>300</output>

<gadget id="calculator">6 - 1</gadget>
<output>5</output>

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">9 + 9</gadget>
<output>18</output>

<gadget id="calculator">(1/5) * 18</gadget>
<output>18/5 = around 3.6</output>

<gadget id="calculator">(18/5) * 10</gadget>
<output>36</output>

<gadget id="calculator">300 + 36</gadget>
<output>336</output>
<result>336</result>

Choices:
A. 315 min
B. 325 min
C. 335 min
D. 345 min
E. none of these

add(multiply(const_100, const_3), multiply(multiply(divide(const_1, subtract(6, const_1)), add(9, 9)), const_10))

Explanation: explanation : do not be confused , take this question same as that of work done question ' s . like work done by 1 st puncture in 1 minute and by second in 1 minute . lets solve it : 1 minute work done by both the punctures = ( 19 + 16 ) = ( 518 ) so both punctures will make the type flat in ( 185 ) mins = 335 mins answer : c


Question: if 15 % of a is the same as 40 % of b , then a : b is :

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">(2/5) / (3/20)</gadget>
<output>8/3 = around 2.666667</output>
<result>8/3 = around 2.666667</result>

Choices:
A. 5 : 4
B. 8 : 3
C. 7 : 16
D. 2 : 17
E. 3 : 5

divide(divide(40, const_100), divide(15, const_100))

Explanation: "expl : 15 % of a i = 40 % of b = 15 a / 100 = 40 b / 100 = 8 / 3 = 8 : 3 answer : b"


Question: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6500 . find the actual price of the good .

<gadget id="calculator">6_500 * 100</gadget>
<output>650_000</output>

<gadget id="calculator">100 - 20</gadget>
<output>80</output>

<gadget id="calculator">80 * 10</gadget>
<output>800</output>

<gadget id="calculator">800 / 100</gadget>
<output>8</output>

<gadget id="calculator">80 - 8</gadget>
<output>72</output>

<gadget id="calculator">72 * 5</gadget>
<output>360</output>

<gadget id="calculator">360 / 100</gadget>
<output>18/5 = around 3.6</output>

<gadget id="calculator">72 - (18/5)</gadget>
<output>342/5 = around 68.4</output>

<gadget id="calculator">650_000 / (342/5)</gadget>
<output>1_625_000/171 = around 9_502.923977</output>
<result>1_625_000/171 = around 9_502.923977</result>

Choices:
A. s . 6000
B. s . 9000
C. s . 10800
D. s . 9503
E. s . 9980

divide(multiply(6500, const_100), subtract(subtract(subtract(const_100, 20), divide(multiply(subtract(const_100, 20), 10), const_100)), divide(multiply(subtract(subtract(const_100, 20), divide(multiply(subtract(const_100, 20), 10), const_100)), 5), const_100)))

Explanation: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6500 1 = 6500 / 68.4 100 = ( 6500 * 100 ) / 68.4 = rs . 9503 . answer : option d"


Question: a box contains 10 tablets of medicine a and 10 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .

<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 12
B. 15
C. 17
D. 19
E. 21

Explanation: "the worst case scenario will be if we remove all 15 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 10 + 2 = 12 tablets . answer : a ."


Question: express a speed of 63 kmph in meters per second ?

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">(5/18) * 63</gadget>
<output>35/2 = around 17.5</output>
<result>35/2 = around 17.5</result>

Choices:
A. 10 mps
B. 14 mps
C. 17.5 mps
D. 19.4 mps
E. 10.8 mps

Explanation: "63 * 5 / 18 = 17.5 mps answer : c"


Question: what least number must be subtracted from 42739 so that remaining no . is divisible by 15

<gadget id="calculator">42_739 / 15</gadget>
<output>42_739/15 = around 2_849.266667</output>

<gadget id="calculator">floor(42_739/15)</gadget>
<output>2_849</output>

<gadget id="calculator">2_849 * 15</gadget>
<output>42_735</output>

<gadget id="calculator">42_739 - 42_735</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 3
B. 4
C. 6
D. 8
E. 9

subtract(42739, multiply(floor(divide(42739, 15)), 15))

Explanation: "explanation : on dividing 42739 by 15 we get the remainder 4 , so 4 should be subtracted option b"


Question: 18 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?

<gadget id="calculator">18 - 1</gadget>
<output>17</output>

<gadget id="calculator">18 * 17</gadget>
<output>306</output>

<gadget id="calculator">306 / 2</gadget>
<output>153</output>

<gadget id="calculator">18 * 7</gadget>
<output>126</output>

<gadget id="calculator">153 + 126</gadget>
<output>279</output>
<result>279</result>

Choices:
A. 144
B. 131
C. 279
D. 90
E. 45

add(divide(multiply(18, subtract(18, const_1)), const_2), multiply(18, 7))

Explanation: "there are 18 business exec and in each handshake 2 business execs are involved . hence 18 c 2 = 153 also , each of 18 exec will shake hand with every 7 other chairmen for total of 126 handshake . total = 153 + 126 = 279 ans : c"


Question: for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 40 color copies at print shop y than at print shop x ?

<gadget id="calculator">2.75 * 40</gadget>
<output>110</output>

<gadget id="calculator">1.25 * 40</gadget>
<output>50</output>

<gadget id="calculator">110 - 50</gadget>
<output>60</output>
<result>60</result>

Choices:
A. $ 48
B. $ 54
C. $ 60
D. $ 66
E. $ 72

subtract(multiply(2.75, 40), multiply(1.25, 40))

Explanation: "the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 40 * $ 1.50 = $ 60 the answer is c ."


Question: the probability of two events a and b are 0.20 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________

<gadget id="calculator">0.2 + 0.4</gadget>
<output>0.6</output>

<gadget id="calculator">0.6 - 0.15</gadget>
<output>0.45</output>

<gadget id="calculator">1 - 0.45</gadget>
<output>0.55</output>
<result>0.55</result>

Choices:
A. 0.45
B. 0.4
C. 0.5
D. 0.55
E. 0.6

subtract(const_1, subtract(add(0.20, 0.40), 0.15))

Explanation: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 20 + . 40 - . 15 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : d"