Question: 17 balls are numbered 1 to 17 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?

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

<gadget id="calculator">8 / 17</gadget>
<output>8/17 = around 0.470588</output>

<gadget id="calculator">8 - 1</gadget>
<output>7</output>

<gadget id="calculator">17 - 1</gadget>
<output>16</output>

<gadget id="calculator">7 / 16</gadget>
<output>7/16 = around 0.4375</output>

<gadget id="calculator">(8/17) * (7/16)</gadget>
<output>7/34 = around 0.205882</output>
<result>7/34 = around 0.205882</result>

Choices:
A. 1 / 7
B. 3 / 14
C. 5 / 23
D. 7 / 34
E. 9 / 41

multiply(divide(add(const_4, const_4), 17), divide(subtract(add(const_4, const_4), 1), subtract(17, 1)))

Explanation: p ( 1 st ball is even ) = 8 / 17 p ( 2 nd ball is also even ) = 7 / 16 p ( both balls are even ) = 8 / 17 * 7 / 16 = 7 / 34 the answer is d .


Question: aarti can do a piece of work in 9 days . in how many days will she complete three time of work of same type ?

<gadget id="calculator">3 * 9</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 6 days
B. 18 days
C. 21 days
D. 27 days
E. 13 days

Explanation: "we have the important relation , more work , more time ( days ) a piece of work can be done in 9 days . three times of work of same type can be done in 9 x 3 = 27 days answer d"


Question: what is the value of n if the sum of the consecutive odd intergers r from 1 to n equals 169 ?

<gadget id="calculator">169 ** (1/2)</gadget>
<output>13</output>

<gadget id="calculator">13 * 2</gadget>
<output>26</output>

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

<gadget id="calculator">26 - 2</gadget>
<output>24</output>

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

Choices:
A. 47
B. 25
C. 37
D. 33
E. 29

add(subtract(multiply(sqrt(169), const_2), multiply(const_2, 1)), 1)

Explanation: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."


Question: there are 7 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .

<gadget id="calculator">binomial(7, 2)</gadget>
<output>21</output>

<gadget id="calculator">21 + 21</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 40
B. 49
C. 41
D. 56
E. 42

Explanation: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 7 and for second = 6 so total methods = 7 * 6 = 42 answer : e"


Question: when a stone is dropped from a building 200 m high , its speed is proportional to the time elapsed after dropping . the distance traveled is proportional to the square of the time elapsed . after 1 second the speed of the train was 10 m / sec and it was 190 m above the ground . when its speed is 25 m / sec , what would be its distance from the ground ?

<gadget id="calculator">200 - 190</gadget>
<output>10</output>

<gadget id="calculator">25 / 10</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">(5/2) ** 2</gadget>
<output>25/4 = around 6.25</output>

<gadget id="calculator">(25/4) * 10</gadget>
<output>125/2 = around 62.5</output>

<gadget id="calculator">200 - (125/2)</gadget>
<output>275/2 = around 137.5</output>
<result>275/2 = around 137.5</result>

Choices:
A. 140 m
B. 137.5 m
C. 125.75 m
D. 142.5 m
E. 152.5 m

subtract(200, multiply(power(divide(25, subtract(200, 190)), const_2), 10))

Explanation: v = x * t and s = y * t ^ 2 10 = x * 1 , hence x = 10 units ( 200 - 190 ) = y * 1 * 1 y = 10 when speed = 25 m / sec , time elapsed = 25 / 10 = 2.5 sec distance travelled by stone = 10 * ( 2.5 ) ^ 2 = 62.5 mts so distance of stone above ground = 200 - 62.5 = 137.5 mtrs answer : b


Question: in a bag of small balls 1 / 4 are green , 1 / 8 are blue , 1 / 12 are yellow and the remaining 26 white . how many balls are blue ?

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

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/4) + (1/8)</gadget>
<output>3/8 = around 0.375</output>

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

<gadget id="calculator">(3/8) + (1/12)</gadget>
<output>11/24 = around 0.458333</output>

<gadget id="calculator">1 - (11/24)</gadget>
<output>13/24 = around 0.541667</output>

<gadget id="calculator">26 / (13/24)</gadget>
<output>48</output>

<gadget id="calculator">48 * (1/8)</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6
B. 5
C. 4
D. 3
E. 8

multiply(divide(26, subtract(const_1, add(add(divide(1, 4), divide(1, 8)), divide(1, 12)))), divide(1, 8))

Explanation: let us first find the fraction of green , blue and yellow balls 1 / 4 + 1 / 8 + 1 / 12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator = 11 / 24 , add numerators the fraction of white balls is given by 24 / 24 - 11 / 24 = 13 / 24 so the fraction 13 / 24 corresponds to 26 balls . if x is the total number of balls then ( 13 / 24 ) of x = 26 balls or ( 13 / 24 ) ? x = 26 x = 26 ? ( 24 / 13 ) = 48 , total number of balls the fraction of blue balls is 1 / 8 of x . the number of blue balls is given by ( 1 / 8 ) of 48 = 6 balls . correct answer a


Question: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 250 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?

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

<gadget id="calculator">250 * 30</gadget>
<output>7_500</output>

<gadget id="calculator">7_500 / 1_000</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">15 / 10</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">(15/2) / (3/2)</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 1
B. 3
C. 4
D. 5
E. 6

divide(divide(multiply(250, multiply(15, const_2)), const_1000), divide(15, const_10))

Explanation: "the distance between the nest and the ditch is 250 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 250 = 7500 . d = st 7500 / 1.5 = t , i think we can take 7500 meters as 7.5 km , then only we get t = 5 . ( 1000 meters = 1 km ) d )"


Question: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 15 percent alcohol by volume ?

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

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

<gadget id="calculator">5 / 15</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) * 300</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 50
B. 100
C. 150
D. 200
E. 250

multiply(divide(subtract(15, 10), subtract(30, 15)), 300)

Explanation: "15 % is 5 % - points higher than 10 % but 15 % - points lower than 30 % . thus there should be 3 parts of solution x for 1 part of solution y . we should add 100 ml of solution y . the answer is b ."


Question: on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 40 percent . what was the total rent the motel actually charged for that night ?

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

<gadget id="calculator">10 * 20</gadget>
<output>200</output>

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

<gadget id="calculator">200 / (2/5)</gadget>
<output>500</output>
<result>500</result>

Choices:
A. $ 500
B. $ 800
C. $ 1,000
D. $ 1,600
E. $ 2,400

divide(multiply(10, subtract(60, 40)), divide(40, const_100))

Explanation: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 40 % . 4 x = 200 = > x = 500 answer a"


Question: the length of the rectangular field is double its width . inside the field there is square shaped pond 9 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?

<gadget id="calculator">9 ** 2</gadget>
<output>81</output>

<gadget id="calculator">81 * 8</gadget>
<output>648</output>

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

<gadget id="calculator">648 / (1/2)</gadget>
<output>1_296</output>

<gadget id="calculator">1_296 ** (1/2)</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 54
B. 36
C. 75
D. 28
E. 11

Explanation: "a / 8 = 9 * 9 = > a = 9 * 9 * 8 x * 2 x = 9 * 9 * 8 x = 18 = > 2 x = 36 answer : b"


Question: how much time will a train of length 380 m moving at a speed of 72 kmph take to cross another train of length 540 m , moving at 36 kmph in the same direction ?

<gadget id="calculator">380 + 540</gadget>
<output>920</output>

<gadget id="calculator">72 - 36</gadget>
<output>36</output>

<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">920 / 10</gadget>
<output>92</output>
<result>92</result>

Choices:
A. 50
B. 99
C. 88
D. 92
E. 12

divide(add(380, 540), multiply(subtract(72, 36), const_0_2778))

Explanation: "the distance to be covered = sum of their lengths = 380 + 540 = 920 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 920 / 10 = 92 sec . answer : d"


Question: let the number which when multiplied by 16 is increased by 375 .

<gadget id="calculator">16 - 1</gadget>
<output>15</output>

<gadget id="calculator">375 / 15</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 14
B. 20
C. 26
D. 25
E. 30

Explanation: "solution let the number be x . then , 16 x - x = 375 ‹ = › 15 x = 375 x ‹ = › 25 . answer d"


Question: jill has 14 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?

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

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

<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">1 + (3/4)</gadget>
<output>7/4 = around 1.75</output>

<gadget id="calculator">14 / (7/4)</gadget>
<output>8</output>

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

Choices:
A. 3
B. 6
C. 9
D. 12
E. 24

multiply(divide(14, add(const_1, add(const_0_25, divide(const_1, const_2)))), const_3)

Explanation: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 14 1 3 / 4 w = 14 w = 8 the total number of jars = 3 w = 24 answer : e


Question: a cricket player whose bowling average was 21.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?

<gadget id="calculator">21.5 - 0.5</gadget>
<output>21</output>

<gadget id="calculator">21 * 5</gadget>
<output>105</output>

<gadget id="calculator">105 - 52</gadget>
<output>53</output>

<gadget id="calculator">53 / 0.5</gadget>
<output>106</output>
<result>106</result>

Choices:
A. 64
B. 72
C. 111
D. 721
E. 108

divide(subtract(multiply(subtract(21.5, 0.5), 5), 52), 0.5)

Explanation: "average = total runs / total wickets total runs after last match = 21.5 w + 52 total wickets after last match = w + 5 ( 21.5 w + 52 ) / ( w + 5 ) = 21.5 - 0.5 = 21 w = 106 so total wickets aftr last match = w + 5 = 111 answer : c"


Question: 8 men , working 8 hours a day can complete a work in 18 days . how many hours a day must 12 men work to complete the same work in 12 days ?

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

<gadget id="calculator">64 * 18</gadget>
<output>1_152</output>

<gadget id="calculator">12 * 12</gadget>
<output>144</output>

<gadget id="calculator">1_152 / 144</gadget>
<output>8</output>
<result>8</result>

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

divide(multiply(multiply(8, 8), 18), multiply(12, 12))

Explanation: "the number of hours required to complete the work is 8 * 8 * 18 = 1152 12 × 12 × ( x ) = 1152 x = 8 the answer is c ."


Question: if 3 men or 4 women can do a piece of work in 16 days , in how many days can 12 men and 8 women do the same piece of work ?

<gadget id="calculator">3 * 16</gadget>
<output>48</output>

<gadget id="calculator">12 / 48</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">4 * 16</gadget>
<output>64</output>

<gadget id="calculator">8 / 64</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/4) + (1/8)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">1 / (3/8)</gadget>
<output>8/3 = around 2.666667</output>
<result>8/3 = around 2.666667</result>

Choices:
A. 8 / 3
B. 6
C. 5
D. 4
E. 3

inverse(add(divide(12, multiply(3, 16)), divide(8, multiply(4, 16))))

Explanation: "3 men can finish a work in 16 days , so in 1 day 3 men finish 1 / 16 th of work and in 1 day 1 men can finish , 1 / 48 th of work . similarly , in 1 day 1 women can finish 1 / 64 th of work . 12 men in 1 day can finish , 12 / 48 = 1 / 4 , 8 women in 1 day can finish = 8 / 64 = 1 / 8 1 / 4 + 1 / 8 = 3 / 8 . hence number of days to complete is 8 / 3 days . answer : a"


Question: john has $ 1,600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 + 600</gadget>
<output>1_600</output>

<gadget id="calculator">600 + 1_600</gadget>
<output>2_200</output>

<gadget id="calculator">2_200 / 2</gadget>
<output>1_100</output>

<gadget id="calculator">1_600 - 1_100</gadget>
<output>500</output>
<result>500</result>

Choices:
A. $ 200
B. $ 400
C. $ 600
D. $ 800
E. $ 500

subtract(add(multiply(const_100, const_10), 600), divide(add(600, add(multiply(const_100, const_10), 600)), const_2))

Explanation: suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e


Question: a , b and c started a business by investing rs . 800 / - , rs . 1000 / - and rs . 1200 / - respectively for two years . total profit is rs . 1000 / - . find the c ' s share ?

<gadget id="calculator">800 + 1_000</gadget>
<output>1_800</output>

<gadget id="calculator">1_800 + 1_200</gadget>
<output>3_000</output>

<gadget id="calculator">1_000 / 3_000</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">1_200 * (1/3)</gadget>
<output>400</output>
<result>400</result>

Choices:
A. rs . 600
B. rs . 500
C. rs . 400
D. rs . 800
E. rs . 900

Explanation: solution : a : b : c = ( 800 * 2 ) : ( 1000 * 2 ) : ( 12000 * 2 ) = 4 : 5 : 6 . so c ' s share = rs . ( 1000 * 6 / 15 ) = rs . 400 . answer : option c


Question: the speed of a car is 85 km in the first hour and 45 km in the second hour . what is the average speed of the car ?

<gadget id="calculator">85 + 45</gadget>
<output>130</output>

<gadget id="calculator">130 / 2</gadget>
<output>65</output>
<result>65</result>

Choices:
A. 72 kmph
B. 65 kmph
C. 30 kmph
D. 80 kmph
E. 82 kmph

Explanation: s = ( 85 + 45 ) / 2 = 65 kmph answer : b


Question: the positive value of x that satisfies the equation ( 3 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is between bunuel , can you please explain this one ?

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

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

Choices:
A. 0 and 0.5
B. 0.5 and 1
C. 1 and 1.5
D. 1.5 and 2
E. 2 and 2.5

Explanation: trial and error would probably be the easiest way to solve this problem . when x is large enough positive number , then because of the exponents ( 5 > 4 ) , lhs will be more than rhs ( as you increase the positive value of x the distance between the values of lhs and rhs will increase ) . try x = 1 - - > lhs = 3 ^ 5 = 81 * 3 = 243 and rhs = 4 ^ 4 = 64 * 4 = 256 , so ( 1 + 2 x ) ^ 5 < ( 1 + 3 x ) ^ 4 . as you can see lhs is still slightly less than than rhs . so , the value of x for which ( 1 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is slightly more than 1 . answer : d .


Question: the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :

<gadget id="calculator">20 * 15</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 276
B. 300
C. 299
D. 322
E. 345

Explanation: "the numbers are ( 20 x 11 ) and ( 20 x 15 ) . larger number = ( 20 x 15 ) = 300 . answer : b"


Question: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 10 inches tall . how tall are the sculpture andbase together ?

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

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

<gadget id="calculator">24 + 10</gadget>
<output>34</output>

<gadget id="calculator">34 + 10</gadget>
<output>44</output>

<gadget id="calculator">44 / 12</gadget>
<output>11/3 = around 3.666667</output>
<result>11/3 = around 3.666667</result>

Choices:
A. 3.1 feet
B. 3.66 feet
C. 3.3 feet
D. 3.4 feet
E. 3.5 feet

Explanation: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 10 = 40 44 / 12 = 3.66 feet answer : b"


Question: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction w of the area of triangle abc is the area of triangle xyz ?

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

<gadget id="calculator">16 / 2</gadget>
<output>8</output>

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

<gadget id="calculator">12 ** 2</gadget>
<output>144</output>

<gadget id="calculator">144 / 2</gadget>
<output>72</output>

<gadget id="calculator">8 / 72</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>

Choices:
A. 1 / 9
B. 1 / 8
C. 1 / 6
D. 1 / 5
E. 1 / 3

divide(divide(power(const_4, const_2), const_2), divide(power(add(const_10, const_2), const_2), const_2))

Explanation: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives w = 1 / 9 . a"


Question: the cash difference between the selling prices of an article at a profit of 4 % and 2 % is rs . 3 . the ratio of the two selling prices is ?

<gadget id="calculator">100 + 4</gadget>
<output>104</output>

<gadget id="calculator">100 + 2</gadget>
<output>102</output>

<gadget id="calculator">104 / 102</gadget>
<output>52/51 = around 1.019608</output>
<result>52/51 = around 1.019608</result>

Choices:
A. 52 : 51
B. 52 : 53
C. 52 : 50
D. 22 : 56
E. 52 : 51

divide(add(const_100, 4), add(const_100, 2))

Explanation: "let c . p . of the article be rs . x . then , required ratio = 104 % of x / 102 % of x = 104 / 102 = 52 / 51 = 52 : 51 answer : a"


Question: two whole numbers whose sum is 100 can not be in the ratio

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

<gadget id="calculator">50 - 10</gadget>
<output>40</output>

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

<gadget id="calculator">50 + 10</gadget>
<output>60</output>

<gadget id="calculator">20 / 60</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>

Choices:
A. 2 : 23
B. 5 : 45
C. 10 : 10
D. 2 : 6
E. 2 : 3

divide(divide(subtract(divide(100, const_2), const_10), const_2), add(divide(100, const_2), const_10))

Explanation: d ) 2 : 6


Question: in a certain warehouse , 30 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?

<gadget id="calculator">100 - 80</gadget>
<output>20</output>

<gadget id="calculator">48 / 20</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">(12/5) * 100</gadget>
<output>240</output>

<gadget id="calculator">240 * 30</gadget>
<output>7_200</output>

<gadget id="calculator">7_200 / 100</gadget>
<output>72</output>

<gadget id="calculator">72 - 48</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 8
B. 64
C. 24
D. 102
E. 144

subtract(divide(multiply(multiply(divide(48, subtract(const_100, 80)), const_100), 30), const_100), 48)

Explanation: "if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 30 % of the packages weigh less than 75 pounds so , 30 % oft = number of packages that weigh less than 75 pounds 30 % of 240 = 72 , so 72 packages weigh less than 75 pounds of those 72 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 72 - 48 = 24 = c"


Question: a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10 . in all papers together , the candidate obtained 60 % of the total marks then , the number of papers in which he got more than 50 % marks is

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

Choices:
A. 1
B. 3
C. 4
D. 5
E. 7

Explanation: solution : let the marks obtained in five subjects be 6 x , 7 x , 8 x , 9 x and 10 x . total marks obtained = 40 x max . marks of the five subjects = 40 x / 0.6 [ 40 x is 60 % of total marks ] max . marks in each subject = 40 x / 0.6 * 5 = 13.33 x hence , % of each subject = 6 x * 100 / 13.33 = 45.01 % or , 7 x * 100 / 13.33 = 52.51 in same way other percentage are 60.01 % , 67.52 % , 75.01 % . hence , number of subjects in which he gets more than 50 % marks = 4 . answer : option c


Question: subtracting 5 % of a from a is equivalent to multiplying a by how much ?

<gadget id="calculator">100 - 5</gadget>
<output>95</output>

<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>
<result>19/20 = around 0.95</result>

Choices:
A. 0.95
B. 9.4
C. 0.094
D. 94
E. none

Explanation: "answer let a - 5 % of a = ab . ⇒ ( 95 x a ) / 100 = ab ∴ b = 0.95 correct option : a"


Question: a bag consists of 20 marbles , of which 5 are blue , 7 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 + 7</gadget>
<output>12</output>

<gadget id="calculator">20 - 12</gadget>
<output>8</output>

<gadget id="calculator">8 + 7</gadget>
<output>15</output>

<gadget id="calculator">15 / 20</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>

Choices:
A. 3 / 4
B. 2 / 4
C. 1 / 4
D. 1 / 8
E. 1 / 16

divide(add(subtract(20, add(5, 7)), 7), 20)

Explanation: "bag consists of 20 marbles , of which 5 are blue , 7 are red remainder are white . so , white = 20 - 5 - 7 = 8 . 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 = 7 / 20 + 8 / 20 = 15 / 20 = 3 / 4 hence , answer will be a ."


Question: a trader bought a car at 20 % discount on its original price . he sold it at a 60 % increase on the price he bought it . what percent of profit did he make on the original price ?

<gadget id="calculator">100 - 20</gadget>
<output>80</output>

<gadget id="calculator">100 + 60</gadget>
<output>160</output>

<gadget id="calculator">80 * 160</gadget>
<output>12_800</output>

<gadget id="calculator">12_800 / 100</gadget>
<output>128</output>

<gadget id="calculator">128 / 100</gadget>
<output>32/25 = around 1.28</output>

<gadget id="calculator">(32/25) - 1</gadget>
<output>7/25 = around 0.28</output>

<gadget id="calculator">(7/25) * 100</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 28 %
B. 72 %
C. 12 %
D. 82 %
E. 16 %

multiply(subtract(divide(divide(multiply(subtract(const_100, 20), add(const_100, 60)), const_100), const_100), const_1), const_100)

Explanation: "original price = 100 cp = 80 s = 80 * ( 160 / 100 ) = 128 100 - 128 = 28 % answer : a"


Question: how many seconds will a 550 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?

<gadget id="calculator">63 - 3</gadget>
<output>60</output>

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

<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">550 / (50/3)</gadget>
<output>33</output>
<result>33</result>

Choices:
A. 12 sec
B. 30 sec
C. 33 sec
D. 16 sec
E. 18 sec

divide(550, multiply(subtract(63, 3), const_0_2778))

Explanation: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 550 * 3 / 50 = 33 sec . answer : c"


Question: jansi went out for shopping . she had in her handbag approximately rs . 15 / - in one rupee notes and 20 p . coins . when she returned she had as many one rupee notes as she originally had and as many 20 p . coins as she originally had one rupee notes . she actually came back with about one - third of what she had started out with . how much did she spend and exactly how much did she have with her when she started out ?

<gadget id="calculator">3 * 100</gadget>
<output>300</output>

<gadget id="calculator">300 - 20</gadget>
<output>280</output>

<gadget id="calculator">3 * 20</gadget>
<output>60</output>

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

<gadget id="calculator">280 / 40</gadget>
<output>7</output>

<gadget id="calculator">15 / 7</gadget>
<output>15/7 = around 2.142857</output>

<gadget id="calculator">floor(15/7)</gadget>
<output>2</output>

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

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

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

<gadget id="calculator">14 + (2/5)</gadget>
<output>72/5 = around 14.4</output>

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

<gadget id="calculator">(72/5) * (1/3)</gadget>
<output>24/5 = around 4.8</output>

<gadget id="calculator">(72/5) - (24/5)</gadget>
<output>48/5 = around 9.6</output>
<result>48/5 = around 9.6</result>

Choices:
A. 9.6
B. 10.6
C. 11.0
D. 9.4
E. 8.1

subtract(add(multiply(floor(divide(15, divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20))))), divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20)))), divide(multiply(floor(divide(15, divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20))))), 20), const_100)), multiply(add(multiply(floor(divide(15, divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20))))), divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20)))), divide(multiply(floor(divide(15, divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20))))), 20), const_100)), divide(const_1, const_3)))

Explanation: a 9.60 let us assume that originally jansi had x rupees and y 20 paise coins . going shopping she had ( 100 x + 20 y ) paise . she returned with only ( 100 y + 20 x ) paise . this last sum , as we know , is one - third of the original and therefore 3 ( 100 y + 20 x ) = 100 x + 20 y simplifying we have x = 7 y if y is 1 thenx is 7 . assuming this so jansi had 7.20 rupees when she set out for shopping . this is wrong because jansi actually had about 15 rupees . let us see now what we get if y = 2 . then x = 14 . the original sum was 14.40 rupees which accords with the condition of the problem . if we assume that y = 3 then the sum will be too big — 21.60 rupees . therefore the only suitable answer is 14.40 rupees . after shopping jansi had 2 one rupee notes and 14 twenty paise coins . this is actually l / 3 rd of the original sum 1,440 : 3 = 480 . jansi ' s purchases , therefore , cost 14.40 — 4.80 = rs 9.60


Question: at a certain organisation , the number of male members went up by 15 % in the year 2001 from year 2000 , and the number of females members went down by 6 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?

<gadget id="calculator">1.2 / 100</gadget>
<output>0.012</output>

<gadget id="calculator">1 + 0.012</gadget>
<output>1.012</output>

<gadget id="calculator">1.012 * 1_000</gadget>
<output>1_012</output>

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>

<gadget id="calculator">1 - (3/50)</gadget>
<output>47/50 = around 0.94</output>

<gadget id="calculator">(47/50) * 1_000</gadget>
<output>940</output>

<gadget id="calculator">1_012 - 940</gadget>
<output>72</output>

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>

<gadget id="calculator">(23/20) * 1_000</gadget>
<output>1_150</output>

<gadget id="calculator">1_150 - 1_012</gadget>
<output>138</output>

<gadget id="calculator">72 / 138</gadget>
<output>12/23 = around 0.521739</output>
<result>12/23 = around 0.521739</result>

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

divide(subtract(multiply(add(const_1, divide(1.2, const_100)), const_1000), multiply(subtract(const_1, divide(6, const_100)), const_1000)), subtract(multiply(add(const_1, divide(15, const_100)), const_1000), multiply(add(const_1, divide(1.2, const_100)), const_1000)))

Explanation: "men increase by 15 % = = > 1.15 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.15 m + 0.94 f = 1.012 * ( m + f ) 1.15 m + 0.94 f = 1.012 m + 1.012 f 1.15 m - 1.012 m = 1.012 f - 0.94 f 0.138 m = 0.072 f m / f = ( 0.072 ) / ( 0.138 ) = 72 / 138 = 1 / 2 answer = ( a )"


Question: in a party every person shakes hands with every other person . if there were a total of 120 handshakes in the party then what is the number of persons present in the party ?

<gadget id="calculator">120 * 2</gadget>
<output>240</output>

<gadget id="calculator">240 * 4</gadget>
<output>960</output>

<gadget id="calculator">960 + 1</gadget>
<output>961</output>

<gadget id="calculator">961 ** (1/2)</gadget>
<output>31</output>

<gadget id="calculator">31 + 1</gadget>
<output>32</output>

<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 15
B. 16
C. 17
D. 18
E. 19

divide(add(sqrt(add(multiply(multiply(120, const_2), const_4), const_1)), const_1), const_2)

Explanation: "explanation : let the number of persons be n ∴ total handshakes = nc 2 = 120 n ( n - 1 ) / 2 = 120 ∴ n = 16 answer : option b"


Question: a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 21 inches and the width of the wall is 28 inches , what is the length of the wall , in inches ?

<gadget id="calculator">21 ** 2</gadget>
<output>441</output>

<gadget id="calculator">2 * 441</gadget>
<output>882</output>

<gadget id="calculator">882 / 28</gadget>
<output>63/2 = around 31.5</output>
<result>63/2 = around 31.5</result>

Choices:
A. 21.5
B. 31.5
C. 41.5
D. 61.5
E. 71.5

Explanation: "since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 21 ^ 2 = 441 . area of rectangle is double of that 2 * 441 = 882 . now a = lw and we need find w so a / l = w ; 882 / 28 = 31.5 answer ! answer is b"


Question: when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 96.15 , what is the value of y ?

<gadget id="calculator">floor(96.15)</gadget>
<output>96</output>

<gadget id="calculator">96.15 - 96</gadget>
<output>0.15</output>

<gadget id="calculator">6 / 0.15</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 96
B. 75
C. 40
D. 25
E. 12

Explanation: "by the definition of a remainder , the remainder here is equal to 6 / y . the remainder in decimal form is given as . 15 therefore , 6 / y = . 15 solve for y and get 40 . c"


Question: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 276 games will be played during the tournament . find the number of participants .

<gadget id="calculator">276 * 2</gadget>
<output>552</output>

<gadget id="calculator">552 * 4</gadget>
<output>2_208</output>

<gadget id="calculator">2_208 + 1</gadget>
<output>2_209</output>

<gadget id="calculator">2_209 ** (1/2)</gadget>
<output>47</output>

<gadget id="calculator">47 + 1</gadget>
<output>48</output>

<gadget id="calculator">48 / 2</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 20
B. 22
C. 24
D. 26
E. 28

divide(add(sqrt(add(multiply(multiply(276, const_2), const_4), const_1)), const_1), const_2)

Explanation: "let p be the number of participants . pc 2 = 276 ( p ) ( p - 1 ) = 552 = 24 * 23 p = 24 the answer is c ."


Question: 3 friends had dinner at a restaurant . when the bill was received , akshitha paid 3 / 4 as much as veena paid and veena paid 1 / 2 as much as lasya paid . what fraction of the bill did veena pay ?

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

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

<gadget id="calculator">7 + 8</gadget>
<output>15</output>

<gadget id="calculator">4 / 15</gadget>
<output>4/15 = around 0.266667</output>
<result>4/15 = around 0.266667</result>

Choices:
A. 4 / 15
B. 3 / 12
C. 3 / 11
D. 3 / 10
E. 3 / 14

divide(4, add(add(3, 4), multiply(4, 2)))

Explanation: let veena paid x , so akshitha paid 3 x / 4 , and lasya paid 2 x , so total bill paid is given by x + ( 3 x / 4 ) + 2 x = 1 , we get i . e . x = 4 / 15 answer : a


Question: a number x is 5 times another number y . the percentage that y is less than x is

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

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

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

Choices:
A. 12.5 %
B. 87.5 %
C. 80 %
D. 11 %
E. 1 %

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

Explanation: "say y = 1 and x = 5 . then y = 1 is less than x = 5 by ( 5 - 1 ) / 5 * 100 = 4 / 5 * 100 = 80 % . answer : c ."


Question: marketing executives for a certain chewing gum company projected a 40 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 30 % . what percent of the projected revenue was the actual revenue ?

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

<gadget id="calculator">40 + 100</gadget>
<output>140</output>

<gadget id="calculator">70 / 140</gadget>
<output>1/2 = around 0.5</output>

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

Choices:
A. 50 %
B. 58 %
C. 62.5 %
D. 64 %
E. 75 %

multiply(divide(subtract(const_100, 30), add(40, const_100)), const_100)

Explanation: last year revenue = 100 ( assume ) ; this year revenue = 70 ; projected revenue = 140 . actual / projected * 100 = 70 / 140 * 100 = 50 % . answer : a .


Question: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 9 m x 6 m x 22.5 cm ?

<gadget id="calculator">9 * 100</gadget>
<output>900</output>

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

<gadget id="calculator">900 * 600</gadget>
<output>540_000</output>

<gadget id="calculator">540_000 * 22.5</gadget>
<output>12_150_000</output>

<gadget id="calculator">25 * 11.25</gadget>
<output>281.25</output>

<gadget id="calculator">281.25 * 6</gadget>
<output>1_687.5</output>

<gadget id="calculator">12_150_000 / 1_687.5</gadget>
<output>7_200</output>
<result>7_200</result>

Choices:
A. 6400
B. 6410
C. 6440
D. 7200
E. 6800

divide(multiply(multiply(multiply(9, const_100), multiply(6, const_100)), 22.5), multiply(multiply(25, 11.25), 6))

Explanation: "number of bricks = volume of wall / volume of bricks = 900 x 600 x 22.5 / 25 x 11.25 x 6 = = 7200 answer : d"


Question: at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 65 . 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 - 65</gadget>
<output>25</output>

<gadget id="calculator">30 / 25</gadget>
<output>6/5 = around 1.2</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">(6/5) - (1/5)</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 1
B. 5
C. 9
D. 15
E. 30

subtract(divide(subtract(120, 90), subtract(90, 65)), 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 60 customers per day . 30 / 30 = 1 day . choice ( a ) . withthe formula , we can set up the following : 90 = ( 60 x + 120 ) / ( x + 1 ) 90 x + 90 = 60 x + 120 30 x = 30 x = 1 answer choice ( a )


Question: stacy has a 63 page history paper due in 7 days . how many pages per day would she have to write to finish on time ?

<gadget id="calculator">63 / 7</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 9
B. 8
C. 10
D. 8.5
E. 6

Explanation: "63 / 7 = 9 a . 9"


Question: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 148 , what is the difference between the ages of patrick and monica ?

<gadget id="calculator">5 * 5</gadget>
<output>25</output>

<gadget id="calculator">3 * 3</gadget>
<output>9</output>

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

<gadget id="calculator">9 + 15</gadget>
<output>24</output>

<gadget id="calculator">24 + 25</gadget>
<output>49</output>

<gadget id="calculator">148 / 49</gadget>
<output>148/49 = around 3.020408</output>

<gadget id="calculator">25 * (148/49)</gadget>
<output>3_700/49 = around 75.510204</output>

<gadget id="calculator">9 * (148/49)</gadget>
<output>1_332/49 = around 27.183673</output>

<gadget id="calculator">(3_700/49) - (1_332/49)</gadget>
<output>2_368/49 = around 48.326531</output>
<result>2_368/49 = around 48.326531</result>

Choices:
A. 27
B. 48
C. 45
D. 72
E. 18

subtract(multiply(multiply(5, 5), divide(148, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5)))), multiply(multiply(3, 3), divide(148, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5)))))

Explanation: "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 148 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"


Question: you collect baseball cards . suppose you start out with 15 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?

<gadget id="calculator">15 - 4</gadget>
<output>11</output>

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

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

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

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

multiply(subtract(subtract(subtract(15, const_4), const_4), 1), const_3)

Explanation: solution start with 15 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 15 + 1 which is 8 , so you ' re left with 15 - 8 = 7 . peter takes 1 baseball card from you : 7 - 1 = 6 baseball cards . paul triples the number of baseball cards you have : 6 × 3 = 18 baseball cards . so you have 18 at the end . correct answer : b


Question: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 4 , 2 / 3 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?

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

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

<gadget id="calculator">(1/4) * (2/3)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">(1/6) * (3/8)</gadget>
<output>1/16 = around 0.0625</output>
<result>1/16 = around 0.0625</result>

Choices:
A. 1 / 16
B. 7 / 8
C. 9 / 64
D. 5 / 64
E. 3 / 64

multiply(multiply(divide(1, 4), divide(2, 3)), subtract(const_1, divide(5, 8)))

Explanation: p ( xavier will solve ) = 1 / 4 p ( yvonne will solve ) = 2 / 3 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 4 ) * ( 2 / 3 ) * ( 3 / 8 ) = 1 / 16 . ans . a .


Question: in a certain lottery , the probability that a number between 1 and 15 , inclusive , is drawn is 1 / 3 . if the probability that a number 1 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 15 is drawn ?

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

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

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

<gadget id="calculator">(4/3) - (2/3)</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>

Choices:
A. 2 / 3
B. 1 / 3
C. 1 / 4
D. 1 / 6
E. 2 / 5

subtract(add(1, divide(1, 3)), divide(2, 3))

Explanation: you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 1 or larger set 2 : number 15 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or less or both ) 2 / 3 + p ( set 2 ) - 1 / 3 = 1 p ( set 2 ) = 2 / 3 answer a


Question: if x is less than y by 25 % then y exceed x by :

<gadget id="calculator">100 - 25</gadget>
<output>75</output>

<gadget id="calculator">100 / 75</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) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>

Choices:
A. 33.33 %
B. 25 %
C. 75 %
D. 66.66 %
E. none of these

multiply(subtract(divide(const_100, subtract(const_100, 25)), const_1), const_100)

Explanation: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 25 ( 100 - 25 ) * 100 = 33.33 % answer : a"


Question: a pharmaceutical company received $ 8 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">8 / 20</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) * 100</gadget>
<output>40</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">40 - (25/3)</gadget>
<output>95/3 = around 31.666667</output>

<gadget id="calculator">(95/3) / 40</gadget>
<output>19/24 = around 0.791667</output>

<gadget id="calculator">(19/24) * 100</gadget>
<output>475/6 = around 79.166667</output>
<result>475/6 = around 79.166667</result>

Choices:
A. 8 %
B. 15 %
C. 45 %
D. 52 %
E. 79 %

multiply(divide(subtract(multiply(divide(8, 20), const_100), multiply(divide(9, 108), const_100)), multiply(divide(8, 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 = 8 / 20 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 = ( 8 / 20 ) x 60 = 24 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 24 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 24 ) / 24 ] x 100 - 475 / 6 x 100 at this point we can stop and consider the answer choices . since we know that 475 / 6 is just a bit less than ½ , we know that - 475 / 6 x 100 is about a 79 % decrease . answer e ."


Question: a square with sides of 15 units each . what would be the area of the square . consider a square as a combination of two right angled triangles .

<gadget id="calculator">(15 * 15) / 2</gadget>
<output>225/2 = around 112.5</output>

<gadget id="calculator">(225/2) * 2</gadget>
<output>225</output>
<result>225</result>

Choices:
A. 100
B. 256
C. 225
D. 81
E. 144

Explanation: a square can be considered as a set of two right angled triangles joined from the hypotenuse . since the sides are 10 units each . the height and base of both the triangles is 10 each . area of a right angled triangle is 1 / 2 * base * height area of both the triangles is 2 * 1 / 2 * base * height . since both triangles are similar . = base * height = 15 * 15 = 225 ans : c


Question: how many digits are required to number a book containing 240 pages ?

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

<gadget id="calculator">9 * 10</gadget>
<output>90</output>

<gadget id="calculator">90 * 2</gadget>
<output>180</output>

<gadget id="calculator">9 + 180</gadget>
<output>189</output>

<gadget id="calculator">240 - 100</gadget>
<output>140</output>

<gadget id="calculator">140 + 1</gadget>
<output>141</output>

<gadget id="calculator">141 * 3</gadget>
<output>423</output>

<gadget id="calculator">189 + 423</gadget>
<output>612</output>
<result>612</result>

Choices:
A. 756
B. 612
C. 492
D. 372
E. 250

add(add(subtract(const_10, const_1), multiply(multiply(subtract(const_10, const_1), const_10), const_2)), multiply(add(subtract(240, const_100), const_1), const_3))

Explanation: 9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 240 - ( 90 + 9 ) = 141 pages will require 141 * 3 = 423 digits . the total number of digits is 9 + 180 + 423 = 612 . the answer is b .


Question: out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many e applicants majored in political science and had a gpa higher than 3.0 ?

<gadget id="calculator">10 + 15</gadget>
<output>25</output>

<gadget id="calculator">40 - 25</gadget>
<output>15</output>

<gadget id="calculator">20 - 15</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 5
B. 10
C. 15
D. 25
E. 35

Explanation: "total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) e = 20 - 15 = 5 answer : a"


Question: george does 3 / 5 th of a piece of work in 9 days . he then calls in paul and they finish the work in 4 days . how long would paul take to do the work by himself ?

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

<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>

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

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

<gadget id="calculator">4 * (1/15)</gadget>
<output>4/15 = around 0.266667</output>

<gadget id="calculator">(2/5) - (4/15)</gadget>
<output>2/15 = around 0.133333</output>

<gadget id="calculator">(2/15) / 4</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 10
B. 20
C. 30
D. 40
E. 50

inverse(divide(subtract(subtract(const_1, divide(3, 5)), multiply(4, divide(const_1, multiply(5, 3)))), 4))

Explanation: "9 day 3 / 5 1 day 1 / 15 remaing 1 - 3 / 5 = 2 / 5 both can do 2 / 5 work in 4 day one day work of both = 1 / 10 therfor paul would take 1 / 10 - 1 / 15 = 1 / 30 or 30 days answer : c"


Question: in august , a cricket team that played 120 matches won 24 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?

<gadget id="calculator">52 / 100</gadget>
<output>13/25 = around 0.52</output>

<gadget id="calculator">(13/25) * 120</gadget>
<output>312/5 = around 62.4</output>

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>

<gadget id="calculator">(6/25) * 120</gadget>
<output>144/5 = around 28.8</output>

<gadget id="calculator">(312/5) - (144/5)</gadget>
<output>168/5 = around 33.6</output>

<gadget id="calculator">1 - (13/25)</gadget>
<output>12/25 = around 0.48</output>

<gadget id="calculator">(168/5) / (12/25)</gadget>
<output>70</output>
<result>70</result>

Choices:
A. 40
B. 52
C. 68
D. 70
E. 98

divide(subtract(multiply(divide(52, const_100), 120), multiply(divide(24, const_100), 120)), subtract(const_1, divide(52, const_100)))

Explanation: let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 28.8 + x by solving we get x = 70 answer : d


Question: in a survey of 340 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?

<gadget id="calculator">12.5 * 104</gadget>
<output>1_300</output>

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

<gadget id="calculator">1_300 / 100</gadget>
<output>13</output>

<gadget id="calculator">54 - 13</gadget>
<output>41</output>

<gadget id="calculator">41 + 104</gadget>
<output>145</output>

<gadget id="calculator">340 - 145</gadget>
<output>195</output>

<gadget id="calculator">195 / 340</gadget>
<output>39/68 = around 0.573529</output>
<result>39/68 = around 0.573529</result>

Choices:
A. 7 / 12
B. 8 / 41
C. 39 / 68
D. 1 / 8
E. 41 / 91

divide(subtract(340, add(subtract(54, divide(multiply(12.5, 104), multiply(const_1, const_100))), 104)), 340)

Explanation: - - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 286 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 340 we have to find not part time and not uninsured . in other words not part time and insured = x / 340 = ( 286 - 104 + 13 ) / 340 = 39 / 68 answer is c .


Question: a ( 3 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 - 1 . what is the value of w ?

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

<gadget id="calculator">9 - 1</gadget>
<output>8</output>

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

<gadget id="calculator">8 ** (1/3)</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 2 .
B. 4 .
C. 5 .
D. 6 .
E. 9 .

power(subtract(power(3, 2), 1), divide(1, 3))

Explanation: y = x ^ 2 - 1 w ^ 3 = 3 ^ 2 - 1 w ^ 3 = 8 w = 2 answer a


Question: in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 120 ?

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

<gadget id="calculator">40 * 3</gadget>
<output>120</output>

<gadget id="calculator">60 - 30</gadget>
<output>30</output>

<gadget id="calculator">30 * 3</gadget>
<output>90</output>

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

Choices:
A. 30
B. 20
C. 25
D. 40
E. 50

subtract(multiply(subtract(60, 20), const_3), multiply(subtract(60, 30), const_3))

Explanation: x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 120 = ( 120 * 30 ) / 40 = 90 . in x game of 100 points , y gives ( 120 - 90 ) = 30 points to c . a


Question: a house wife saved $ 2.50 in buying an item on sale . if she spent $ 25 for the item , approximately how much percent she saved in the transaction ?

<gadget id="calculator">25 + 2.5</gadget>
<output>27.5</output>

<gadget id="calculator">2.5 / 27.5</gadget>
<output>0.090909</output>

<gadget id="calculator">0.090909 * 100</gadget>
<output>9.0909</output>
<result>9.0909</result>

Choices:
A. 8 %
B. 9 %
C. 10 %
D. 11 %
E. 12 %

multiply(divide(2.5, add(25, 2.5)), const_100)

Explanation: actual price = 25 + 2.50 = $ 27.50 saving = 2.50 / 27.50 * 100 = 100 / 11 = 9 % approximately answer is b


Question: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6700 . find the actual price of the good .

<gadget id="calculator">6_700 * 100</gadget>
<output>670_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">670_000 / (342/5)</gadget>
<output>1_675_000/171 = around 9_795.321637</output>
<result>1_675_000/171 = around 9_795.321637</result>

Choices:
A. s . 6000
B. s . 9000
C. s . 10800
D. s . 9795
E. s . 9980

divide(multiply(6700, 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 = 6700 1 = 6700 / 68.4 100 = ( 6700 * 100 ) / 68.4 = rs . 9795 . answer : option d


Question: in a factory , an average of 60 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?

<gadget id="calculator">25 + 5</gadget>
<output>30</output>

<gadget id="calculator">30 * 58</gadget>
<output>1_740</output>

<gadget id="calculator">25 * 60</gadget>
<output>1_500</output>

<gadget id="calculator">1_740 - 1_500</gadget>
<output>240</output>

<gadget id="calculator">240 / 5</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 20
B. 36
C. 48
D. 50
E. 59

divide(subtract(multiply(add(25, 5), 58), multiply(25, 60)), 5)

Explanation: production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 60 = 240 ∴ average for last 5 days = 240 / 5 = 48 c


Question: the ratio between the present ages of a and b is 5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?

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

<gadget id="calculator">5 - 3</gadget>
<output>2</output>

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

<gadget id="calculator">5 * 5</gadget>
<output>25</output>

<gadget id="calculator">25 + 5</gadget>
<output>30</output>

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

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

<gadget id="calculator">30 / 10</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 3 : 9
B. 3 : 6
C. 3 : 1
D. 3 : 4
E. 3 : 2

divide(add(multiply(5, divide(add(5, 5), subtract(5, 3))), 5), subtract(multiply(3, divide(add(5, 5), subtract(5, 3))), 5))

Explanation: "let the present ages of a and b be 5 x and 3 x years respectively . then , ( 5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 2 x = 8 = > x = 4 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 24 : 8 = 3 : 1 answer : c"


Question: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors s ?

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

<gadget id="calculator">60 / 2</gadget>
<output>30</output>

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

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

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

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

Choices:
A. 2
B. 3
C. 5
D. 6
E. 8

add(divide(add(const_1, const_4), divide(divide(divide(60, const_2), const_2), const_3)), const_2)

Explanation: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have s = 2 * 3 * 5 * 7 = 840 thus , answer b"


Question: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 40 cm , find the sum of the perimeters of all the triangles .

<gadget id="calculator">40 + 40 + 40</gadget>
<output>120</output>

<gadget id="calculator">120 + 120</gadget>
<output>240</output>
<result>240</result>

Choices:
A. 180 cm
B. 220 cm
C. 240 cm
D. 270 cm
E. 300 cm

add(triangle_perimeter(40, 40, 40), triangle_perimeter(40, 40, 40))

Explanation: we have 40 for first triangle , when we join mid - points of first triangle we get the second equilateral traingle then the length of second one is 20 and continues . so we have 40 , 20,10 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 40 / 1 - ( 1 / 2 ) = 80 equilateral triangle perimeter is 3 a = 3 * 80 = 240 . so option c .


Question: two pipes a and b can fill a tank in 10 hours and 20 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?

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

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

<gadget id="calculator">(1/10) + (1/20)</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">1 / (3/20)</gadget>
<output>20/3 = around 6.666667</output>
<result>20/3 = around 6.666667</result>

Choices:
A. 10 / 3
B. 20 / 3
C. 15 / 7
D. 11 / 17
E. 1 / 4

divide(const_1, add(divide(const_1, 10), divide(const_1, 20)))

Explanation: "part filled by a in 1 hour = 1 / 10 part filled by b in 1 hour = 1 / 20 part filled by ( a + b ) in 1 hour = 1 / 10 + 1 / 20 = 3 / 20 both the pipes together fill the tank in 20 / 3 hours answer is b"


Question: the number obtained by interchanging the digits of a two - digit number is less than the original number by 36 . the sum of the digits of the number is 8 . what is the original number ?

<gadget id="calculator">10 + 8</gadget>
<output>18</output>

<gadget id="calculator">36 / 18</gadget>
<output>2</output>

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

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

<gadget id="calculator">60 + 2</gadget>
<output>62</output>
<result>62</result>

Choices:
A. 71
B. 62
C. 53
D. 35
E. 45

add(multiply(subtract(8, divide(36, add(const_10, 8))), const_10), divide(36, add(const_10, 8)))

Explanation: explanation : let the number be 10 x + y . ∴ x + y = 8 . . . . . ( i ) 10 x + y - ( 10 y + x ) = 36 ∴ 9 ( x - y ) = 3 ∴ x - y = 4 . . . . . . . ( ii ) from equation ( i ) and ( ii ) : x = 6 , y = 2 ∴ number = 62 answer : option b


Question: in one alloy there is 10 % chromium while in another alloy it is 6 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .

<gadget id="calculator">10 * 15</gadget>
<output>150</output>

<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">6 * 35</gadget>
<output>210</output>

<gadget id="calculator">210 / 100</gadget>
<output>21/10 = around 2.1</output>

<gadget id="calculator">(3/2) + (21/10)</gadget>
<output>18/5 = around 3.6</output>

<gadget id="calculator">15 + 35</gadget>
<output>50</output>

<gadget id="calculator">(18/5) / 50</gadget>
<output>9/125 = around 0.072</output>

<gadget id="calculator">(9/125) * 100</gadget>
<output>36/5 = around 7.2</output>
<result>36/5 = around 7.2</result>

Choices:
A. 7.2 %
B. 9 %
C. 9.2 %
D. 8.6 %
E. 8.4 %

multiply(divide(add(divide(multiply(10, 15), const_100), divide(multiply(6, 35), const_100)), add(15, 35)), const_100)

Explanation: "the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.10 * 15 + 0.06 * 35 = 3.6 kg , so the percentage is 3.6 / 50 * 100 = 7.2 % . answer : a ."


Question: the food in a camp lasts for 10 men for 20 days . if 30 more men join , how many days will the food last ?

<gadget id="calculator">10 * 20</gadget>
<output>200</output>

<gadget id="calculator">10 + 30</gadget>
<output>40</output>

<gadget id="calculator">200 / 40</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 8 days
B. 4 days
C. 5 days
D. 10 days
E. 17 days

Explanation: "one man can consume the same food in 10 * 20 = 200 days . 30 more men join , the total number of men = 40 the number of days the food will last = 200 / 40 = 5 days . answer : c"


Question: surface area of a sphere is 2464 cm 2 . if its radius is doubled , then the surface area of the new sphere will be

<gadget id="calculator">4 * pi</gadget>
<output>4*pi = around 12.566371</output>

<gadget id="calculator">2_464 / (4*pi)</gadget>
<output>616/pi = around 196.07889</output>

<gadget id="calculator">(616/pi) ** (1/2)</gadget>
<output>2*sqrt(154)/sqrt(pi) = around 14.002817</output>

<gadget id="calculator">(2*sqrt(154)/sqrt(pi)) * 2</gadget>
<output>4*sqrt(154)/sqrt(pi) = around 28.005634</output>

<gadget id="calculator">4 * pi * ((4*sqrt(154)/sqrt(pi)) ** 2)</gadget>
<output>9_856</output>
<result>9_856</result>

Choices:
A. 4920 cm 2
B. 4727 cm 2
C. 9856 cm 2
D. 19712 cm 2
E. none

surface_sphere(multiply(sqrt(divide(2464, multiply(const_4, const_pi))), const_2))

Explanation: sol . let the original radius be r . then , original surface area = 4 π r 2 = 2464 cm 2 ( given ) . new radius = 2 r . ∴ new surface area = 4 π ( 2 r ) 2 = 4 x 4 π r 2 = ( 4 x 2464 ) cm 2 = 9856 cm 2 answer c


Question: how long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 80 m in length ?

<gadget id="calculator">100 + 80</gadget>
<output>180</output>

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

<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">180 / (50/3)</gadget>
<output>54/5 = around 10.8</output>
<result>54/5 = around 10.8</result>

Choices:
A. 15.8 sec
B. 14.9 sec
C. 12.4 sec
D. 10.8 sec
E. 11.8 sec

Explanation: "d 16.8 sec d = 100 + 80 = 180 m s = 60 * 5 / 18 = 50 / 3 t = 180 * 3 / 50 = 10.8 sec"


Question: - 74 x 29 + 265 = ?

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

<gadget id="calculator">74 * 29</gadget>
<output>2_146</output>

<gadget id="calculator">2_146 - 265</gadget>
<output>1_881</output>

<gadget id="calculator">(-1) * 1_881</gadget>
<output>-1_881</output>
<result>-1_881</result>

Choices:
A. 2436
B. - 1881
C. - 2801
D. - 2071
E. none of them

multiply(subtract(const_1, const_2), subtract(multiply(74, 29), 265))

Explanation: "given exp . = - 74 x ( 30 - 1 ) + 265 = - ( 74 x 30 ) + 74 + 265 = - 2220 + 339 = - 1881 answer is b"


Question: the population of 6 villages is 803 , 9001100 , 1023945 and 980 . what is the population of the seventh village if the average population of the 7 villages is 1000 ?

<gadget id="calculator">1_000 * 7</gadget>
<output>7_000</output>

<gadget id="calculator">10 + 10</gadget>
<output>20</output>

<gadget id="calculator">980 * 6</gadget>
<output>5_880</output>

<gadget id="calculator">7 * 7</gadget>
<output>49</output>

<gadget id="calculator">5_880 - 49</gadget>
<output>5_831</output>

<gadget id="calculator">5_831 - 100</gadget>
<output>5_731</output>

<gadget id="calculator">20 + 5_731</gadget>
<output>5_751</output>

<gadget id="calculator">7_000 - 5_751</gadget>
<output>1_249</output>
<result>1_249</result>

Choices:
A. 1134
B. 1238
C. 1348
D. 1500
E. 1249

subtract(multiply(1000, 7), add(add(const_10, const_10), subtract(subtract(multiply(980, 6), multiply(7, 7)), const_100)))

Explanation: population of seventh village = 7 * 1000 - ( 803 + 900 + 1100 + 1023 + 945 + 980 ) = 1249 answer is e


Question: if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 14 , what is the value of x ?

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

Choices:
A. - 4
B. - 1 / 4
C. 0
D. 1 / 4
E. 4

Explanation: "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . d"


Question: the radius of the wheel of a bus is 70 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is

<gadget id="calculator">1_000 * 66</gadget>
<output>66_000</output>

<gadget id="calculator">100 * 66_000</gadget>
<output>6_600_000</output>

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

<gadget id="calculator">6_600_000 / 60</gadget>
<output>110_000</output>

<gadget id="calculator">2 * 70</gadget>
<output>140</output>

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

<gadget id="calculator">2 + 12</gadget>
<output>14</output>

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

<gadget id="calculator">2 + 8</gadget>
<output>10</output>

<gadget id="calculator">10 ** 2</gadget>
<output>100</output>

<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>

<gadget id="calculator">3 + (7/50)</gadget>
<output>157/50 = around 3.14</output>

<gadget id="calculator">140 * (157/50)</gadget>
<output>2_198/5 = around 439.6</output>

<gadget id="calculator">110_000 / (2_198/5)</gadget>
<output>275_000/1_099 = around 250.22748</output>
<result>275_000/1_099 = around 250.22748</result>

Choices:
A. 200
B. 250
C. 300
D. 330
E. none of these

divide(divide(multiply(const_100, multiply(const_1000, 66)), multiply(const_60, const_1)), multiply(multiply(const_2, 70), add(const_3, divide(add(const_2, multiply(const_3, const_4)), power(add(const_2, multiply(const_4, const_2)), const_2)))))

Explanation: "radius of the wheel of bus = 70 cm . then , circumference of wheel = 2 π r = 140 π = 440 cm distance covered by bus in 1 minute = 66 ⁄ 60 × 1000 × 100 cms distance covered by one revolution of wheel = circumference of wheel = 440 cm ∴ revolutions per minute = 6600000 / 60 × 440 = 250 answer b"


Question: harry started a 4 - mile hike with a full 6 - cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 1 cups of water during the last mile , how many cups did he drink per mile during the first 3 miles of the hike ?

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

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

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

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

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

divide(subtract(subtract(subtract(6, 2), 1), 1), 3)

Explanation: no of cups leaked during the trip = 2 cups . no of cups harry drank = 3 cups . no of cups harry drank during the first 3 miles = 2 . drink / mile = 2 / 3 answer : b


Question: two taps a and b can fill a cistern in 12 minutes and 18 minutes respectively . they are turned on at the same time . if the tap a is turned off after 4 minutes , how long will tap b take to fill the rest of the cistern ?

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

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

<gadget id="calculator">(1/12) + (1/18)</gadget>
<output>5/36 = around 0.138889</output>

<gadget id="calculator">(5/36) * 4</gadget>
<output>5/9 = around 0.555556</output>

<gadget id="calculator">1 - (5/9)</gadget>
<output>4/9 = around 0.444444</output>

<gadget id="calculator">(4/9) / (1/18)</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 8 min .
B. 9 min .
C. 10 min .
D. 7 min .
E. none of these

divide(subtract(const_1, multiply(add(divide(const_1, 12), divide(const_1, 18)), 4)), divide(const_1, 18))

Explanation: in one min , ( a + b ) fill the cistern = 1 ⁄ 12 + 1 ⁄ 18 = 5 ⁄ 36 th in 4 min , ( a + b ) fill the cistern = 5 ⁄ 36 × 4 = 5 ⁄ 9 th rest part = 1 - 5 ⁄ 9 = 4 ⁄ 9 th ∵ 1 ⁄ 18 th part is filled by b in one min . ∴ 4 ⁄ 9 th part is filled by b in 18 × 4 ⁄ 9 = 8 min answer a


Question: jack and christina are standing 240 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 3 feet per second and christina walks in a straight line toward jack at a constant speed of 3 feet per second . lindy runs at a constant speed of 10 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?

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

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

<gadget id="calculator">40 * 10</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 340
B. 360
C. 380
D. 400
E. 420

Explanation: "the relative speed of jack and christina is 3 + 3 = 6 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 240 / 6 = 40 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 10 * 40 = 400 feet . answer : d ."


Question: a solution of 70 litres contains oil and water in the ratio 9 : x . if 6 litres of water is added to the solution , the ratio becomes 6 : 4 , find the value of x ?

<gadget id="calculator">70 + 6</gadget>
<output>76</output>

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

<gadget id="calculator">76 / 10</gadget>
<output>38/5 = around 7.6</output>

<gadget id="calculator">4 * (38/5)</gadget>
<output>152/5 = around 30.4</output>

<gadget id="calculator">(152/5) - 6</gadget>
<output>122/5 = around 24.4</output>

<gadget id="calculator">70 - (122/5)</gadget>
<output>228/5 = around 45.6</output>

<gadget id="calculator">(228/5) / (122/5)</gadget>
<output>114/61 = around 1.868852</output>

<gadget id="calculator">9 / (114/61)</gadget>
<output>183/38 = around 4.815789</output>
<result>183/38 = around 4.815789</result>

Choices:
A. 6
B. 8.5
C. 9
D. 6.5
E. 5

divide(9, divide(subtract(70, subtract(multiply(4, divide(add(70, 6), add(6, 4))), 6)), subtract(multiply(4, divide(add(70, 6), add(6, 4))), 6)))

Explanation: exp . total new quantity = original sol + water = 70 + 6 = 76 new ratio = 6 : 4 , new quantity of oil = 6 / 10 * 76 = 45.6 lit , new quantity of water = 4 / 10 * 76 = 30.4 lit water present initially = ( 30.4 - 6 ) = 24.4 lit ratio = 45.6 / 24.4 = 9 / x there for x = 4.81 approx 5 answer : e


Question: if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number d of integers that can be negative ?

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

<gadget id="calculator">5 + 0</gadget>
<output>5</output>
<result>5</result>

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

Explanation: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see d = 5 or 1 will give you same equation . . ans d"


Question: the length of the rectangular field is double its width . inside the field there is square shaped pond 6 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?

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

<gadget id="calculator">36 * 8</gadget>
<output>288</output>

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

<gadget id="calculator">288 / (1/2)</gadget>
<output>576</output>

<gadget id="calculator">576 ** (1/2)</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 24
B. 32
C. 75
D. 28
E. 11

Explanation: "a / 8 = 6 * 6 = > a = 6 * 6 * 8 x * 2 x = 6 * 6 * 8 x = 12 = > 2 x = 24 answer : a"


Question: the area of a triangle is with base 2 m and height 3 m ?

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

Choices:
A. 11
B. 10
C. 787
D. 3
E. 12

Explanation: "1 / 2 * 2 * 3 = 3 m 2 answer : d"


Question: if the price of a certain computer increased 30 percent from c dollars to 351 dollars , then 2 c =

<gadget id="calculator">100 + 30</gadget>
<output>130</output>

<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>

<gadget id="calculator">351 / (13/10)</gadget>
<output>270</output>

<gadget id="calculator">270 * 2</gadget>
<output>540</output>
<result>540</result>

Choices:
A. 540
B. 570
C. 619
D. 649
E. 700

multiply(divide(351, divide(add(const_100, 30), const_100)), 2)

Explanation: "before price increase price = c after 30 % price increase price = c + ( 30 / 100 ) * c = 1.3 c = 351 ( given ) i . e . c = 351 / 1.3 = $ 270 i . e . 2 c = 2 * 270 = 540 answer : option a"


Question: the purchase price of an article is $ 48 . in order to include 5 % of cost for overhead and to provide $ 12 of net profit , the markup should be

<gadget id="calculator">12 / 48</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>

<gadget id="calculator">25 + 5</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 15 %
B. 25 %
C. 30 %
D. 40 %
E. 45 %

add(multiply(divide(12, 48), const_100), 5)

Explanation: "cost price of article = 48 $ % of overhead cost = 5 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 5 = 30 % answer c"


Question: a store reduced the price of all items in the store by 12 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?

<gadget id="calculator">100 - 12</gadget>
<output>88</output>

<gadget id="calculator">88 / 100</gadget>
<output>22/25 = around 0.88</output>

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

<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">(22/25) * (9/10)</gadget>
<output>99/125 = around 0.792</output>

<gadget id="calculator">(99/125) * 100</gadget>
<output>396/5 = around 79.2</output>
<result>396/5 = around 79.2</result>

Choices:
A. 80.0
B. 79.2
C. 81.0
D. 81.1
E. 81.9

multiply(multiply(divide(subtract(const_100, 12), const_100), divide(subtract(const_100, 10), const_100)), const_100)

Explanation: "consider price of the all items as $ 100 after a initial reduction of 12 % price becomes = 0.88 * 100 = $ 88 after the final reduction of 10 % price becomes = 0.9 * 88 = $ 79.2 price of all items on second day is 79.2 % of price on first day correct answer option b"


Question: darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?

<gadget id="calculator">60 / 2</gadget>
<output>30</output>

<gadget id="calculator">30 - 10</gadget>
<output>20</output>

<gadget id="calculator">20 / 1.5</gadget>
<output>13.333333</output>

<gadget id="calculator">60 / 13.333333</gadget>
<output>4.5</output>

<gadget id="calculator">20 - 4.5</gadget>
<output>15.5</output>
<result>15.5</result>

Choices:
A. 10.5
B. 15
C. 15.5
D. 30
E. 60

subtract(subtract(divide(const_60, const_2), 10), divide(const_60, divide(20, 1.5)))

Explanation: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 10 x = 15.5 minutes answer : c"


Question: when the smallest of 3 consecutive odd integers is added to 4 times the largest , it produces a result 732 more than 4 times the middle integer . find the numbers ?

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

<gadget id="calculator">732 + 8</gadget>
<output>740</output>

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

<gadget id="calculator">740 - 16</gadget>
<output>724</output>

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

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

<gadget id="calculator">724 / 1</gadget>
<output>724</output>
<result>724</result>

Choices:
A. 732
B. 678
C. 698
D. 710
E. 729

divide(subtract(add(732, multiply(4, const_2)), multiply(4, const_4)), subtract(add(const_1, 4), 4))

Explanation: x + 4 ( x + 4 ) = 732 + 4 ( x + 2 ) solve for x and find all three numbers x + 4 x + 16 = 732 + 4 x + 8 x = 724 x + 2 = 726 x + 4 = 728 check : the smallest is added to four times the largest 724 + 4 * 728 = 3636 four times the middle 4 * 726 = 2904 3636 is more than 2904 by 3636 - 2904 = 732 a


Question: in a particular city there are 100 homes numbered from 1 , 23 , . . , 100 . the city was build by a builder from chennai . there was 4 to 5 shops in the town which was build by a builder from mumbai . the 2 nd builder can build in 1 ½ times as compared to time by 1 st builder . the 2 nd builder builds in 15 days , then how many 2 ' s are used by the builder from chennai in numbering the 100 homes ?

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

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

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

Explanation: in the last line it should be given the builder from chennai in numbering the 100 homes ? then ans is 20 answer : d


Question: p and q can complete a work in 40 days and 24 days respectively . p alone started the work and q joined him after 8 days till the completion of the work . how long did the work last ?

<gadget id="calculator">8 / 40</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">1 / 40</gadget>
<output>1/40 = around 0.025</output>

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

<gadget id="calculator">(1/40) + (1/24)</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(4/5) / (1/15)</gadget>
<output>12</output>

<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 5 days
B. 10 days
C. 14 days
D. 20 days
E. 26 days

add(8, divide(subtract(const_1, divide(8, 40)), add(inverse(40), inverse(24))))

Explanation: "explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 8 days = 8 ã — ( 1 / 40 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 1 / 15 ) = 12 total days = 8 + 12 = 20 answer : option d"


Question: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 2 of the remaining paint . how many gallons of paint has joe used ?

<gadget id="calculator">360 / 4</gadget>
<output>90</output>

<gadget id="calculator">90 * 1</gadget>
<output>90</output>

<gadget id="calculator">360 - 90</gadget>
<output>270</output>

<gadget id="calculator">270 / 2</gadget>
<output>135</output>

<gadget id="calculator">90 + 135</gadget>
<output>225</output>
<result>225</result>

Choices:
A. 18
B. 225
C. 175
D. 216
E. 250

add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 2))

Explanation: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 2 ) * 270 = 135 gallons total paint used = 225 gallons . option b"


Question: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 5 per unit . further , the manufacturer has costs of $ 16500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?

<gadget id="calculator">80 + 5</gadget>
<output>85</output>

<gadget id="calculator">85 * 150</gadget>
<output>12_750</output>

<gadget id="calculator">12_750 + 16_500</gadget>
<output>29_250</output>

<gadget id="calculator">29_250 / 150</gadget>
<output>195</output>
<result>195</result>

Choices:
A. $ 28
B. $ 82
C. $ 110
D. $ 138
E. $ 195

Explanation: by the question , the equation would be 150 p - 85 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 195 . answer e for me .


Question: the average runs scored by a batsman in 30 matches is 50 . in the next 15 matches the batsman scored an average of 26 runs . find his average in all the 45 matches ?

<gadget id="calculator">50 * 30</gadget>
<output>1_500</output>

<gadget id="calculator">26 * 15</gadget>
<output>390</output>

<gadget id="calculator">1_500 + 390</gadget>
<output>1_890</output>

<gadget id="calculator">30 + 15</gadget>
<output>45</output>

<gadget id="calculator">1_890 / 45</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 31
B. 42
C. 29
D. 97
E. 27

divide(add(multiply(50, 30), multiply(26, 15)), add(30, 15))

Explanation: total score of the batsman in 30 matches = 1500 . total score of the batsman in the next 15 matches = 390 . total score of the batsman in the 30 matches = 1890 . average score of the batsman = 1890 / 45 = 42 . answer : b


Question: the owner of a furniture shop charges his customer 60 % more than the cost price . if a customer paid rs . 2000 for a computer table , then what was the cost price of the computer table ?

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">2_000 / (8/5)</gadget>
<output>1_250</output>
<result>1_250</result>

Choices:
A. 2789
B. 2772
C. 1250
D. 6725
E. 2099

divide(2000, add(const_1, divide(60, const_100)))

Explanation: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1250 ( 100 / 160 ) = rs . 1250 . answer : c"


Question: a shipment of 240 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?

<gadget id="calculator">84 - 1</gadget>
<output>83</output>

<gadget id="calculator">84 * 83</gadget>
<output>6_972</output>

<gadget id="calculator">240 - 1</gadget>
<output>239</output>

<gadget id="calculator">240 * 239</gadget>
<output>57_360</output>

<gadget id="calculator">6_972 / 57_360</gadget>
<output>581/4_780 = around 0.121548</output>
<result>581/4_780 = around 0.121548</result>

Choices:
A. 1 / 250
B. 9 / 74
C. 1 / 11
D. 1 / 9
E. 1 / 3

divide(multiply(84, subtract(84, const_1)), multiply(240, subtract(240, const_1)))

Explanation: "probability of chosing one defective phone from a lot of 240 which ontains 84 defective phones is = ( 84 / 240 ) probability of chosing one defective phone from a lot of 239 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 239 ) combined probability of series of events = product of the probabilities = ( 84 / 240 ) * ( 83 / 239 ) 84 / 240 is close to ( 7 / 20 ) and ( 83 / 239 ) = ( 25 / 72 ) so answer is ( 7 / 20 ) * ( 25 / 72 ) ( 9 / 74 ) so , answer will be b"


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 8 ?

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

Choices:
A. 1
B. 2
C. 4
D. 8
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: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 600 per sq . metre .

<gadget id="calculator">5.5 * 3.75</gadget>
<output>20.625</output>

<gadget id="calculator">600 * 20.625</gadget>
<output>12_375</output>
<result>12_375</result>

Choices:
A. $ 12375
B. $ 13575
C. $ 16575
D. $ 14575
E. $ 18575

Explanation: "a area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 600 hence , total cost = 5.5 × 3.75 × 600 = $ 12375 a"


Question: what is the sum of the multiples of 4 between 63 and 151 inclusive ?

<gadget id="calculator">151 - 3</gadget>
<output>148</output>

<gadget id="calculator">63 + 2</gadget>
<output>65</output>

<gadget id="calculator">148 + 65</gadget>
<output>213</output>

<gadget id="calculator">213 / 2</gadget>
<output>213/2 = around 106.5</output>

<gadget id="calculator">148 - 65</gadget>
<output>83</output>

<gadget id="calculator">83 / 4</gadget>
<output>83/4 = around 20.75</output>

<gadget id="calculator">(83/4) + 1</gadget>
<output>87/4 = around 21.75</output>

<gadget id="calculator">(213/2) * (87/4)</gadget>
<output>18_531/8 = around 2_316.375</output>
<result>18_531/8 = around 2_316.375</result>

Choices:
A. 2240
B. 2250
C. 2310
D. 2330
E. 2332

multiply(divide(add(subtract(151, const_3), add(63, const_2)), const_2), add(divide(subtract(subtract(151, const_3), add(63, const_2)), 4), const_1))

Explanation: "the fastest way in an ap is to find the average and multiply with total integers . . between 63 and 151 , the smallest multiple of 4 is 64 and largest = 148 . . average = ( 64 + 148 ) / 2 = 106 . . total numbers = ( 148 - 64 ) / 4 + 1 = 21 + 1 = 22 . . sum = 22 * 106 = 2332 ans e"


Question: if the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3 , what is the ratio of apples to cucumbers ?

<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">(4/3) / 3</gadget>
<output>4/9 = around 0.444444</output>
<result>4/9 = around 0.444444</result>

Choices:
A. 4 : 9
B. 4 : 3
C. 3 : 7
D. 2 : 5
E. 1 : 6

Explanation: "the ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9 . the ratio of apples to bananas to cucumbers is 4 to 3 to 9 . the answer is a ."


Question: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 46.24 , the number of the member is the group is :

<gadget id="calculator">46.24 * 100</gadget>
<output>4_624</output>

<gadget id="calculator">4_624 ** (1/2)</gadget>
<output>68</output>
<result>68</result>

Choices:
A. 57
B. 68
C. 77
D. 87
E. 97

Explanation: "explanation : money collected = ( 46.24 x 100 ) paise = 4624 paise . ∴ number of members = √ ( 4624 ) = 68 . answer : b"


Question: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 15 from the product of their ages a year from today . what is their age today ?

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

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

Choices:
A. 2 .
B. 4 .
C. 5 .
D. 7 .
E. 9 .

Explanation: "ad = ( a + 1 ) ( d + 1 ) - 15 0 = a + d - 14 a + d = 14 a = d ( as they are twin brothers ) a = d = 7 d is the answer"


Question: for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 99 true ?

<gadget id="calculator">log(99)</gadget>
<output>log(99) = around 4.59512</output>

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

<gadget id="calculator">log(5)</gadget>
<output>log(5) = around 1.609438</output>

<gadget id="calculator">log(99) / log(5)</gadget>
<output>log(99)/log(5) = around 2.855108</output>
<result>log(99)/log(5) = around 2.855108</result>

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

Explanation: "answer c ( a + b ) ( a - b ) = 99 3 cases for ( a + b ) , ( a - b ) 99 , 1 33 , 3 11 , 9 answer b"


Question: when x is multiplied by 2 , the result is 19 more than the result of subtracting x from 26 . what is the value of x ?

<gadget id="calculator">26 + 19</gadget>
<output>45</output>

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

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

Choices:
A. - 4
B. - 2
C. 15
D. 13
E. 22

Explanation: "the equation that can be formed is : 2 x - 19 = 26 - x or , 3 x = 45 or , x = 15 . c answer ."


Question: a can give b 60 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 - 200</gadget>
<output>800</output>

<gadget id="calculator">1_000 * 800</gadget>
<output>800_000</output>

<gadget id="calculator">1_000 - 60</gadget>
<output>940</output>

<gadget id="calculator">800_000 / 940</gadget>
<output>40_000/47 = around 851.06383</output>

<gadget id="calculator">1_000 - (40_000/47)</gadget>
<output>7_000/47 = around 148.93617</output>
<result>7_000/47 = around 148.93617</result>

Choices:
A. 148.94
B. 148.13
C. 148.22
D. 111.0
E. 111.12

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 200)), subtract(multiply(const_100, const_10), 60)))

Explanation: "a runs 1000 m while b runs 940 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 940 = 851.06 m . b can give c = 1000 - 851.06 = 148.94 m . answer : a"


Question: the average of marks obtained by 120 boys was 38 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?

<gadget id="calculator">38 * 120</gadget>
<output>4_560</output>

<gadget id="calculator">120 * 15</gadget>
<output>1_800</output>

<gadget id="calculator">4_560 - 1_800</gadget>
<output>2_760</output>

<gadget id="calculator">39 - 15</gadget>
<output>24</output>

<gadget id="calculator">2_760 / 24</gadget>
<output>115</output>
<result>115</result>

Choices:
A. 100
B. 110
C. 115
D. 125
E. 140

divide(subtract(multiply(38, 120), multiply(120, 15)), subtract(39, 15))

Explanation: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 38 24 x = 4560 - 1800 = > x = 2760 / 24 x = 115 . hence , the number of boys passed = 115 . answer : c"


Question: if x , y , and z are positive integers , and 2 x = 5 y = 8 z , then the least possible value of x + y + z is

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

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

<gadget id="calculator">80 / 2</gadget>
<output>40</output>

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

<gadget id="calculator">40 / 5</gadget>
<output>8</output>

<gadget id="calculator">20 + 8</gadget>
<output>28</output>

<gadget id="calculator">40 / 8</gadget>
<output>5</output>

<gadget id="calculator">28 + 5</gadget>
<output>33</output>
<result>33</result>

Choices:
A. 15
B. 28
C. 33
D. 42
E. 60

add(add(divide(divide(multiply(multiply(2, 5), 8), const_2), 2), divide(divide(multiply(multiply(2, 5), 8), const_2), 5)), divide(divide(multiply(multiply(2, 5), 8), const_2), 8))

Explanation: "take lcm of 2,5 and 8 = 40 now 2 x = 40 = > x = 20 5 y = 40 = > y = 8 8 z = 40 = > z = 5 20 + 8 + 5 = 33 . option c ."