Question: 9 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?

<gadget id="calculator">9 * 8</gadget>
<output>72</output>

<gadget id="calculator">72 / 30</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">(12/5) * 50</gadget>
<output>120</output>

<gadget id="calculator">120 / 6</gadget>
<output>20</output>

<gadget id="calculator">20 - 9</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 33
B. 66
C. 88
D. 11
E. 281

subtract(divide(multiply(divide(multiply(9, 8), 30), 50), 6), 9)

Explanation: "( 9 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 20 20 – 9 = 11 answer : d"


Question: a building contractor employs 20 male , 15 female and 5 child workers . to a male worker he pays rs . 25 per day , to a female worker rs . 20 per day and a child worker rs . 8 per day . the average wage per day paid by the contractor is ?

<gadget id="calculator">20 * 25</gadget>
<output>500</output>

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

<gadget id="calculator">500 + 300</gadget>
<output>800</output>

<gadget id="calculator">5 * 8</gadget>
<output>40</output>

<gadget id="calculator">800 + 40</gadget>
<output>840</output>

<gadget id="calculator">20 + 15</gadget>
<output>35</output>

<gadget id="calculator">35 + 5</gadget>
<output>40</output>

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

Choices:
A. 19
B. 21
C. 23
D. 25
E. 27

divide(add(add(multiply(20, 25), multiply(15, 20)), multiply(5, 8)), add(add(20, 15), 5))

Explanation: explanation : 20 15 5 25 20 8 500 + 300 + 40 = 840 / 40 = 21 b


Question: find ( 7 x + 2 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?

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

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

<gadget id="calculator">3 * 7</gadget>
<output>21</output>

<gadget id="calculator">21 + 2</gadget>
<output>23</output>

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

<gadget id="calculator">23 / 1</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 23
B. 25
C. 26
D. 27
E. 29

divide(add(multiply(multiply(divide(3, 2), 2), 7), 2), subtract(multiply(divide(3, 2), 2), 2))

Explanation: "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 2 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 2 y ) / ( 3 y - 2 y ) = > 23 y / y = 23 answer : a"


Question: john left home and drove at the rate of 45 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 45 mph to reach his destination . how many miles did john drive ?

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

<gadget id="calculator">3 * 45</gadget>
<output>135</output>

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

Choices:
A. 235 miles .
B. 245 miles .
C. 225 miles .
D. 265 miles .
E. 275 miles .

Explanation: "the total distance d traveled by john is given by d = 45 * 2 + 3 * 45 = 225 miles . answer c"


Question: a statue is being carved by a sculptor . the original piece of marble weighed 190 kg . in the first week 25 percent is cut away . in the second week 15 percent of the remainder is cut away . in the third week the statue is completed when 10 percent of the remainder is cut away . what is the weight of the final statue ?

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

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

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

<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

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

<gadget id="calculator">190 * (3/4)</gadget>
<output>285/2 = around 142.5</output>

<gadget id="calculator">(17/20) * (285/2)</gadget>
<output>969/8 = around 121.125</output>

<gadget id="calculator">(9/10) * (969/8)</gadget>
<output>8_721/80 = around 109.0125</output>
<result>8_721/80 = around 109.0125</result>

Choices:
A. 105 kg
B. 103 kg
C. 109 kg
D. 125 kg
E. 117 kg

multiply(subtract(const_1, divide(10, const_100)), multiply(subtract(const_1, divide(15, const_100)), multiply(190, subtract(const_1, divide(25, const_100)))))

Explanation: "c 109 kg 190 ã — 0.75 ã — 0.85 ã — 0.9 = 109 kg ."


Question: the population of a town increased from 1 , 75,000 to 2 , 97,500 in a decade . the average percent increase of population per year is

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

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

<gadget id="calculator">100_000 - 1_000</gadget>
<output>99_000</output>

<gadget id="calculator">99_000 - 1_000</gadget>
<output>98_000</output>

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

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

<gadget id="calculator">98_000 - 500</gadget>
<output>97_500</output>

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

<gadget id="calculator">7 * 10</gadget>
<output>70</output>

<gadget id="calculator">70 + 5</gadget>
<output>75</output>

<gadget id="calculator">75 * 1_000</gadget>
<output>75_000</output>

<gadget id="calculator">97_500 / 75_000</gadget>
<output>13/10 = around 1.3</output>

<gadget id="calculator">(13/10) - 1</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) / 10</gadget>
<output>3/100 = around 0.03</output>

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

Choices:
A. 4.37 %
B. 5 %
C. 6 %
D. 8.75 %
E. 7 %

add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(const_2, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(const_2, const_3)), const_1000)), const_1), const_10), const_100), const_4)

Explanation: solution increase in 10 years = ( 297500 - 175000 ) = 122500 increase % = ( 122500 / 175000 ã — 100 ) % = 70 % . required average = ( 70 / 10 ) % = 7 % . answer e


Question: in an exam , gibi scored 59 percent , jigi scored 55 percent , mike scored 99 percent and lizzy 67 percent . the maximum score awarded in the exam is 700 . find the average mark scored by all the 4 students ?

<gadget id="calculator">59 + 55</gadget>
<output>114</output>

<gadget id="calculator">99 + 67</gadget>
<output>166</output>

<gadget id="calculator">114 + 166</gadget>
<output>280</output>

<gadget id="calculator">280 * 700</gadget>
<output>196_000</output>

<gadget id="calculator">196_000 / 100</gadget>
<output>1_960</output>

<gadget id="calculator">1_960 / 4</gadget>
<output>490</output>
<result>490</result>

Choices:
A. 471
B. 490
C. 480
D. 453
E. 456

divide(divide(multiply(add(add(59, 55), add(99, 67)), 700), const_100), 4)

Explanation: average mark scored by all the three boys = [ 59 / 100 ( 700 ) + 55 / 100 ( 700 ) + 99 / 100 ( 700 ) + 67 / 100 ( 700 ) ] / 4 ( 413 + 385 + 693 + 469 ) / 4 = 490 answer : b


Question: in how many no . between 10 and 50 exactly two of the digits is 5 ?

<gadget id="calculator">50 / 10</gadget>
<output>5</output>

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

Choices:
A. 47
B. 65
C. 1
D. 35
E. 65

Explanation: "it ' s simple can be solved by elimination of answer choices . option b and d are too large , not possible . even ae are large to have correct choice . ans : c"


Question: john and david work at a hospital with 8 other workers . for an internal review , 2 of the 8 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ?

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

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>

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

<gadget id="calculator">(1/7) * (1/8)</gadget>
<output>1/56 = around 0.017857</output>

<gadget id="calculator">2 * (1/56)</gadget>
<output>1/28 = around 0.035714</output>
<result>1/28 = around 0.035714</result>

Choices:
A. 1 / 30
B. 1 / 25
C. 1 / 20
D. 1 / 28
E. 1 / 30

multiply(2, multiply(divide(const_1, subtract(8, const_1)), divide(const_1, 8)))

Explanation: probability that john and david will both be chosen out of 8 workers = ( 2 / 8 ) * ( 1 / 7 ) = 1 / 28 answer d


Question: by selling 8 pens for a rupee a woman loses 25 % . how many for a rupee should he sell in order to gain 25 % ?

<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) / 8</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/6) * 25</gadget>
<output>25/6 = around 4.166667</output>

<gadget id="calculator">(25/6) / 100</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">(1/6) + (1/24)</gadget>
<output>5/24 = around 0.208333</output>

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

Choices:
A. 2
B. 14
C. 3
D. 5
E. 6

inverse(add(divide(divide(const_100, subtract(const_100, 25)), 8), divide(multiply(divide(divide(const_100, subtract(const_100, 25)), 8), 25), const_100)))

Explanation: "d 75 % - - - 8 125 % - - - ? 75 / 125 * 8 = 5"


Question: 3.20 can be expressed in terms of percentage as

<gadget id="calculator">3.2 * 100</gadget>
<output>320</output>
<result>320</result>

Choices:
A. 3.20 %
B. 30.2 %
C. 320.00 %
D. 0.320 %
E. none of these

Explanation: explanation : while calculation in terms of percentage we need to multiply by 100 , so 3.20 * 100 = 320 answer : option c


Question: a person was asked to subtract 25 % of a number from the original but he subtracted 25 from the number . his answer was 25 more than correct one . what was the original number ?

<gadget id="calculator">25 + 25</gadget>
<output>50</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

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

<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">50 / (1/4)</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 288
B. 266
C. 288
D. 200
E. 111

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

Explanation: 25 + 25 = 50 25 % - - - - - - 50 100 % - - - - - ? = > 200 answer : d


Question: if x : y is 1 : 5 and y : z is 5 : 7 then x : z is equal to

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<result>1/7 = around 0.142857</result>

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

Explanation: the two ratios given are having the same number 5 for y in both the ratios . hence - x : y = 1 : 5 y : z = 5 : 7 = > x : z = 1 : 7 answer d


Question: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 72 kilometers , maxwell ' s walking speed is 6 km / h , and brad ' s running speed is 12 km / h . what is the distance traveled by maxwell when they meet in the middle ?

<gadget id="calculator">6 + 12</gadget>
<output>18</output>

<gadget id="calculator">72 / 18</gadget>
<output>4</output>

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

Choices:
A. 14
B. 24
C. 16
D. 18
E. 20

Explanation: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 6 xt = 72 - 12 xt ( i . e distance = speed x time ) = > 18 t = 72 hence t = 4 oa = 6 x 4 = 24 km answer : b"


Question: carolyn bought 17 gumballs , lew bought 12 gumballs , and carey bought x gumballs . the average ( arithmetic mean ) number of gumballs the 3 bought is between 19 and 25 , inclusive . what is the difference between the greatest number and the smallest number of gumballs carey could have bought ?

<gadget id="calculator">25 * 3</gadget>
<output>75</output>

<gadget id="calculator">17 + 12</gadget>
<output>29</output>

<gadget id="calculator">75 - 29</gadget>
<output>46</output>

<gadget id="calculator">19 * 3</gadget>
<output>57</output>

<gadget id="calculator">57 - 29</gadget>
<output>28</output>

<gadget id="calculator">46 - 28</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 18
B. 20
C. 22
D. 24
E. 26

subtract(subtract(multiply(25, 3), add(17, 12)), subtract(multiply(19, 3), add(17, 12)))

Explanation: smallest gumballs = ( 19 - 17 ) + ( 19 - 12 ) + 19 = 28 largest gumballs = ( 25 - 17 ) + ( 25 - 12 ) + 25 = 46 difference = 46 - 28 = 18 a


Question: a train 250 m long passed a pole in 10 sec . how long will it take to pass a platform 1250 m long ?

<gadget id="calculator">250 + 1_250</gadget>
<output>1_500</output>

<gadget id="calculator">250 / 10</gadget>
<output>25</output>

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

Choices:
A. 60 sec
B. 90 sec
C. 120 sec
D. 150 sec
E. 180 sec

Explanation: speed = 250 / 10 = 25 m / sec . required time = ( 250 + 1250 ) / 25 = 60 sec answer : a


Question: one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 225 cm when it touches the floor on third time . what is the value of the original height ?

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

<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">225 / (5/2)</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 80 cm
B. 90 cm
C. 100 cm
D. 120 cm
E. 130 cm

divide(225, add(const_2, divide(50, const_100)))

Explanation: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 225 2.5 h = 225 h = 90 . b is the answer ."


Question: a man fell in a 30 meter deep well , in one day he climbs 4 meters up and slips 3 meters down . how many days would it take for him to come out of the well ?

<gadget id="calculator">30 - 3</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 22
B. 46
C. 17
D. 27
E. 33

Explanation: d i will take 27 days to come out of that well for that man , he climbs 4 meter every day and slips 3 meter down that means he climbs 1 meter in total each day , so like this on 26 th day he would have climbed 26 meter and on 27 th day he will climb 4 meeter again so total 30 meter he will climb in 27 days .


Question: if a mixture is 2 ⁄ 7 alcohol by volume and 3 ⁄ 7 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?

<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>

<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>

<gadget id="calculator">(2/7) / (3/7)</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>

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

Explanation: should be a sub - 600 level q . . volume = { 2 / 7 } / { 3 / 7 } = 2 / 3 c


Question: 20 percent of country y ' s yearly exports come from fruit exports . one - sixth of all fruit exports from country y are orange exports . if country y generates $ 4.25 million from its orange exports , how much money does it generate from its yearly total of exports ?

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

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

<gadget id="calculator">4.25 / (1/6)</gadget>
<output>25.5</output>

<gadget id="calculator">25.5 * 100</gadget>
<output>2_550</output>

<gadget id="calculator">2_550 / 20</gadget>
<output>255/2 = around 127.5</output>
<result>255/2 = around 127.5</result>

Choices:
A. $ 21.25 m
B. $ 25.5 m
C. $ 106.25 m
D. $ 127.5 m
E. $ 153 m

divide(multiply(divide(4.25, divide(const_1, multiply(const_2, const_3))), const_100), 20)

Explanation: 2 / 10 * 1 / 6 * ( total ) = 4.25 1 / 30 * ( total ) = 4.25 ( total ) = 4.25 * 30 = 127.5 answer : d .


Question: what is the value of n if the sum of the consecutive odd intergers w 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: indu gave bindu rs . 7500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?

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

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

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

<gadget id="calculator">7_500 * (676/625)</gadget>
<output>8_112</output>

<gadget id="calculator">8_112 - 7_500</gadget>
<output>612</output>

<gadget id="calculator">7_500 * (1/25)</gadget>
<output>300</output>

<gadget id="calculator">300 * 2</gadget>
<output>600</output>

<gadget id="calculator">612 - 600</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 5
B. 2
C. 9
D. 5
E. 12

subtract(subtract(multiply(7500, power(add(const_1, divide(4, const_100)), 2)), 7500), multiply(multiply(7500, divide(4, const_100)), 2))

Explanation: "7500 = d ( 100 / 4 ) 2 d = 12 answer : e"


Question: evaluate : 7899665 - 12 * 3 * 2 = ?

<gadget id="calculator">12 * 3</gadget>
<output>36</output>

<gadget id="calculator">36 * 2</gadget>
<output>72</output>

<gadget id="calculator">7_899_665 - 72</gadget>
<output>7_899_593</output>
<result>7_899_593</result>

Choices:
A. 2455835
B. 2789255
C. 6868575
D. 7899657
E. 1023666

subtract(7899665, multiply(multiply(12, 3), 2))

Explanation: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 7899665 - 12 * 3 * 2 = 7899665 - 8 = 7899657 correct answer d"


Question: a can do a half of certain work in 70 days and b one third of the same in 35 days . they together will do the whole work in ?

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

<gadget id="calculator">1 / 140</gadget>
<output>1/140 = around 0.007143</output>

<gadget id="calculator">35 * 3</gadget>
<output>105</output>

<gadget id="calculator">1 / 105</gadget>
<output>1/105 = around 0.009524</output>

<gadget id="calculator">(1/140) + (1/105)</gadget>
<output>1/60 = around 0.016667</output>
<result>1/60 = around 0.016667</result>

Choices:
A. 1 / 65
B. 1 / 62
C. 1 / 63
D. 1 / 60
E. 1 / 61

add(inverse(multiply(70, const_2)), inverse(multiply(35, const_3)))

Explanation: a = 140 days b = 105 days 1 / 140 + 1 / 105 = 7 / 420 = 1 / 60 = > 60 days answer : d


Question: if 9 / ( 1 + 4 / x ) = 1 , then x =

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

<gadget id="calculator">4 / 8</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

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

Explanation: "the expression 9 / ( 1 + 4 / x ) = 1 should have been equal to something . if 9 / ( 1 + 4 / x ) = 1 = 1 = > 9 x / ( x + 4 ) = 1 = > 9 x = x + 4 = > 8 x = 4 = > x = 1 / 2 correct option : b"


Question: an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 15 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?

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

<gadget id="calculator">25 * (4/5)</gadget>
<output>20</output>

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

<gadget id="calculator">60 * (3/20)</gadget>
<output>9</output>

<gadget id="calculator">60 - 9</gadget>
<output>51</output>

<gadget id="calculator">51 - 9</gadget>
<output>42</output>

<gadget id="calculator">42 - 10</gadget>
<output>32</output>

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

<gadget id="calculator">25 * 10</gadget>
<output>250</output>

<gadget id="calculator">640 + 250</gadget>
<output>890</output>

<gadget id="calculator">25 * 9</gadget>
<output>225</output>

<gadget id="calculator">225 + 225</gadget>
<output>450</output>

<gadget id="calculator">890 + 450</gadget>
<output>1_340</output>
<result>1_340</result>

Choices:
A. 1340
B. 1445
C. 1375
D. 1415
E. 1455

add(add(multiply(multiply(25, divide(4, 5)), subtract(subtract(subtract(60, multiply(60, divide(15, const_100))), multiply(60, divide(15, const_100))), 10)), multiply(25, 10)), add(multiply(25, multiply(60, divide(15, const_100))), multiply(25, multiply(60, divide(15, const_100)))))

Explanation: $ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 15 % of the gaskets to x = 9 gaskets = 25 * 9 = 225 2 . he sold 15 % of the gaskets to y = 9 gaskets = 25 * 9 = 225 3 . he sold remaining 70 % to z = 42 gaskets = 25 * 10 = 250 + 20 * 32 = 890 thus , total money earned 225 + 225 + 890 = 1340 answer is a


Question: suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3982 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?

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

<gadget id="calculator">12 - 3</gadget>
<output>9</output>

<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">12_000 * (3/4)</gadget>
<output>9_000</output>

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

<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">9_000 * (2/3)</gadget>
<output>6_000</output>

<gadget id="calculator">9_000 - 6_000</gadget>
<output>3_000</output>

<gadget id="calculator">18_000 + 9_000</gadget>
<output>27_000</output>

<gadget id="calculator">27_000 + 6_000</gadget>
<output>33_000</output>

<gadget id="calculator">3_982 / 33_000</gadget>
<output>181/1_500 = around 0.120667</output>

<gadget id="calculator">3_000 * (181/1_500)</gadget>
<output>362</output>
<result>362</result>

Choices:
A. rs . 362
B. rs . 383
C. rs . 398
D. rs . 399
E. rs . 400

multiply(subtract(multiply(12000, divide(subtract(multiply(3, 4), 3), multiply(3, 4))), multiply(9000, divide(subtract(multiply(3, 4), 4), multiply(3, 4)))), divide(3982, add(add(18000, multiply(12000, divide(subtract(multiply(3, 4), 3), multiply(3, 4)))), multiply(9000, divide(subtract(multiply(3, 4), 4), multiply(3, 4))))))

Explanation: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3982 × 1 / 11 = rs . 362 . a )"


Question: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 360 kilograms of pears that day , how many kilograms did he sell in the morning and how many in the afternoon ?

<gadget id="calculator">360 / 3</gadget>
<output>120</output>

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

Choices:
A. 120
B. 180
C. 240
D. 280
E. 320

Explanation: "let x be the number of kilograms he sold in the morning . then in the afternoon he sold 2 x kilograms . so , the total is x + 2 x = 3 x . this must be equal to 360 . 3 x = 360 x = 3603 x = 120 therefore , the salesman sold 120 kg in the morning and 2 ⋅ 120 = 240 kg in the afternoon . so answer is c ."


Question: the average of the marks of 25 students in a class is 70 . if the marks of each student are doubled , find the new average ?

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

Choices:
A. 140
B. 100
C. 85
D. 160
E. 190

Explanation: "sum of the marks for the 25 students = 25 * 70 = 1750 . the marks of each student are doubled , the sum also will be doubled . the new sum = 1750 * 2 = 3500 . so , the new average = 3500 / 25 = 140 . answer : a"


Question: a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed w of the train .

<gadget id="calculator">24 * 4</gadget>
<output>96</output>

<gadget id="calculator">96 / 3</gadget>
<output>32</output>

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

<gadget id="calculator">35 - 25</gadget>
<output>10</output>

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

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

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

Choices:
A. 45
B. 33
C. 48
D. 55
E. 61

multiply(subtract(divide(multiply(24, 4), 3), 24), divide(add(subtract(35, 25), 50), subtract(35, 25)))

Explanation: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = w ans = c"


Question: amit and ananthu can do a work in 10 days and 20 days respectively . amit started the work and left after 2 days . ananthu took over and completed the work . in how many days was the total work completed ?

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

<gadget id="calculator">(1/10) * 2</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 / 20</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(4/5) / (1/20)</gadget>
<output>16</output>

<gadget id="calculator">16 + 2</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 18 days
B. 20 days
C. 23 days
D. 25 days
E. 27 days

add(divide(subtract(const_1, multiply(inverse(10), const_2)), inverse(20)), const_2)

Explanation: amit ’ s one day ’ s work = 1 / 10 amit ’ s 2 day ’ s work = 1 / 10 * 2 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 20 ananthu can do work in = 4 / 5 * 20 = 16 days so total days = 16 + 2 = 18 days answer : a


Question: cheese , bologna , and peanut butter sandwiches were made for a picnic in a ratio of 1 to 7 to 8 . if a total of 80 sandwiches were made , how many bologna sandwiches were made ?

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

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

<gadget id="calculator">80 / 16</gadget>
<output>5</output>

<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 15
B. 30
C. 35
D. 42
E. 48

multiply(divide(80, add(add(1, 7), 8)), 7)

Explanation: for deciding such task we should calculate all parts 1 + 7 + 8 = 16 parts and we should calculate how many sandwiches holds 1 part : 80 / 16 = 5 sandwiches in one part for bologna we have 7 parts so : 7 * 5 = 35 answer is c


Question: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 110 units raises the average to 55 units per day , what is the value of n ?

<gadget id="calculator">110 - 50</gadget>
<output>60</output>

<gadget id="calculator">55 - 50</gadget>
<output>5</output>

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

<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 9
B. 11
C. 13
D. 15
E. 17

subtract(divide(subtract(110, 50), subtract(55, 50)), const_1)

Explanation: "the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 110 - 55 = 55 n = 11 the answer is b ."


Question: a train is 360 meter long is running at a speed of 50 km / hour . in what time will it pass a bridge of 140 meter length ?

<gadget id="calculator">360 + 140</gadget>
<output>500</output>

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

<gadget id="calculator">50_000 / 3_600</gadget>
<output>125/9 = around 13.888889</output>

<gadget id="calculator">500 / (125/9)</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 87
B. 69
C. 36
D. 72
E. 21

divide(add(360, 140), divide(multiply(50, const_1000), const_3600))

Explanation: "speed = 50 km / hr = 50 * ( 5 / 18 ) m / sec = 125 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 9 / 125 ) = 36 seconds answer : c"


Question: the cash difference between the selling prices of an book at a profit of 12 % and 20 % is $ 3 . the ratio of the two selling prices is :

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

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

<gadget id="calculator">112 / 120</gadget>
<output>14/15 = around 0.933333</output>
<result>14/15 = around 0.933333</result>

Choices:
A. 55 : 23
B. 52 : 33
C. 52 : 53
D. 45 : 53
E. 14 : 15

divide(add(const_100, 12), add(const_100, 20))

Explanation: "let c . p . of the book be $ x . then , required ratio = 112 % of x / 120 % of x = 112 / 120 = 14 / 15 = 14 : 15 e"


Question: mixture contains alcohol and water in the ratio 4 : 3 . if 5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .

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

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

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

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

<gadget id="calculator">20 / 8</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">(5/2) * 4</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 10
B. 99
C. 27
D. 22
E. 29

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

Explanation: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 20 x = 4 ( 3 x + 5 ) 8 x = 20 x = 2.5 quantity of alcohol = ( 4 x 2.5 ) litres = 10 litres . answer : a"


Question: two pipes a and b can fill a tank in 36 hours and 46 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?

<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>

<gadget id="calculator">1 / 46</gadget>
<output>1/46 = around 0.021739</output>

<gadget id="calculator">(1/36) + (1/46)</gadget>
<output>41/828 = around 0.049517</output>

<gadget id="calculator">1 / (41/828)</gadget>
<output>828/41 = around 20.195122</output>
<result>828/41 = around 20.195122</result>

Choices:
A. 20.195 hrs
B. 21.195 hrs
C. 22.195 hrs
D. 23.195 hrs
E. 20.495 hrs

divide(const_1, add(divide(const_1, 36), divide(const_1, 46)))

Explanation: "a fill in one hour = 1 / 36 b fill in one hour = 1 / 46 both fill in one hour = 1 / 36 + 1 / 46 = 82 / 1656 time taken by both pipes = 1656 / 82 = 20.195 hrs answer : a"


Question: a grocer has a sale of rs . 5435 , rs . 5927 , rs . 5855 , rs . 6230 and rs . 5562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5500 ?

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

<gadget id="calculator">6 * 5_500</gadget>
<output>33_000</output>

<gadget id="calculator">5_435 + 5_927</gadget>
<output>11_362</output>

<gadget id="calculator">11_362 + 5_855</gadget>
<output>17_217</output>

<gadget id="calculator">17_217 + 6_230</gadget>
<output>23_447</output>

<gadget id="calculator">23_447 + 5_562</gadget>
<output>29_009</output>

<gadget id="calculator">33_000 - 29_009</gadget>
<output>3_991</output>
<result>3_991</result>

Choices:
A. 4991
B. 5991
C. 3991
D. 6542
E. 6995

Explanation: "total sale for 5 months = rs . ( 5435 + 5927 + 5855 + 6230 + 5562 ) = rs . 29009 . required sale = rs . [ ( 5500 x 6 ) - 29009 ] = rs . ( 33000 - 29009 ) = rs . 3991 answer : option c"


Question: find the result of equation of the ellipse whose foci are at ( 0 , - 5 ) and ( 0 , 5 ) and the length of its major axis is 14 .

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

<gadget id="calculator">10 + 4</gadget>
<output>14</output>

<gadget id="calculator">14 / 14</gadget>
<output>1</output>
<result>1</result>

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

Explanation: from the coordinates of the foci , c = 5 and the major axis is the y axis . from the length of the major axis , we obtain a = 7 . also b 2 = a 2 - c 2 = 24 . the equation of the ellipse is given by x 2 / 24 + y 2 / 49 = 1 correct answer is e ) 1


Question: if 12 machine can finish a job in 40 days , then how many more machines would be needed to finish the job in one - fourth less time ?

<gadget id="calculator">12 * 40</gadget>
<output>480</output>

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

<gadget id="calculator">(3/4) * 40</gadget>
<output>30</output>

<gadget id="calculator">480 / 30</gadget>
<output>16</output>

<gadget id="calculator">16 - 12</gadget>
<output>4</output>
<result>4</result>

Choices:
A. a . 4
B. b . 8
C. c . 10
D. d . 12
E. e . 16

subtract(divide(multiply(12, 40), multiply(divide(const_3, const_4), 40)), 12)

Explanation: you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 12 machines ( identical ones , i assume ) work simultaneously for 40 days , they will do a total of 12 * 40 machine - days of work . so the job requires 12 * 40 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 30 days . so we ' ll need 12 * 40 / 30 = 16 machines , or 4 additional machines . a


Question: following an increase in prices , the price of a candy box was 20 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?

<gadget id="calculator">20 * 100</gadget>
<output>2_000</output>

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

<gadget id="calculator">2_000 / 125</gadget>
<output>16</output>

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

<gadget id="calculator">100 + 50</gadget>
<output>150</output>

<gadget id="calculator">600 / 150</gadget>
<output>4</output>

<gadget id="calculator">16 + 4</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 11 .
B. 20 .
C. 13 .
D. 14 .
E. 14.5

add(divide(multiply(20, const_100), add(const_100, 25)), divide(multiply(6, const_100), add(const_100, 50)))

Explanation: "price of candy before price increase = 20 / 1.25 = 16 price of soda before price increase = 6 / 1.5 = 4 total price = 16 + 4 = 20 b is the answer"


Question: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 14 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?

<gadget id="calculator">1_200 / 30</gadget>
<output>40</output>

<gadget id="calculator">30 + 40</gadget>
<output>70</output>

<gadget id="calculator">30 ** 2</gadget>
<output>900</output>

<gadget id="calculator">40 ** 2</gadget>
<output>1_600</output>

<gadget id="calculator">900 + 1_600</gadget>
<output>2_500</output>

<gadget id="calculator">2_500 ** (1/2)</gadget>
<output>50</output>

<gadget id="calculator">70 + 50</gadget>
<output>120</output>

<gadget id="calculator">120 * 14</gadget>
<output>1_680</output>
<result>1_680</result>

Choices:
A. 1276
B. 1680
C. 2832
D. 1299
E. 1236

Explanation: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 14 = 1680 answer : option b"


Question: . a car covers a distance of 810 km in 5 hours . find its speed ?

<gadget id="calculator">810 / 5</gadget>
<output>162</output>
<result>162</result>

Choices:
A. 104
B. 55
C. 162
D. 174
E. 2761

Explanation: "810 / 5 = 162 kmph answer : c"


Question: the compounded ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is

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

<gadget id="calculator">6 / 11</gadget>
<output>6/11 = around 0.545455</output>

<gadget id="calculator">(2/3) * (6/11)</gadget>
<output>4/11 = around 0.363636</output>

<gadget id="calculator">11 / 2</gadget>
<output>11/2 = around 5.5</output>

<gadget id="calculator">(4/11) * (11/2)</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 2 : 0
B. 2 : 1
C. 2 : 9
D. 2 : 2
E. 2 : 5

multiply(multiply(divide(2, 3), divide(6, 11)), divide(11, 2))

Explanation: answer : b ) 2 : 1


Question: in a photography exhibition , some photographs were taken by octavia the photographer , and some photographs were framed by jack the framer . jack had framed 24 photographs taken by octavia , and 12 photographs taken by other photographers . if 36 of the photographs in the exhibition were taken by octavia , how many photographs were either framed by jack or taken by octavia ?

<gadget id="calculator">24 + 12</gadget>
<output>36</output>

<gadget id="calculator">36 - 24</gadget>
<output>12</output>

<gadget id="calculator">36 + 12</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 36
B. 48
C. 72
D. 96
E. 108

Explanation: the number of photographs either framed by jack or taken by octavia = { jack } + { octavia } - { overlap } = 36 + 36 - 24 = 48 ( { overlap } is green box ) . answer : b


Question: what is value of ( p + q ) / ( p - q ) if p / q = 7 ?

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

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

<gadget id="calculator">8 / 6</gadget>
<output>4/3 = around 1.333333</output>
<result>4/3 = around 1.333333</result>

Choices:
A. 1 / 3
B. 2 / 3
C. 4 / 3
D. 5 / 3
E. none of these

divide(add(7, const_1), subtract(7, const_1))

Explanation: explanation : ( p + q ) / ( p - q ) = ( p / q + 1 ) / ( p / q - 1 ) = ( 7 + 1 ) / ( 7 - 1 ) = 4 / 3 . answer : c


Question: find the area of a cuboid of length 8 cm , breadth 6 cm . and height 9 cm .

<gadget id="calculator">8 * 6</gadget>
<output>48</output>

<gadget id="calculator">48 * 9</gadget>
<output>432</output>
<result>432</result>

Choices:
A. 400 cm cube
B. 410 cm cube
C. 420 cm cube
D. 432 cm cube
E. 480 cm cube

Explanation: "area of a cuboid = lxbxh = 8 cm x 6 cm x 9 cm = 432 cm cube answer : d"


Question: a windmill is taking advantage of strong air currents in order to produce electrical energy . on a typical day the wind speed is around 20 mph and in that speed the windmill produces 400 kw / h ( kilowatts per hour ) . on a stormy day a windmill produces 20 % more energy . how much kw / h can 3 windmills produce in two hours on a stormy day ?

<gadget id="calculator">400 * 20</gadget>
<output>8_000</output>

<gadget id="calculator">8_000 / 100</gadget>
<output>80</output>

<gadget id="calculator">400 + 80</gadget>
<output>480</output>

<gadget id="calculator">480 * 3</gadget>
<output>1_440</output>

<gadget id="calculator">1_440 * 2</gadget>
<output>2_880</output>
<result>2_880</result>

Choices:
A. 2880 .
B. 4860 .
C. 5780
D. 5760
E. 6380 .

multiply(multiply(add(400, divide(multiply(400, 20), const_100)), 3), const_2)

Explanation: normal day = 400 kw / h stormy day = 400 * 1.2 = 480 kw / h 3 windmills for 2 hours on stormy day 480 * 3 * 2 = 2880 answer : a


Question: ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 18 % if no discount was offered ?

<gadget id="calculator">100 + 18</gadget>
<output>118</output>

<gadget id="calculator">12_500 * 100</gadget>
<output>1_250_000</output>

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

<gadget id="calculator">1_250_000 / 80</gadget>
<output>15_625</output>

<gadget id="calculator">125 + 250</gadget>
<output>375</output>

<gadget id="calculator">15_625 + 375</gadget>
<output>16_000</output>

<gadget id="calculator">118 * 16_000</gadget>
<output>1_888_000</output>

<gadget id="calculator">1_888_000 / 100</gadget>
<output>18_880</output>
<result>18_880</result>

Choices:
A. 17608
B. 17606
C. 17604
D. 17600
E. 18880

divide(multiply(add(const_100, 18), add(divide(multiply(12500, const_100), subtract(const_100, 20)), add(125, 250))), const_100)

Explanation: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at whichthe tv should be sold to get a profit of 18 % if no discount was offered = 16000 * 118 / 100 = rs . 18880 . answer : e"


Question: a hall is 15 meters long and 15 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?

<gadget id="calculator">15 * 15</gadget>
<output>225</output>

<gadget id="calculator">225 * 2</gadget>
<output>450</output>

<gadget id="calculator">2 * (15 + 15)</gadget>
<output>60</output>

<gadget id="calculator">450 / 60</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">15 * 15 * (15/2)</gadget>
<output>3_375/2 = around 1_687.5</output>
<result>3_375/2 = around 1_687.5</result>

Choices:
A. 975.5
B. 1250.5
C. 1465.5
D. 1687.5
E. 1824.5

volume_rectangular_prism(15, 15, divide(multiply(rectangle_area(15, 15), const_2), rectangle_perimeter(15, 15)))

Explanation: "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 1687.5 the answer is d ."


Question: what is the total surface area in square meters of a rectangular solid whose length is 9 meters , width is 8 meters , and depth is 5 meters ?

<gadget id="calculator">2 * (8 * 9 + 9 * 5 + 8 * 5)</gadget>
<output>314</output>
<result>314</result>

Choices:
A. 152 m 2
B. 162 m 2
C. 180 m 2
D. 300 m 2
E. 314 m 2

Explanation: "surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 9 * 8 + 8 * 5 + 9 * 5 ) = 2 ( 72 + 40 + 45 ) = 2 * 157 = 314 m 2 answer : e"


Question: a car traveling at a certain constant speed takes 4 seconds longer to travel 1 km than it would take to travel 1 km at 80 km / hour . at what speed , in km / hr , is the car traveling ?

<gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>

<gadget id="calculator">3_600 * (1/80)</gadget>
<output>45</output>

<gadget id="calculator">45 + 4</gadget>
<output>49</output>

<gadget id="calculator">49 / 3_600</gadget>
<output>49/3_600 = around 0.013611</output>

<gadget id="calculator">1 / (49/3_600)</gadget>
<output>3_600/49 = around 73.469388</output>
<result>3_600/49 = around 73.469388</result>

Choices:
A. 70
B. 72
C. 74
D. 75
E. 78

divide(1, divide(add(multiply(const_3600, divide(1, 80)), 4), const_3600))

Explanation: "time to cover 1 kilometer at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover 1 kilometer at regular speed is 45 + 4 = 49 seconds = 49 / 3,600 hours = 1 / 74 hours ; so , we get that to cover 1 kilometer 1 / 74 hours is needed - - > regular speed 74 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : c"


Question: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12500 after a year ?

<gadget id="calculator">6_300 + 4_200</gadget>
<output>10_500</output>

<gadget id="calculator">10_500 + 10_500</gadget>
<output>21_000</output>

<gadget id="calculator">6_300 / 21_000</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) * 12_500</gadget>
<output>3_750</output>
<result>3_750</result>

Choices:
A. 3630
B. 2881
C. 2887
D. 3750
E. 2212

Explanation: 6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12100 = 3750 . answer : d


Question: a student needs 30 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .

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

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">180 / (3/10)</gadget>
<output>600</output>
<result>600</result>

Choices:
A. 400
B. 600
C. 800
D. 1000
E. 1200

divide(add(80, 100), divide(30, const_100))

Explanation: "30 % = 180 marks 1 % = 6 marks 100 % = 600 marks the answer is b ."


Question: to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 8 hours a day ?

<gadget id="calculator">30 * 12</gadget>
<output>360</output>

<gadget id="calculator">360 * 8</gadget>
<output>2_880</output>

<gadget id="calculator">2_880 * 2</gadget>
<output>5_760</output>

<gadget id="calculator">20 * 8</gadget>
<output>160</output>

<gadget id="calculator">5_760 / 160</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 40
B. 36
C. 42
D. 44
E. 46

divide(multiply(multiply(multiply(30, 12), 8), 2), multiply(20, 8))

Explanation: "man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 8 = 160 therefore number of days = 5760 / 240 = 36 days ans = b"


Question: if x and j are integers and 2 x – j = 11 , then 4 x + j can not be

<gadget id="calculator">11 * 2</gadget>
<output>22</output>

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

<gadget id="calculator">11 - 6</gadget>
<output>5</output>

<gadget id="calculator">22 - 5</gadget>
<output>17</output>
<result>17</result>

Choices:
A. – 5
B. 1
C. 13
D. 17
E. 551

subtract(multiply(11, 2), subtract(11, add(4, 2)))

Explanation: 2 x - j = 11 . . . . j = 2 x - 11 4 x + j = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d


Question: an investment yields an interest payment of $ 228 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?

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

<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">228 / (3/4)</gadget>
<output>304</output>

<gadget id="calculator">304 * 100</gadget>
<output>30_400</output>
<result>30_400</result>

Choices:
A. $ 28,300
B. $ 30,400
C. $ 31,300
D. $ 32,500
E. $ 35,100

multiply(divide(228, divide(9, multiply(const_3, const_4))), const_100)

Explanation: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 228 = > p = ( 228 * 4 * 10 ^ 2 ) / 3 = 76 * 4 * 10 ^ 2 = 304 * 10 ^ 2 answer b"


Question: joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 45 . he was allowed to drop his lowest score . after doing so , his average test score improved to 50 . what is the lowest test score that was dropped ?

<gadget id="calculator">45 * 4</gadget>
<output>180</output>

<gadget id="calculator">50 * 3</gadget>
<output>150</output>

<gadget id="calculator">180 - 150</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 20
B. 30
C. 55
D. 65
E. 80

subtract(multiply(45, 4), multiply(50, const_3))

Explanation: "the arithmetic mean of 4 equally weighted tests was 45 . so what we can assume is that we have 4 test scores , each 45 . he dropped his lowest score and the avg went to 50 . this means that the lowest score was not 45 and other three scores had given the lowest score 5 each to make it up to 45 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 45 . so the lowest score = 45 - 15 = 30 answer ( b )"


Question: if y > 0 , ( 4 y ) / 20 + ( 3 y ) / 10 is what percent of y ?

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

<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(1/5) + (3/10)</gadget>
<output>1/2 = around 0.5</output>

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

Choices:
A. 40 %
B. 50 %
C. 60 %
D. 70 %
E. 80 %

multiply(const_100, add(divide(4, 20), divide(3, 10)))

Explanation: "can be reduced to 2 y / 10 + 3 y / 10 = y / 2 = 50 % answer b"


Question: in how many years rs 100 will produce the same interest at 5 % as rs . 600 produce in 4 years at 10 %

<gadget id="calculator">600 * 10</gadget>
<output>6_000</output>

<gadget id="calculator">6_000 / 100</gadget>
<output>60</output>

<gadget id="calculator">60 * 4</gadget>
<output>240</output>

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

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

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

Choices:
A. 44
B. 52
C. 50
D. 46
E. 48

divide(multiply(divide(multiply(600, 10), const_100), 4), multiply(divide(5, const_100), 100))

Explanation: "explanation : clue : firstly we need to calculate the si with prinical 600 , time 4 years and rate 10 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 100 * 5 ) = 48 option e"


Question: in the number 10,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 55 , what is the greatest possible value of b × a ?

<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>

<gadget id="calculator">10_000 + 1_000</gadget>
<output>11_000</output>

<gadget id="calculator">11_000 / 55</gadget>
<output>200</output>

<gadget id="calculator">200 + 1</gadget>
<output>201</output>

<gadget id="calculator">201 * 55</gadget>
<output>11_055</output>

<gadget id="calculator">11_055 % 100</gadget>
<output>55</output>

<gadget id="calculator">55 % 10</gadget>
<output>5</output>

<gadget id="calculator">55 - 5</gadget>
<output>50</output>

<gadget id="calculator">50 / 10</gadget>
<output>5</output>

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

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

Choices:
A. 0
B. 5
C. 10
D. 15
E. 25

subtract(multiply(reminder(reminder(multiply(add(divide(add(power(const_100, const_2), const_1000), 55), const_1), 55), const_100), const_10), divide(subtract(reminder(multiply(add(divide(add(power(const_100, const_2), const_1000), 55), const_1), 55), const_100), reminder(reminder(multiply(add(divide(add(power(const_100, const_2), const_1000), 55), const_1), 55), const_100), const_10)), const_10)), const_10)

Explanation: you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d


Question: if mn ≠ 0 and 25 percent of n equals 37 1 / 2 percent of m , what is the value of 12 n / m ?

<gadget id="calculator">37 / 100</gadget>
<output>37/100 = around 0.37</output>

<gadget id="calculator">(37/100) * 100</gadget>
<output>37</output>

<gadget id="calculator">37 * 10</gadget>
<output>370</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

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

<gadget id="calculator">370 / 25</gadget>
<output>74/5 = around 14.8</output>

<gadget id="calculator">(74/5) + 3</gadget>
<output>89/5 = around 17.8</output>
<result>89/5 = around 17.8</result>

Choices:
A. 18
B. 323323
C. 8
D. 3
E. 98

add(divide(multiply(multiply(divide(37, const_100), const_100), const_10), multiply(divide(25, const_100), const_100)), const_3)

Explanation: given : 25 percent of n equals 37 ( 1 / 2 ) percent of m = > ( 25 / 100 ) * n = ( 75 / 200 ) * m = > 2 n = 3 m . 12 n / m = 6 * 2 n / m = 6 * 3 m / m = 18 . hence a .


Question: if the cost price of 18 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?

<gadget id="calculator">100 * 16</gadget>
<output>1_600</output>

<gadget id="calculator">1_600 / 18</gadget>
<output>800/9 = around 88.888889</output>

<gadget id="calculator">100 - (800/9)</gadget>
<output>100/9 = around 11.111111</output>

<gadget id="calculator">(100/9) / (800/9)</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">100 * (1/8)</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>

Choices:
A. 20 % loss
B. 12.5 % profit
C. 33.33 % loss
D. 30.33 % loss
E. none of these

multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 16), 18)), divide(multiply(const_100, 16), 18)))

Explanation: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 18 articles = rs . 18 . selling price of 16 articles = rs . 18 therefore , selling price of 18 articles is : - = > 18 / 16 ã — 18 = > 20.25 . therefore , profit = selling price - cost price . = > 20.25 â ˆ ’ 18 = 2.25 . hence , the percentage of profit = profit x 100 / c . p . = > 2.25 / 18 ã — 100 . = > 12.5 % profit . answer : b"


Question: if the length of an edge of cube p is thrice the length of an edge of cube q , what is the ratio of the volume of cube q to the volume of cube p ?

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

<gadget id="calculator">(1/3) ** 3</gadget>
<output>1/27 = around 0.037037</output>
<result>1/27 = around 0.037037</result>

Choices:
A. 1 / 4
B. 1 / 5
C. 1 / 6
D. 1 / 27
E. 1 / 9

Explanation: the length of cube q = 1 ; the length of cube p = 3 ; the ratio of the volume of cube q to the volume of cube p = 1 ^ 3 / 3 ^ 3 = 1 / 27 answer : d


Question: si on a certain sum of money for 3 yrs at 8 percent / annum is 1 / 2 the ci on rs . 4000 for 2 yrs at 10 percent / annum . the sum placed on si is ?

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

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

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

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

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

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

<gadget id="calculator">420 * 100</gadget>
<output>42_000</output>

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

<gadget id="calculator">42_000 / 24</gadget>
<output>1_750</output>
<result>1_750</result>

Choices:
A. rs . 1700
B. rs . 1720
C. rs . 1750
D. rs . 1850
E. rs . 2000

divide(multiply(divide(subtract(multiply(4000, power(add(1, divide(10, const_100)), const_2)), 4000), const_2), const_100), multiply(3, 8))

Explanation: c . i . = rs . 4000 x 1 + 10 2 - 4000 100 = rs . 4000 x 11 x 11 - 4000 10 10 = rs . 840 . sum = rs . 420 x 100 = rs . 1750 . 3 x 8 c


Question: what is the sum of the first 23 natural numbers ( starting from 1 ) ?

<gadget id="calculator">23 / 2</gadget>
<output>23/2 = around 11.5</output>

<gadget id="calculator">23 - 1</gadget>
<output>22</output>

<gadget id="calculator">22 + 2</gadget>
<output>24</output>

<gadget id="calculator">(23/2) * 24</gadget>
<output>276</output>
<result>276</result>

Choices:
A. 256
B. 266
C. 276
D. 286
E. 296

multiply(divide(23, const_2), add(subtract(23, 1), const_2))

Explanation: the sum of n natural numbers = n * ( n + 1 ) / 2 = 23 * 24 / 2 = 276 the answer is c .


Question: in a garden , 26 trees are planted at equal distances along a yard 700 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?

<gadget id="calculator">26 - 1</gadget>
<output>25</output>

<gadget id="calculator">700 / 25</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 10
B. 28
C. 12
D. 14
E. 16

Explanation: "26 trees have 25 gaps between them . length of each gap = 700 / 25 = 28 i . e . , distance between two consecutive trees = 28 answer is b ."


Question: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 20 % ?

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

<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) ** 2</gadget>
<output>36/25 = around 1.44</output>

<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>

<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 33 %
B. 44 %
C. 55 %
D. 56 %
E. 73 %

multiply(subtract(power(add(const_1, divide(20, const_100)), const_2), const_1), const_100)

Explanation: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 20 % increase a surface = 6 * ( ( 1.2 a ) ^ 2 ) = 6 * 1.44 * a ^ 2 the increase in the surface area = ( 6 * 1.44 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.44 - 1 ) ) / ( 6 * a ^ 2 ) = 1.44 - 1 = 0.44 = 44 % answer : b"


Question: a semicircular shaped window has diameter of 63 cm . its perimeter equals

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

<gadget id="calculator">2 * pi * (63/2)</gadget>
<output>63*pi = around 197.920337</output>

<gadget id="calculator">(63*pi) / 2</gadget>
<output>63*pi/2 = around 98.960169</output>

<gadget id="calculator">(63*pi/2) + 63</gadget>
<output>63 + 63*pi/2 = around 161.960169</output>
<result>63 + 63*pi/2 = around 161.960169</result>

Choices:
A. 162
B. 766
C. 298
D. 277
E. 198

add(divide(circumface(divide(63, const_2)), const_2), 63)

Explanation: explanation : perimeter of window = { \ color { blue } \ pi } r + 2 r = [ { ( 22 / 7 ) * ( 63 / 2 ) } + 63 ] = 99 + 63 = 162 cm answer : a ) 162


Question: by selling 100 pens , a trader gains the cost of 30 pens . find his gain percentage ?

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 30 %
B. 33 %
C. 31 %
D. 32 %
E. 34 %

Explanation: "let the cp of each pen be rs . 1 . cp of 100 pens = rs . 100 profit = cost of 30 pens = rs . 30 profit % = 30 / 100 * 100 = 30 % answer : a"


Question: out of 3 consecutive odd numbers 11 times the first number is equal to addition of thrice the third number and adding 16 to 4 times the second . what is the first number ?

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

<gadget id="calculator">16 - 7</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 5
B. 6
C. 7
D. 8
E. 9

Explanation: description : = > 11 x = 4 ( x + 2 ) + 16 + 3 ( x + 4 ) = > 11 x = 7 x + 36 = > 4 x = 36 x = 9 answer e


Question: working together at their respective constant rates , machine a and machine b can produce 1600 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1600 unit total would it produce ?

<gadget id="calculator">1_600 / 8</gadget>
<output>200</output>

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

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

<gadget id="calculator">(3/2) * 8</gadget>
<output>12</output>

<gadget id="calculator">1_600 / 12</gadget>
<output>400/3 = around 133.333333</output>

<gadget id="calculator">200 - (400/3)</gadget>
<output>200/3 = around 66.666667</output>

<gadget id="calculator">(200/3) * 8</gadget>
<output>1_600/3 = around 533.333333</output>

<gadget id="calculator">(1_600/3) / 1_600</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. 25
B. 33
C. 50
D. 67
E. 75

multiply(divide(multiply(subtract(divide(1600, 8), divide(1600, multiply(add(divide(50, const_100), const_1), 8))), 8), 1600), const_100)

Explanation: 1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 1600 units in 24 hrs , so it can produce 1600 * 8 / 24 = 533.33 units is 8 hrs . 533.33 is 33.33 % of 1600 . b is the answer


Question: according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 26 , by how much does the temperature in degrees celsius ( c ) increase ?

<gadget id="calculator">26 * 5</gadget>
<output>130</output>

<gadget id="calculator">130 / 9</gadget>
<output>130/9 = around 14.444444</output>
<result>130/9 = around 14.444444</result>

Choices:
A. 9
B. 14.44
C. 47
D. 48 3 / 5
E. 59

Explanation: "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 26 = 58 - - > c = 5 / 9 * 26 = 14.44 . increase = 14.44 degrees . answer : b ."


Question: if price of t . v set is reduced by 20 % , then its sale increases by 80 % , find net effect on sale value

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

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>

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

<gadget id="calculator">180 / 100</gadget>
<output>9/5 = around 1.8</output>

<gadget id="calculator">(4/5) * (9/5)</gadget>
<output>36/25 = around 1.44</output>

<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>

<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 44
B. 45
C. 46
D. 47
E. 48

multiply(subtract(multiply(divide(subtract(const_100, 20), const_100), divide(add(const_100, 80), const_100)), const_1), const_100)

Explanation: "- a + b + ( ( - a ) ( b ) / 100 ) = - 20 + 80 + ( - 20 * 80 ) / 100 = - 20 + 80 - 16 = 44 answer : a"


Question: the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average of the team ?

<gadget id="calculator">26 + 3</gadget>
<output>29</output>

<gadget id="calculator">26 + 29</gadget>
<output>55</output>

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

<gadget id="calculator">55 - 9</gadget>
<output>46</output>

<gadget id="calculator">46 / 2</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 23
B. 25
C. 30
D. 22
E. 40

divide(subtract(add(26, add(26, 3)), multiply(3, 3)), const_2)

Explanation: "let the average of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = 11 x - 9 x = 46 = 2 x = 46 = > x = 23 so , average age of the team is 23 years . answer a"


Question: tom and marry each have a bag of marbles , each of which contains 4 red marbles , 10 blue marbles , and 6 yellow marbles . if tom and marry each select one marble from their respective bags , what is the probability that either tom or marry select a blue marble ?

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

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

<gadget id="calculator">10 / 20</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) * (1/2)</gadget>
<output>1/4 = around 0.25</output>

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

Choices:
A. 1 / 7
B. 2 / 4
C. 3 / 4
D. 1 / 8
E. 1 / 16

subtract(const_1, multiply(divide(10, add(add(4, 6), 10)), divide(10, add(add(4, 6), 10))))

Explanation: probability that either selects a red marble , p ( either ) = 1 - probability that neither selects a blue marble , p ( neither ) probability that tom selects non blue = 10 c 1 / 20 c 1 = 1 / 2 probability that marry selects non blue = 10 c 1 / 20 c 1 = 1 / 2 = > p ( either ) = 1 - ( 1 / 2 * 1 / 2 ) = 1 - 1 / 4 = 3 / 4 . c )


Question: if 7 cats can kill 7 rats in 7 minutes , how long will it take 100 cats to kill 100 rats ?

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

Choices:
A. 5 minutes
B. 6 minutes
C. 7 minutes
D. 8 minutes
E. 9 minutes

Explanation: "it will take 7 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 7 minutes , so 100 cats can kill 100 rats in 7 minutes answer c"


Question: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 20.95 . what is the greatest number of hot dogs you can buy at this store with $ 300 ?

<gadget id="calculator">300 / 20.95</gadget>
<output>14.319809</output>

<gadget id="calculator">14.319809 * 250</gadget>
<output>3_579.95225</output>
<result>3_579.95225</result>

Choices:
A. 3,108
B. 3,100
C. 3,108
D. 3,540
E. 3,256

Explanation: to maximize number of hot dogs with 300 $ total number of hot dogs bought in 250 - pack = 20.95 * 14 = 293.30 $ amount remaining = 300 - 293.30 = 6.7 $ total number of hot dogs bought in 20 - pack = 3.05 * 2 = 6.10 $ amount remaining = 6.70 - 6.10 = 0.6 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 300 $ = 250 * 14 + 20 * 2 = 3,540 answer d


Question: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 200 . how much did he have with him in the beginning ?

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

<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) / 5</gadget>
<output>2/15 = around 0.133333</output>

<gadget id="calculator">(2/3) - (2/15)</gadget>
<output>8/15 = around 0.533333</output>

<gadget id="calculator">(8/15) / 4</gadget>
<output>2/15 = around 0.133333</output>

<gadget id="calculator">(8/15) - (2/15)</gadget>
<output>2/5 = around 0.4</output>

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

Choices:
A. s 200
B. s 500
C. s 300
D. s 450
E. s 550

divide(200, subtract(subtract(subtract(1, divide(1, 3)), divide(subtract(1, divide(1, 3)), 5)), divide(subtract(subtract(1, divide(1, 3)), divide(subtract(1, divide(1, 3)), 5)), 4)))

Explanation: suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 200 = 500 answer : b


Question: the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 76 % of the required amount . what is the net difference in the expenditure on that product ?

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

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

<gadget id="calculator">125 * 76</gadget>
<output>9_500</output>

<gadget id="calculator">10_000 - 9_500</gadget>
<output>500</output>

<gadget id="calculator">500 * 100</gadget>
<output>50_000</output>

<gadget id="calculator">50_000 / 10_000</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 12.5 %
B. 13 %
C. 5 %
D. 17 %
E. 19 %

divide(multiply(subtract(multiply(const_100, const_100), multiply(add(const_100, 25), 76)), const_100), multiply(const_100, const_100))

Explanation: quantity x rate = price 1 x 1 = 1 0.76 x 1.25 = 0.95 decrease in price = ( 0.05 / 1 ) × 100 = 5 % c )


Question: if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability r that n is divisible by 3 ?

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

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

<gadget id="calculator">5 / 16</gadget>
<output>5/16 = around 0.3125</output>
<result>5/16 = around 0.3125</result>

Choices:
A. 1 / 3
B. ¼
C. 9 / 25
D. 5 / 16
E. 0

divide(add(3, const_2), multiply(const_4, const_4))

Explanation: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."


Question: 0 - - - : - | - - - : - - | - : - - : - | - - : - - - | - : - - - - 1 on the number line above , the segment from 0 to 1 has been divided into fifths , as indicated by the large tick marks , and also into sevenths , as indicated by the small tick marks . what is the least possible distance x between any two of the tick marks ?

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

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

<gadget id="calculator">5 * 7</gadget>
<output>35</output>

<gadget id="calculator">1 / 35</gadget>
<output>1/35 = around 0.028571</output>
<result>1/35 = around 0.028571</result>

Choices:
A. 1 / 70
B. 1 / 35
C. 2 / 35
D. 1 / 12
E. 1 / 7

divide(1, multiply(add(const_2, const_3), add(const_3, const_4)))

Explanation: divisions are 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 1 / 5 2 / 5 3 / 5 4 / 5 5 / 5 expressing the same in terms of the lcm of 57 , i . e 35 0 7 / 35 14 / 35 21 / 35 28 / 35 35 / 35 5 / 35 10 / 35 15 / 35 20 / 35 25 / 35 30 / 35 by comparing the divisions with each other we can see 1 / 35 is the shortest possible distance between any two selected divisions . x = 1 / 35 answer is b .


Question: find the area of a parallelogram with base 21 cm and height 11 cm ?

<gadget id="calculator">21 * 11</gadget>
<output>231</output>
<result>231</result>

Choices:
A. 231 cm 2
B. 384 cm 2
C. 672 cm 2
D. 267 cm 2
E. 286 cm 2

Explanation: "area of a parallelogram = base * height = 21 * 11 = 231 cm 2 answer : a"


Question: a cycle is bought for rs . 1120 and sold for rs . 1200 , find the gain percent ?

<gadget id="calculator">1_200 - 1_120</gadget>
<output>80</output>

<gadget id="calculator">80 / 1_120</gadget>
<output>1/14 = around 0.071429</output>

<gadget id="calculator">(1/14) * 100</gadget>
<output>50/7 = around 7.142857</output>
<result>50/7 = around 7.142857</result>

Choices:
A. 7 %
B. 2 %
C. 6 %
D. 1 %
E. 8 %

multiply(divide(subtract(1200, 1120), 1120), const_100)

Explanation: "explanation : 1120 - - - - 80 100 - - - - ? = > 7 % answer : a"


Question: a trader bought a car at 20 % discount on its original price . he sold it at a 70 % 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 + 70</gadget>
<output>170</output>

<gadget id="calculator">80 * 170</gadget>
<output>13_600</output>

<gadget id="calculator">13_600 / 100</gadget>
<output>136</output>

<gadget id="calculator">136 / 100</gadget>
<output>34/25 = around 1.36</output>

<gadget id="calculator">(34/25) - 1</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(9/25) * 100</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 17 %
B. 72 %
C. 12 %
D. 82 %
E. 36 %

multiply(subtract(divide(divide(multiply(subtract(const_100, 20), add(const_100, 70)), const_100), const_100), const_1), const_100)

Explanation: "original price = 100 cp = 80 s = 80 * ( 170 / 100 ) = 136 100 - 136 = 36 % answer : e"


Question: a boat having a length 9 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :

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

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

<gadget id="calculator">27 * (1/100)</gadget>
<output>27/100 = around 0.27</output>

<gadget id="calculator">(27/100) * 1_000</gadget>
<output>270</output>
<result>270</result>

Choices:
A. 100 kg
B. 120 kg
C. 189 kg
D. 180 kg
E. 270 kg

multiply(multiply(multiply(9, 3), divide(1, const_100)), const_1000)

Explanation: "volume of water displaced = ( 9 x 3 x 0.01 ) m 3 = 0.27 m 3 . mass of man = volume of water displaced x density of water = ( 0.27 x 1000 ) kg = 270 kg . answer : e"


Question: what annual payment will discharge a debt of rs . 1030 due in 2 years at the rate of 5 % compound interest ?

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

<gadget id="calculator">(1/20) + 1</gadget>
<output>21/20 = around 1.05</output>

<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>

<gadget id="calculator">(441/400) * 1_030</gadget>
<output>45_423/40 = around 1_135.575</output>

<gadget id="calculator">(45_423/40) / 2</gadget>
<output>45_423/80 = around 567.7875</output>
<result>45_423/80 = around 567.7875</result>

Choices:
A. 553.94
B. 551.25
C. 534.33
D. 543.33
E. 646.33

divide(multiply(power(add(divide(5, const_100), const_1), 2), 1030), 2)

Explanation: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1030 820 x + 1030 * 441 x = 553.94 so , value of each installment = rs . 553.94 answer : option a"


Question: in a factory , there are 90 % technicians and 10 % non - technicians . if the 90 % of the technicians and 10 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?

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

<gadget id="calculator">90 * (1/10)</gadget>
<output>9</output>

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

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

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

<gadget id="calculator">100 - 18</gadget>
<output>82</output>
<result>82</result>

Choices:
A. 62 %
B. 57 %
C. 52 %
D. 82 %
E. 42 %

subtract(const_100, add(multiply(90, divide(10, const_100)), multiply(divide(90, const_100), 10)))

Explanation: "total = 100 t = 90 nt = 10 90 * ( 10 / 100 ) = 910 * ( 90 / 100 ) = 9 9 + 9 = 18 = > 100 - 18 = 82 % answer : d"


Question: how many seconds will a 450 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 60 km / hr ?

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

<gadget id="calculator">60 - 6</gadget>
<output>54</output>

<gadget id="calculator">(5/18) * 54</gadget>
<output>15</output>

<gadget id="calculator">450 / 15</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 25
B. 30
C. 40
D. 45
E. 60

divide(450, multiply(const_0_2778, subtract(60, 6)))

Explanation: explanation : speed of train relatively to man = ( 60 - 6 ) km / hr = 54 km / hr = ( 54 x 5 / 18 ) m / sec = 15 m / sec time taken to pass the man = ( 450 / 15 ) sec = 30 sec . answer : b


Question: 90 kg of an alloy a is mixed with 140 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 4 and alloy b has tin and copper in the ratio 2 : 5 , then the amount of tin in the new alloy is ?

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

<gadget id="calculator">90 / 7</gadget>
<output>90/7 = around 12.857143</output>

<gadget id="calculator">(90/7) * 4</gadget>
<output>360/7 = around 51.428571</output>

<gadget id="calculator">2 + 5</gadget>
<output>7</output>

<gadget id="calculator">140 / 7</gadget>
<output>20</output>

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

<gadget id="calculator">(360/7) + 40</gadget>
<output>640/7 = around 91.428571</output>
<result>640/7 = around 91.428571</result>

Choices:
A. 100.6 kg
B. 95.4 kg
C. 117.5 kg
D. 91.4 kg
E. 92 kg

add(multiply(divide(90, add(3, 4)), 4), multiply(divide(140, add(2, 5)), 2))

Explanation: "quantity of tin in 90 kg of a = 90 * 4 / 7 = 51.4 kg quantity of tin in 140 kg of b = 140 * 2 / 7 = 40 kg quantity of tin in the new alloy = 51.4 + 40 = 91.4 kg answer is d"


Question: a rectangular garden is to be twice as long as it is wide . if 180 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?

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

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

<gadget id="calculator">180 / 6</gadget>
<output>30</output>

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

Choices:
A. 60
B. 70
C. 80
D. 90
E. 100

multiply(divide(180, multiply(add(const_2, const_1), const_2)), const_2)

Explanation: "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 180 so , 2 ( l + b ) = 180 or , l + b = 90 now use the answer options ( given length ; breath will be half the length ) ( a ) 60 l = 60 ; b = 30 l + b = 90 ( b ) 70 l = 70 ; b = 35 l + b = 105 ( c ) 80 l = 80 ; b = 40 l + b = 120 ( d ) 90 l = 90 ; b = 45 l + b = 135 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( a )"


Question: if the sides of a cube are in the ratio 9 : 7 . what is the ratio of their diagonals ?

<gadget id="calculator">9 / 7</gadget>
<output>9/7 = around 1.285714</output>
<result>9/7 = around 1.285714</result>

Choices:
A. 4 : 3
B. 16 : 9
C. 9 : 7
D. 3 : 4
E. 3 : 8

Explanation: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 9 : 7 d 1 : d 2 = 9 : 7 where √ 3 cancelled both side answer : c"


Question: last year elaine spent 20 % of her annual earnings on rent . this year she earned 20 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?

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

<gadget id="calculator">(1/5) + 1</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) * 30</gadget>
<output>36</output>

<gadget id="calculator">36 / 20</gadget>
<output>9/5 = around 1.8</output>

<gadget id="calculator">(9/5) * 100</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 185.5
B. 180.0
C. 167.5
D. 172.5
E. 177.5

multiply(divide(multiply(add(divide(20, const_100), const_1), 30), 20), const_100)

Explanation: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 20 % more , or $ 120 she would ' ve spent 30 % of this on rent , or $ 36 do $ 36 / $ 20 this will give you 180 % b is the correct answer ."


Question: two bullet train s 140 m and 200 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :

<gadget id="calculator">140 + 200</gadget>
<output>340</output>

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

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

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

<gadget id="calculator">340 / (250/9)</gadget>
<output>306/25 = around 12.24</output>
<result>306/25 = around 12.24</result>

Choices:
A. 15.8 sec .
B. 12.24 sec .
C. 11.8 sec .
D. 10.8 sec .
E. 08.8 sec .

Explanation: relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 200 ) m = 340 m . required time = 340 x 9 / 250 = 54 / 5 = 12.24 sec . answer b


Question: in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.5 times as old as robert ?

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

<gadget id="calculator">1.5 + 7</gadget>
<output>8.5</output>

<gadget id="calculator">1_950 + 8.5</gadget>
<output>1_958.5</output>
<result>1_958.5</result>

Choices:
A. 1960
B. 1965
C. 1970
D. 1975
E. 2000

Explanation: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 2000 : ri = 60 , ro = 90 thus ans : e"


Question: in what ratio must tea at rs . 60 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 67.5 per kg ?

<gadget id="calculator">70 - 67.5</gadget>
<output>2.5</output>

<gadget id="calculator">67.5 - 60</gadget>
<output>7.5</output>

<gadget id="calculator">2.5 / 7.5</gadget>
<output>0.333333</output>
<result>0.333333</result>

Choices:
A. 3 : 1
B. 3 : 2
C. 4 : 3
D. 1 : 3
E. none

divide(subtract(70, 67.5), subtract(67.5, 60))

Explanation: "required ratio = 250 : 750 = 1 : 3 answer d"


Question: in what time will a train 50 m long cross an electric pole , it its speed be 360 km / hr ?

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

<gadget id="calculator">360 * (5/18)</gadget>
<output>100</output>

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

Choices:
A. 0.25
B. 0.5
C. 1.5
D. 2.5
E. 3.5

Explanation: "speed = 360 * 5 / 18 = 100 m / sec time taken = 50 / 100 = 0.5 sec . answer : b"


Question: each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.74 % , what fraction of the products was checked by worker y ?

<gadget id="calculator">0.74 - 0.5</gadget>
<output>0.24</output>

<gadget id="calculator">0.8 - 0.5</gadget>
<output>0.3</output>

<gadget id="calculator">0.24 / 0.3</gadget>
<output>0.8</output>
<result>0.8</result>

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

divide(subtract(0.74, 0.5), subtract(0.8, 0.5))

Explanation: "x : 0.5 % is 0.24 % - points from 0.74 % . y : 0.8 % is 0.06 % - points from 0.74 % . therefore the ratio of products checked by y : x is 4 : 1 . thus , worker y checked 4 / 5 of the products . the answer is e ."


Question: workers at a campaign office have 2000 fliers to send out . if they send out 1 / 4 of them in the morning and 1 / 5 of the remaining ones out during the afternoon , how many are left for the next day ?

<gadget id="calculator">2_000 / 4</gadget>
<output>500</output>

<gadget id="calculator">2_000 - 500</gadget>
<output>1_500</output>

<gadget id="calculator">1_500 / 5</gadget>
<output>300</output>

<gadget id="calculator">1_500 - 300</gadget>
<output>1_200</output>
<result>1_200</result>

Choices:
A. 300
B. 800
C. 1100
D. 1200
E. 1180

subtract(subtract(2000, divide(2000, 4)), divide(subtract(2000, divide(2000, 4)), 5))

Explanation: "( 1 / 4 ) * 2000 = 500 remaining = 2000 - 500 = 1500 ( 1 / 5 ) of remaining = ( 1 / 5 ) * 1600 = 320 remaining now = 1500 - 320 = 1180 answer : option e"


Question: abcd is a square where ab = â ˆ š 4032 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .

<gadget id="calculator">4_032 / 2</gadget>
<output>2_016</output>
<result>2_016</result>

Choices:
A. 3008
B. 2002
C. 1008
D. 2016
E. 3000

Explanation: note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4032 / 2 = 2016 . correct answer d


Question: a sports equipment store sold ping pong rackets for a total of $ 637 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?

<gadget id="calculator">637 / 9.8</gadget>
<output>65</output>
<result>65</result>

Choices:
A. 50
B. 100
C. 65
D. 500
E. 980

Explanation: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 637 x = 65 pairs were sold . answer : c"


Question: a farmer has enough food to feed her 1000 cows for 50 days . after 10 days some of the cows run away and the food was now enough for the same period of 50 days as before . how many cows ran away ?

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

<gadget id="calculator">1 / 50</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">40 * (1/50)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1_000 * (1/5)</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 300
B. 200
C. 500
D. 400
E. 250

multiply(1000, subtract(const_1, multiply(subtract(50, 10), divide(const_1, 50))))

Explanation: 1000 - - - - 50 1000 - - - - 40 x - - - - 50 x * 50 = 1000 * 40 x = 800 1000 - - - - - - - 200 answer = b


Question: a certain number of men can do a work in 60 days . if there were 8 men less it could be finished in 10 days more . how many men are there ?

<gadget id="calculator">60 + 10</gadget>
<output>70</output>

<gadget id="calculator">70 * 8</gadget>
<output>560</output>

<gadget id="calculator">560 / 10</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 56
B. 42
C. 60
D. 45
E. 36

Explanation: "the original number of men = 8 ( 60 + 10 ) / 10 = 56 men answer is a"


Question: if - 3 x + 4 y = 28 and 3 x - 2 y = 8 , what is the product of x and y ?

<gadget id="calculator">28 + 8</gadget>
<output>36</output>

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

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

<gadget id="calculator">8 + 36</gadget>
<output>44</output>

<gadget id="calculator">44 / 3</gadget>
<output>44/3 = around 14.666667</output>

<gadget id="calculator">(44/3) * 18</gadget>
<output>264</output>
<result>264</result>

Choices:
A. 264 .
B. 428
C. 464 .
D. 622
E. 642

multiply(divide(add(8, multiply(divide(add(28, 8), 2), 2)), 3), divide(add(28, 8), 2))

Explanation: given - 3 x + 4 y = 28 - - - eq 1 3 x - 2 y = 8 - - eq 2 sum both eqns we get 2 y = 36 = > y = 18 sub 2 y in eq 2 = > 3 x - 36 = 8 . = > x = 44 / 3 now xy = 44 / 3 * 18 = 264 . option a is correct answer .


Question: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 25 hours and 81 hours respectively . the ratio of their speeds is :

<gadget id="calculator">81 ** (1/2)</gadget>
<output>9</output>

<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>

<gadget id="calculator">9 / 5</gadget>
<output>9/5 = around 1.8</output>
<result>9/5 = around 1.8</result>

Choices:
A. 2 : 3
B. 4 : 3
C. 9 : 5
D. 9 : 16
E. none of these

Explanation: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 81 : â ˆ š 25 = 9 : 5 . answer c"


Question: a train 100 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?

<gadget id="calculator">100 / 6</gadget>
<output>50/3 = around 16.666667</output>

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

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

<gadget id="calculator">60 - 5</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 45 kmph
B. 55 kmph
C. 32 kmph
D. 61 kmph
E. 70 kmph

subtract(divide(divide(100, 6), const_0_2778), 5)

Explanation: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 100 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 1800 x = 55 kmph answer is b"


Question: evaluate : 96385 + 12 * 3 * 25 = ?

<gadget id="calculator">12 * 3</gadget>
<output>36</output>

<gadget id="calculator">36 * 25</gadget>
<output>900</output>

<gadget id="calculator">96_385 - 900</gadget>
<output>95_485</output>
<result>95_485</result>

Choices:
A. 96385
B. 96358
C. 96785
D. 96485
E. 96855

subtract(96385, multiply(multiply(12, 3), 25))

Explanation: "according to order of operations , 12 ? 3 ? 25 ( division and multiplication ) is done first from left to right 12 / 2 = 4 * 25 = 100 hence 96385 + 12 * 3 * 2 = 96385 + 100 = 96485 correct answer d"


Question: if y > 0 , ( 9 y ) / 20 + ( 3 y ) / 10 is what percent of y ?

<gadget id="calculator">9 / 20</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(9/20) + (3/10)</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">100 * (3/4)</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 40 %
B. 50 %
C. 60 %
D. 70 %
E. 75 %

multiply(const_100, add(divide(9, 20), divide(3, 10)))

Explanation: "can be reduced to 9 y / 20 + 6 y / 20 = 15 y / 20 = 75 % answer e"


Question: all the students of class are told to sit in circle shape . here the boy at the 5 th position is exactly opposite to 20 th boy . total number of boys in the class ?

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

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

Choices:
A. 30
B. 40
C. 45
D. 25
E. 20

Explanation: "as half the circle shape consist of 20 - 5 = 15 boys , so total number of boys in full circle = 2 * 15 = 30 answer : a"


Question: an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters f long ?

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

<gadget id="calculator">4 * 1.5</gadget>
<output>6</output>

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

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

Choices:
A. 0.5
B. 1
C. 1.5
D. 2
E. 3

subtract(15, add(multiply(const_4, 2), multiply(const_4, 1.5)))

Explanation: "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1"


Question: for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 24 ) ?

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

<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 23
B. 19
C. 17
D. 13
E. 11

Explanation: f ( 24 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 = 2 ^ 12 * ( 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 ) - - > the greatest prime factor is 11 . answer : e .


Question: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 66 books in the special collection at that time , how many books of the special collection were loaned out during that month ?

<gadget id="calculator">75 - 66</gadget>
<output>9</output>

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">9 / (1/5)</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 20
B. 30
C. 35
D. 45
E. 55

divide(subtract(75, 66), subtract(const_1, divide(80, const_100)))

Explanation: "there are 9 books less ( 75 - 66 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 45 answer d"


Question: find the simple interest on rs . 70,000 at 16 2 / 3 % per year for 9 months .

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

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

<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>

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

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

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

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

<gadget id="calculator">900 * 10</gadget>
<output>9_000</output>

<gadget id="calculator">60_000 + 9_000</gadget>
<output>69_000</output>

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

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

<gadget id="calculator">50 / 3</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">69_000 * (50/3)</gadget>
<output>1_150_000</output>

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

<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">1_150_000 * (3/4)</gadget>
<output>862_500</output>

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

<gadget id="calculator">862_500 * (1/100)</gadget>
<output>8_625</output>
<result>8_625</result>

Choices:
A. 7500
B. 6500
C. 8750
D. 9500
E. none of them

multiply(multiply(multiply(add(multiply(multiply(multiply(2, 3), const_100), const_100), multiply(multiply(multiply(3, 3), const_100), multiply(add(3, 2), 2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(3, 3), multiply(2, multiply(2, 3)))), divide(const_1, const_100))

Explanation: "p = rs . 70000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 70,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8750 answer is c ."


Question: a is twice as good a workman as b and they took 6 days together to do the work b alone can do it in .

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

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

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

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

Choices:
A. 18 days
B. 12 days
C. 29 days
D. 25 days
E. 27 days

multiply(divide(multiply(6, add(const_2, const_1)), const_2), const_2)

Explanation: "wc = 2 : 1 2 x + x = 1 / 6 x = 1 / 18 = > 18 days answer : a"