Question: a dishonest dealer professes to sell goods at the cost price but uses a weight of 720 grams per kg , what is his percent ?

<gadget id="calculator">100 / 720</gadget>
<output>5/36 = around 0.138889</output>

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

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

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

<gadget id="calculator">(5/36) * 1_000</gadget>
<output>1_250/9 = around 138.888889</output>

<gadget id="calculator">(1_250/9) - 100</gadget>
<output>350/9 = around 38.888889</output>
<result>350/9 = around 38.888889</result>

Choices:
A. 15 %
B. 25 %
C. 38.9 %
D. 45 %
E. 35 %

subtract(multiply(divide(const_100, 720), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)

Explanation: "explanation : 720 - - - 280 100 - - - ? = > 38.9 % answer : c"


Question: machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 80 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 20 minutes ?

<gadget id="calculator">100 / 80</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) * 2</gadget>
<output>5/2 = around 2.5</output>

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

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

multiply(multiply(divide(100, 80), const_2), 20)

Explanation: machine b produces 100 part in 80 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 80 / 2 = 40 minutes . now , machine a produces 100 parts in 40 minutes which is 100 / 40 = 10 / 4 parts / minute . 10 / 4 parts x a total of 20 minutes = 10 / 4 * 20 = 50 e


Question: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 66 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?

<gadget id="calculator">100 - 66</gadget>
<output>34</output>

<gadget id="calculator">34 / 2</gadget>
<output>17</output>

<gadget id="calculator">100 - 17</gadget>
<output>83</output>
<result>83</result>

Choices:
A. 16 %
B. 32 %
C. 83 %
D. 84 %
E. 92 %

subtract(const_100, divide(subtract(const_100, 66), const_2))

Explanation: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 66 % is one st . dev , then on either side of m we have 66 / 2 = 33 % . so , 33 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 33 = 83 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 83 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it c"


Question: in a class of 54 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?

<gadget id="calculator">54 + 12</gadget>
<output>66</output>

<gadget id="calculator">66 - 22</gadget>
<output>44</output>

<gadget id="calculator">44 - 12</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 30
B. 10
C. 18
D. 28
E. 32

Explanation: "total = english + german - both + neither - - > 54 = english + 22 - 12 + 0 - - > english = 44 - - > only english = english - both = 44 - 12 = 32 . answer : e ."


Question: usc invited each south carolina high school to send up to 39 students to watch a football game . a section which has 199 seats in each row is reserved for those students . what is the least number of rows needed to guarantee that if 2006 students show up , then all students from the same high school can be seated in the same row ?

Choices:
A. 11
B. 12
C. 13
D. 14
E. 15

Explanation: the answer is 12 rows . if 59 schools send 34 students each , then we can sit at most 5 groups of students in the same row , so we will need 12 rows . next , 12 rows are sufficient . assume that this is not the case . suppose the groups of students are seated like this : first the largest group , then the second largest group , then the third largest group , etc . suppose we run out of space - there are not enough seats in any row to seat together the next group . suppose the first group that can not be seated together is the kth group and it consists of n students . then k 61 since any row fits at least 5 groups . also , n 2006 / k 2006 / 61 < 33 ( all groups already seated are no smaller than the kth group ) . so , n 32 . since there is not enough space in any of the 12 rows to seat the kth group , then there must be at least 168 students seated in each of the 12 rows . now , 12 × 168 = 2016 > 2006 a contradiction . so , 12 rows are sufficient . correct answer b


Question: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 3 inches wide on each side , the total area would have been ( m + 64 ) square inches . what is the perimeter of the photograph , in inches ?

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

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

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

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

<gadget id="calculator">36 - 4</gadget>
<output>32</output>

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

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

Choices:
A. 16
B. 24
C. 32
D. 40
E. 48

divide(subtract(64, subtract(power(multiply(3, const_2), const_2), power(multiply(1, const_2), const_2))), const_2)

Explanation: let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 6 ) ( y + 6 ) = m and so ( 2 ) xy + 6 x + 6 y + 36 = m + 64 let ' s subtract equation ( 1 ) from equation ( 2 ) . 4 x + 4 y + 32 = 64 2 x + 2 y = 16 , which is the perimeter of the photograph . the answer is a .


Question: the unit digit in the product 4556 * 3432 * 4581 * 2784 is ?

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

subtract(multiply(multiply(multiply(4556, 3432), 4581), 2784), subtract(multiply(multiply(multiply(4556, 3432), 4581), 2784), add(const_4, const_4)))

Explanation: unit digit in the given product = unit digit in 6 * 2 * 1 * 4 = 8 answer is a


Question: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276 metres long in 20 seconds . the length of the train ( in metres ) is :

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

<gadget id="calculator">276 / 12</gadget>
<output>23</output>

<gadget id="calculator">23 * 8</gadget>
<output>184</output>
<result>184</result>

Choices:
A. 184
B. 176
C. 175
D. 96
E. none of these

multiply(divide(276, subtract(20, 8)), 8)

Explanation: "explanation : let the length of train be l m . acc . to question ( 276 + l ) / 20 = l / 8 2208 + 8 l = 20 l l = 2208 / 12 = 184 m answer a"


Question: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 760 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?

<gadget id="calculator">760 / 4</gadget>
<output>190</output>
<result>190</result>

Choices:
A. 191
B. 190
C. 193
D. 212
E. 213

Explanation: "total movies submitted are 760 . as per question we need to take 1 / 4 of 760 to be considered for top 10 movies = 190 approximate the value we 190 . imo option b is the correct answer . . ."


Question: each child has 4 crayons and 14 apples . if there are 9 children , how many crayons are there in total ?

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

Choices:
A. 22
B. 65
C. 12
D. 36
E. 10

Explanation: 4 * 9 = 36 . answer is d .


Question: a man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes . if the ratio between the length and breadth of the park be 3 : 2 , then its area is :

<gadget id="calculator">12 * 1_000</gadget>
<output>12_000</output>

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

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

<gadget id="calculator">12_000 / 60</gadget>
<output>200</output>

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

<gadget id="calculator">1_600 / 10</gadget>
<output>160</output>

<gadget id="calculator">160 * 2</gadget>
<output>320</output>

<gadget id="calculator">160 * 3</gadget>
<output>480</output>

<gadget id="calculator">320 * 480</gadget>
<output>153_600</output>
<result>153_600</result>

Choices:
A. 1536 m 2
B. 15360 m 2
C. 153600 m 2
D. 163600 m 2
E. none of these

multiply(multiply(divide(multiply(8, divide(multiply(12, const_1000), multiply(multiply(const_3, const_2), const_10))), const_10), 2), multiply(divide(multiply(8, divide(multiply(12, const_1000), multiply(multiply(const_3, const_2), const_10))), const_10), 3))

Explanation: perimeter = distance covered in 8 min = ( 12000 / 60 * 8 ) m = 1600 m let , length = 3 x meters and breadth = 2 x meters then , 2 ( 3 x + 2 x ) = 1600 or x = 160 therefore , length = 480 m and breadth = 320 m therefore , area = ( 480 * 320 ) m 2 = 153600 m 2 answer : c


Question: find the value of m 12519 x 9999 = m ?

<gadget id="calculator">9_999 - 4</gadget>
<output>9_995</output>

<gadget id="calculator">9_995 * 12_519</gadget>
<output>125_127_405</output>
<result>125_127_405</result>

Choices:
A. 125177481
B. 353654655
C. 545463251
D. 725117481
E. 477899932

Explanation: "12519 x 9999 = 12519 x ( 10000 - 1 ) = 12519 x 10000 - 12519 x 1 = 125190000 - 12519 = 125177481 a"


Question: a is twice as good a workman as b and they took 9 days together to do the work b alone can do it in .

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

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

<gadget id="calculator">27 / 2</gadget>
<output>27/2 = around 13.5</output>

<gadget id="calculator">(27/2) * 2</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 17 days
B. 12 days
C. 29 days
D. 25 days
E. 27 days

multiply(divide(multiply(9, add(const_2, const_1)), const_2), const_2)

Explanation: "wc = 2 : 1 2 x + x = 1 / 9 x = 1 / 27 = > 27 days answer : e"


Question: find the value of ( 875 233 / 899 ) × 899

Choices:
A. 786845
B. 786857
C. 786858
D. 786859
E. 786860

Explanation: "( 875 233 / 899 ) × 899 ( 786625 + 233 ) / 899 × 899 786858 / 899 × 899 786858 c"


Question: the length of a rectangular floor is more than its breadth by 200 % . if rs . 150 is required to paint the floor at the rate of rs . 2 per sq m , then what would be the length of the floor ?

<gadget id="calculator">150 / 2</gadget>
<output>75</output>

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

<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>

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

Choices:
A. 65
B. 15
C. 18
D. 16
E. 14

multiply(sqrt(divide(divide(150, 2), const_3)), const_3)

Explanation: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 150 / 2 = 75 sq m l b = 75 i . e . , l * l / 3 = 75 l 2 = 225 = > l = 15 answer : b"


Question: a car traveled from san diego to san francisco at an average speed of 66 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?

<gadget id="calculator">1 / 66</gadget>
<output>1/66 = around 0.015152</output>

<gadget id="calculator">(1/66) / 2</gadget>
<output>1/132 = around 0.007576</output>

<gadget id="calculator">(1/66) + (1/132)</gadget>
<output>1/44 = around 0.022727</output>

<gadget id="calculator">1 / (1/44)</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 24 .
B. 32 .
C. 36 .
D. 42 .
E. 44 .

Explanation: "let the time taken be = x one way distance = 66 x total distance traveled = 2 * 66 x = 132 x total time taken = x + 2 x = 3 x average speed = 132 x / 3 x = 44 answer : e"


Question: rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 2 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?

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

<gadget id="calculator">40 * 2</gadget>
<output>80</output>

<gadget id="calculator">500 + 80</gadget>
<output>580</output>

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

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

<gadget id="calculator">580 + 40</gadget>
<output>620</output>
<result>620</result>

Choices:
A. $ 430
B. $ 620
C. $ 650
D. $ 680
E. $ 770

add(add(multiply(100, 5), multiply(40, 2)), multiply(multiply(10, 2), const_2))

Explanation: "for 100 - 40 - 10 = 50 pages only cost is 5 $ per page for the first time page is typed - 50 * 5 = 250 $ ; for 40 pages the cost is : first time 5 $ + 2 $ of the first revision - 40 * ( 5 + 2 ) = 280 $ ; for 10 pages the cost is : first time 5 $ + 2 $ of the first revision + 2 $ of the second revision - 10 ( 5 + 2 + 2 ) = 90 $ ; total : 250 + 280 + 90 = 620 $ . answer : b ."


Question: some persons can do a piece of work in 32 days . two times the number of these people will do half of that work in ?

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

<gadget id="calculator">32 * (1/2)</gadget>
<output>16</output>

<gadget id="calculator">16 * (1/2)</gadget>
<output>8</output>
<result>8</result>

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

multiply(multiply(32, divide(const_1, const_2)), divide(const_1, const_2))

Explanation: 32 / ( 2 * 2 ) = 8 days answer : e


Question: a department of 10 people - 6 men and 4 women - needs to send a team of 5 to a conference . if they want to make sure that there are no more than 3 members of the team from any one gender , how many distinct groups are possible to send ?

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

<gadget id="calculator">30 * 4</gadget>
<output>120</output>

<gadget id="calculator">120 + 30</gadget>
<output>150</output>

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

Choices:
A. 120
B. 150
C. 180
D. 210
E. 240

add(add(multiply(multiply(6, 5), 4), multiply(6, 5)), multiply(6, 5))

Explanation: they can make a team of 3 men and 2 women . the number of ways to do this is 6 c 3 * 4 c 2 = 20 * 6 = 120 they can make a team of 2 men and 3 women . the number of ways to do this is 6 c 2 * 4 c 3 = 15 * 4 = 60 the total number of distinct groups is 180 . the answer is c .


Question: forks , spoons , and knives in drawer are in the ratio of 4 : 4 : 3 . if there are 16 forks , the number of knives in the drawer is :

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

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

Choices:
A. 8
B. 4
C. 12
D. 16
E. 14

Explanation: explanation : let forks = 4 x , spoons = 4 x & knives = 3 x . now , 4 x = 16 hence x = 4 . number of knives = 3 x = 12 . answer : c


Question: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 6000 , the number of valid votes that the other candidate got , was :

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

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

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

<gadget id="calculator">1 - (11/20)</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">(4/5) * (9/20)</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(9/25) * 6_000</gadget>
<output>2_160</output>
<result>2_160</result>

Choices:
A. 2800
B. 2700
C. 2160
D. 2200
E. 2300

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 6000)

Explanation: "c number of valid votes = 80 % of 6000 = 4800 . valid votes polled by other candidate = 45 % of 4800 = ( 45 / 100 x 4800 ) = 2160 ."


Question: 10 : 4 seconds : : ? : 6 minutes

<gadget id="calculator">10 / 4</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">6 * (5/2)</gadget>
<output>15</output>
<result>15</result>

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

Explanation: "10 * 6 = 4 * x x = 15 answer : b"


Question: a train passes a platform in 36 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is

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

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

<gadget id="calculator">36 - 20</gadget>
<output>16</output>

<gadget id="calculator">15 * 16</gadget>
<output>240</output>
<result>240</result>

Choices:
A. 240
B. 250
C. 260
D. 230
E. 220

multiply(multiply(const_0_2778, 54), subtract(36, 20))

Explanation: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 36 = > 300 + l = 15 × 36 = 540 = > l = 540 - 300 = 240 meter answer is a ."


Question: if two dice are thrown together , the probability of getting a doublet on the dice is

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

<gadget id="calculator">6 / 36</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>

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

Explanation: "the number of exhaustive outcomes is 36 . let e be the event of getting doublet on the dies is 6 / 36 = 1 / 6 p ( e ) = 1 / 6 . a )"


Question: a 6 % stock yields 9 % . the market value of the stock is :

<gadget id="calculator">100 / 9</gadget>
<output>100/9 = around 11.111111</output>

<gadget id="calculator">(100/9) * 6</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>

Choices:
A. rs 66.55
B. rs 68.55
C. rs 69.55
D. rs 65.55
E. rs 66.66

Explanation: "explanation : for an income of rs . 9 , investment = rs . 100 . for an income of rs 6 , investment = rs . 100 / 9 x 6 = rs 66.66 market value of rs . 100 stock = rs . 66.66 answer is e"


Question: jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 25 / 36 , what is the probability that the next one she draws will be pink ?

<gadget id="calculator">25 / 36</gadget>
<output>25/36 = around 0.694444</output>

<gadget id="calculator">(25/36) ** (1/2)</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">1 - (5/6)</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>

Choices:
A. 1 / 6
B. 4 / 7
C. 3 / 7
D. 16 / 49
E. 40 / 49

Explanation: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 25 / 36 = ( 5 / 6 ) * ( 5 / 6 ) therefore probability that the next one she draws is pink = 1 / 6 option ( a )"


Question: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 253 games will be played during the tournament . what is the number of participants ?

<gadget id="calculator">253 * 2</gadget>
<output>506</output>

<gadget id="calculator">506 * 4</gadget>
<output>2_024</output>

<gadget id="calculator">2_024 + 1</gadget>
<output>2_025</output>

<gadget id="calculator">2_025 ** (1/2)</gadget>
<output>45</output>

<gadget id="calculator">45 + 1</gadget>
<output>46</output>

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

Choices:
A. 21
B. 22
C. 23
D. 24
E. 25

divide(add(sqrt(add(multiply(multiply(253, const_2), const_4), const_1)), const_1), const_2)

Explanation: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 253 n * ( n - 1 ) = 506 = 23 * 22 ( trial and error ) the answer is c ."


Question: it takes 10 days for digging a trench of 100 m long , 50 m broad and 10 m deep . what length of trench , 25 m broad and 15 m deep can be dug in 30 days ?

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

<gadget id="calculator">1_500 * 10</gadget>
<output>15_000</output>

<gadget id="calculator">15_000 * 100</gadget>
<output>1_500_000</output>

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

<gadget id="calculator">15 * 250</gadget>
<output>3_750</output>

<gadget id="calculator">1_500_000 / 3_750</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 400 m
B. 200 m
C. 100 m
D. 89 m
E. 79 m

divide(multiply(multiply(multiply(30, 50), 10), 100), multiply(15, multiply(10, 25)))

Explanation: more days , more length ( direct ) less breadth , more length ( indirect ) more depth , less length ( indirect days 10 : 30 ; breadth 25 : 50 ; : : 100 : x depth 15 : 10 ; : . 10 * 25 * 15 * x = 30 * 50 * 10 * 100 x = ( 30 * 50 * 10 * 100 ) / 10 * 25 * 15 = 400 so the required length = 400 m answer : a


Question: if 20 men can build a water fountain 56 metres long in 3 days , what length of a similar water fountain can be built by 35 men in 3 days ?

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

<gadget id="calculator">56 / 60</gadget>
<output>14/15 = around 0.933333</output>

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

<gadget id="calculator">(14/15) * 105</gadget>
<output>98</output>
<result>98</result>

Choices:
A. 40 m
B. 64 m
C. 77 m
D. 89 m
E. 98 m

multiply(divide(56, multiply(20, 3)), multiply(35, 3))

Explanation: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 3 : 3 : : 56 : x therefore ( 20 x 3 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 60 = 98 hence , the required length is 98 m . answer : e"


Question: p has $ 63 more than what q and r together would have had if both b and c had 1 / 9 of what p has . how much does p have ?

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

<gadget id="calculator">(1/9) * 2</gadget>
<output>2/9 = around 0.222222</output>

<gadget id="calculator">1 - (2/9)</gadget>
<output>7/9 = around 0.777778</output>

<gadget id="calculator">63 / (7/9)</gadget>
<output>81</output>
<result>81</result>

Choices:
A. $ 69
B. $ 72
C. $ 75
D. $ 78
E. $ 81

divide(63, subtract(const_1, multiply(divide(1, 9), const_2)))

Explanation: p = ( 2 / 9 ) * p + 63 ( 7 / 9 ) * p = 63 p = 81 the answer is e .


Question: a train running at the speed of 110 km / hr crosses a pole in 9 sec . what is the length of the train ?

<gadget id="calculator">110 * 1_000</gadget>
<output>110_000</output>

<gadget id="calculator">110_000 / 3_600</gadget>
<output>275/9 = around 30.555556</output>

<gadget id="calculator">(275/9) * 9</gadget>
<output>275</output>
<result>275</result>

Choices:
A. 298 m
B. 275 m
C. 208 m
D. 988 m
E. 299 m

multiply(divide(multiply(110, const_1000), const_3600), 9)

Explanation: "speed = 110 * 5 / 18 = 275 / 9 m / sec length of the train = speed * time = 275 / 9 * 9 = 275 m answer : b"


Question: if 2 ^ y = 4 ^ ( 5 x + 3 ) and 3 ^ ( x - 7 ) = 9 ^ y , what is the value of x + y ?

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

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

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

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

<gadget id="calculator">(-7) + (-12)</gadget>
<output>-19</output>

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

<gadget id="calculator">20 - 1</gadget>
<output>19</output>

<gadget id="calculator">(-19) / 19</gadget>
<output>-1</output>

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

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

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

Choices:
A. - 10
B. - 5
C. - 4
D. 3
E. 7

add(divide(add(divide(add(negate(7), negate(multiply(multiply(2, 3), 2))), subtract(multiply(2, const_10), const_1)), negate(7)), 2), divide(add(negate(7), negate(multiply(multiply(2, 3), 2))), subtract(multiply(2, const_10), const_1)))

Explanation: 2 ^ y = 4 ^ ( 5 x + 3 ) 2 ^ y = 2 ^ 2 ( 5 x + 3 ) y = 10 x + 6 . . . . . . . . . . . 1 3 ^ ( x - 7 ) = 9 ^ y 3 ^ ( x - 7 ) = 3 ^ 2 y x - 7 = 2 y . . . . . . . . . . . . . 2 put value of y = 10 x + 6 in eq 2 x - 7 = 2 ( 10 x + 6 ) x - 7 = 20 x + 12 19 x = - 19 x = - 1 therefore , y = - 10 + 6 y = - 4 x + y = - 1 - 4 = - 5 answer : b


Question: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 140 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?

<gadget id="calculator">240 + 140</gadget>
<output>380</output>

<gadget id="calculator">45 - 9</gadget>
<output>36</output>

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

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

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

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

<gadget id="calculator">380 / 10</gadget>
<output>38</output>
<result>38</result>

Choices:
A. 28 sec
B. 16 sec
C. 38 sec
D. 18 sec
E. 17 sec

divide(add(240, 140), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2))))

Explanation: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 140 = 380 m . time taken = 380 / 10 = 38 sec . answer : c"


Question: of the 75 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?

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

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

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

<gadget id="calculator">20 + 35</gadget>
<output>55</output>

<gadget id="calculator">75 - 55</gadget>
<output>20</output>
<result>20</result>

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

subtract(75, add(add(subtract(50, 35), subtract(40, 35)), 35))

Explanation: "neither car nor garage = total - garage - ( swim - common ) = 75 - 50 - ( 40 - 35 ) = 75 - 55 = 20 answer c"


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

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

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

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

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

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

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

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


Question: in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability w this college graduate has a graduate degree ?

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

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

<gadget id="calculator">(1/8) / (2/3)</gadget>
<output>3/16 = around 0.1875</output>

<gadget id="calculator">(3/16) + 1</gadget>
<output>19/16 = around 1.1875</output>

<gadget id="calculator">(3/16) / (19/16)</gadget>
<output>3/19 = around 0.157895</output>
<result>3/19 = around 0.157895</result>

Choices:
A. 1 / 11
B. 1 / 12
C. 1 / 13
D. 3 / 19
E. 3 / 43

divide(divide(divide(1, 8), divide(2, 3)), add(divide(divide(1, 8), divide(2, 3)), 1))

Explanation: "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability w of cgd / ( cg ) - > 3 / 19 answer d"


Question: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 25 % ?

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

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

<gadget id="calculator">75 / (2/3)</gadget>
<output>225/2 = around 112.5</output>

<gadget id="calculator">(225/2) - 100</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>

Choices:
A. 20 %
B. 26 %
C. 42 %
D. 27 %
E. 12.5 %

subtract(divide(subtract(const_100, 25), divide(2, 3)), const_100)

Explanation: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 75 2 / 3 sp 1 = 75 sp 1 = 112.50 100 - - - 12.5 = > 12.5 % answer : e"


Question: how many 5 - digit numbers are there , if the two leftmost digits are even , the other digits are odd and the digit 2 can not appear more than once in the number .

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

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

<gadget id="calculator">12 + 7</gadget>
<output>19</output>

<gadget id="calculator">5 ** 3</gadget>
<output>125</output>

<gadget id="calculator">19 * 125</gadget>
<output>2_375</output>
<result>2_375</result>

Choices:
A. 2200
B. 2295
C. 2375
D. 2380
E. 2385

multiply(add(multiply(const_3, const_4), add(const_3, const_4)), power(5, const_3))

Explanation: n = ( 4 * 5 - 1 ) * 5 * 5 * 5 = 2375 where 4 cases of first digit { 2,4 , 6,8 } 5 cases of second digit { 0 , 2,4 , 6,8 } 1 case of 22 for two leftmost digit 5 cases of third digit { 1 , 3,5 , 7,9 } 5 cases of fourth digit { 1 , 3,5 , 7,9 } 5 cases of fifth digit { 1 , 3,5 , 7,9 } c


Question: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1081 . find the cost of each ice - cream cup ?

<gadget id="calculator">16 * 6</gadget>
<output>96</output>

<gadget id="calculator">1_081 - 96</gadget>
<output>985</output>

<gadget id="calculator">5 * 45</gadget>
<output>225</output>

<gadget id="calculator">985 - 225</gadget>
<output>760</output>

<gadget id="calculator">7 * 70</gadget>
<output>490</output>

<gadget id="calculator">760 - 490</gadget>
<output>270</output>

<gadget id="calculator">270 / 6</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 25
B. 66
C. 77
D. 99
E. 45

divide(subtract(subtract(subtract(1081, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6)

Explanation: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1081 96 + 225 + 490 + 6 x = 1081 6 x = 270 = > x = 45 . answer : e"


Question: selling an kite for rs . 30 , a shop keeper gains 40 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?

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

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

<gadget id="calculator">(3/10) * 90</gadget>
<output>27</output>

<gadget id="calculator">30 * 100</gadget>
<output>3_000</output>

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

<gadget id="calculator">3_000 / 140</gadget>
<output>150/7 = around 21.428571</output>

<gadget id="calculator">27 - (150/7)</gadget>
<output>39/7 = around 5.571429</output>

<gadget id="calculator">(39/7) / (150/7)</gadget>
<output>13/50 = around 0.26</output>

<gadget id="calculator">(13/50) * 100</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 8 %
B. 10 %
C. 11 %
D. 15 %
E. 26 %

multiply(divide(subtract(multiply(divide(30, const_100), subtract(const_100, 10)), divide(multiply(30, const_100), add(40, const_100))), divide(multiply(30, const_100), add(40, const_100))), const_100)

Explanation: "explanation : marked price = rs . 30 c . p . = 100 / 140 * 30 = rs . 21.42 sale price = 90 % of rs . 30 = rs . 27 required gain % = 5.57 / 21.42 * 100 = 26 % . answer : e"


Question: at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 75 . if the restaurant serves 120 customers today , raising the average to 80 customers per day , what is the value of x ?

<gadget id="calculator">120 - 80</gadget>
<output>40</output>

<gadget id="calculator">80 - 75</gadget>
<output>5</output>

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

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

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

<gadget id="calculator">8 - (1/5)</gadget>
<output>39/5 = around 7.8</output>
<result>39/5 = around 7.8</result>

Choices:
A. 2
B. 5
C. 7
D. 8
E. 20

subtract(divide(subtract(120, 80), subtract(80, 75)), divide(subtract(120, const_100), const_100))

Explanation: "withoutusing the formula , we can see that today the restaurant served 40 customers above the average . the total amount above the average must equal total amount below the average . this additional 40 customers must offset the “ deficit ” below the average of 80 created on the x days the restaurant served only 75 customers per day . 40 / 5 = 8 days . choice ( a ) . withthe formula , we can set up the following : 80 = ( 75 x + 120 ) / ( x + 1 ) 80 x + 80 = 75 x + 120 5 x = 40 x = 8 answer choice ( d )"


Question: an inspector rejects 15 % of the meters as defective . how many will he examine to reject 15 ?

<gadget id="calculator">15 * 100</gadget>
<output>1_500</output>

<gadget id="calculator">1_500 / 15</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 100
B. 120
C. 250
D. 200
E. 160

Explanation: "then , 15 % of x = 15 ( 15 / 100 ) x = 15 x = ( 15 * 100 * ) / 15 = 100 answer is a"


Question: pipe a fills a tank of capacity 700 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?

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

<gadget id="calculator">70 - 20</gadget>
<output>50</output>

<gadget id="calculator">700 / 50</gadget>
<output>14</output>

<gadget id="calculator">14 * 3</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 42 minutes
B. 14 minutes
C. 39 minutes
D. 40 minutes 20 seconds
E. none of these

multiply(divide(700, subtract(add(40, 30), 20)), const_3)

Explanation: "in one cycle they fill 40 + 30 - 20 = 50 liters 700 = 50 * n = > n = 14 here n = number of cycles . total time = 14 * 3 = 42 as in one cycle there are 3 minutes . thus 42 minutes answer : a"


Question: the area of a parallelogram is 72 sq m and its altitude is twice the corresponding base . then the length of the base is ?

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

<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6
B. 16
C. 8
D. 36
E. none

Explanation: "2 x * x = 72 = > x = 6 answer : a"


Question: a and b can finish a work together in 12 days , and b and c together in 16 days . if a alone works for 5 days and then b alone continues for 7 days , then remaining work is done by c in 13 days . in how many days can c alone finish the complete work ?

<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>

<gadget id="calculator">2 / 16</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(5/12) + (1/8)</gadget>
<output>13/24 = around 0.541667</output>

<gadget id="calculator">1 - (13/24)</gadget>
<output>11/24 = around 0.458333</output>

<gadget id="calculator">5 + 13</gadget>
<output>18</output>

<gadget id="calculator">18 - 7</gadget>
<output>11</output>

<gadget id="calculator">(11/24) / 11</gadget>
<output>1/24 = around 0.041667</output>

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

Choices:
A. 22 days
B. 21 days
C. 25 days
D. 24 days
E. 23 days

divide(const_1, divide(subtract(const_1, add(divide(5, 12), divide(const_2, 16))), subtract(add(5, 13), 7)))

Explanation: here lcm of 12 and 16 is taken as total work . ( becomes easy to solve ) assume total work = 48 units then workdone by ( a + b ) in one day = 48 / 12 = 4 units similarly , by ( b + c ) in one day = 48 / 16 = 3 units now according to question , a works 5 days , b for 7 days and c for 13 days to complete total work so , 5 a + 7 b + 13 c = 48 units 5 ( a + b ) + 2 ( b + c ) + 11 c = 48 units 5 * 4 + 2 * 3 + 11 c = 48 units 11 c = 22 units c = 2 units ( c does 2 units of work daily ) therefore , 48 / 2 = 24 days c requires 24 days to complete the work alone . answer d


Question: the ages of two person , differ by 20 years . if 5 years ag , the elder one be 5 times as old as the younger one their present ages ( in years ) are respectively

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

Choices:
A. 30 , 10
B. 2010
C. 3515
D. 5117
E. 20,17

Explanation: let their ages be x and ( x + 20 ) years ( x - 5 ) * 5 = ( x + 20 - 5 ) after solving this we get x = 10 years the age of elder one = 10 + 20 = 30 years so the present ages are 30 and 10 years answer : a


Question: the price of stock increased by 8 % last year and decreased by 6 % this year . what is the net percentage change in the price of the stock ?

<gadget id="calculator">100 + 8</gadget>
<output>108</output>

<gadget id="calculator">108 / 100</gadget>
<output>27/25 = around 1.08</output>

<gadget id="calculator">100 - 6</gadget>
<output>94</output>

<gadget id="calculator">94 / 100</gadget>
<output>47/50 = around 0.94</output>

<gadget id="calculator">(27/25) * (47/50)</gadget>
<output>1_269/1_250 = around 1.0152</output>

<gadget id="calculator">(1_269/1_250) * 100</gadget>
<output>2_538/25 = around 101.52</output>

<gadget id="calculator">(2_538/25) - 100</gadget>
<output>38/25 = around 1.52</output>
<result>38/25 = around 1.52</result>

Choices:
A. 0.2 %
B. 0.8 %
C. 1.2 %
D. 1.52 %
E. 2 %

subtract(multiply(multiply(divide(add(const_100, 8), const_100), divide(subtract(const_100, 6), const_100)), const_100), const_100)

Explanation: ( 100 % + 8 % ) * ( 100 % - 6 % ) = 1.08 * 0.94 = 1.0152 = 101.52 % . the net percentage change in the price of the stock is ( + ) 1.52 % the answer is d


Question: the mass of 1 cubic meter of a substance is 400 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )

<gadget id="calculator">1_000 * 1_000</gadget>
<output>1_000_000</output>

<gadget id="calculator">400 * 1_000</gadget>
<output>400_000</output>

<gadget id="calculator">1_000_000 / 400_000</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>

Choices:
A. 1.5
B. 2.5
C. 3.5
D. 4.5
E. 5.5

Explanation: "400 kg - 1 cubic meter ; 400,000 g - 1 cubic meter ; 400,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 400,000 = 10 / 4 = 2.5 cubic centimeters . answer : b ."


Question: a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 24 cm . what is the length of the wire ?

<gadget id="calculator">12 ** 3</gadget>
<output>1_728</output>

<gadget id="calculator">24 ** 2</gadget>
<output>576</output>

<gadget id="calculator">1_728 / 576</gadget>
<output>3</output>

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

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

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

divide(multiply(const_4, divide(power(12, const_3), power(24, const_2))), const_3)

Explanation: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 24 ) ^ 2 * h = ( 4 / 3 ) π ( 12 ) ^ 3 = > h = 4 cm answer : b"


Question: boys and girls in a class are writing letters . there are twice as many girls as boys in the class , and each girl writes 3 more letters than each boy . if boys write 24 of the 90 total letters written by the class , how many letters does each boy write ?

<gadget id="calculator">3 * 24</gadget>
<output>72</output>

<gadget id="calculator">90 - 72</gadget>
<output>18</output>

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

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

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

Choices:
A. 3
B. 4
C. 6
D. 8
E. 12

divide(24, divide(subtract(90, multiply(3, 24)), multiply(3, const_2)))

Explanation: there are twice as many girls as boys in the class - - > g = 2 b . each girl writes 3 more letters than each boy - - > boys write x letters , girls write x + 3 letters . boys write 24 letters - - > bx = 24 . girls write 90 - 24 = 66 letters - - > ( 2 b ) ( x + 3 ) = 66 - - > 2 bx + 6 b = 66 - - > 2 * 24 + 6 b = 66 - - > b = 3 . bx = 24 - - > 3 x = 24 - - > x = 8 . answer : d .


Question: a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in meters ) is :

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

<gadget id="calculator">5_000 / 60</gadget>
<output>250/3 = around 83.333333</output>

<gadget id="calculator">(250/3) * 15</gadget>
<output>1_250</output>
<result>1_250</result>

Choices:
A. 600
B. 750
C. 1000
D. 1250
E. none of these

multiply(divide(multiply(5, const_1000), const_60), 15)

Explanation: "speed = ( 5 * 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 * 15 * 60 ) m = 1250 m . correct option : d"


Question: mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8010 / - . find out the amount that he borrowed .

<gadget id="calculator">6 * 9</gadget>
<output>54</output>

<gadget id="calculator">54 / 100</gadget>
<output>27/50 = around 0.54</output>

<gadget id="calculator">1 + (27/50)</gadget>
<output>77/50 = around 1.54</output>

<gadget id="calculator">8_010 / (77/50)</gadget>
<output>400_500/77 = around 5_201.298701</output>
<result>400_500/77 = around 5_201.298701</result>

Choices:
A. s . 5266
B. s . 5269
C. s . 5228
D. s . 5201
E. s . 52192

divide(8010, add(const_1, divide(multiply(6, 9), const_100)))

Explanation: "explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8010 = p + ( 54 p / 100 ) 8010 = ( 100 p + 54 p ) / 100 8010 = 154 p / 100 p = ( 8010 * 100 ) / 154 = rs . 5201.298 answer : d"


Question: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 6500 , the number of valid votes that the other candidate got , was :

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

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

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

<gadget id="calculator">1 - (11/20)</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">(4/5) * (9/20)</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(9/25) * 6_500</gadget>
<output>2_340</output>
<result>2_340</result>

Choices:
A. 2800
B. 2700
C. 2900
D. 2340
E. 2300

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 6500)

Explanation: "d number of valid votes = 80 % of 6500 = 5200 . valid votes polled by other candidate = 45 % of 5200 = ( 45 / 100 x 5200 ) = 2340 ."


Question: if 9 ! / 3 ^ x is an integer , what is the greatest possible value of x ?

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

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

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

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

add(divide(9, 3), divide(3, divide(9, 3)))

Explanation: 9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 4 is allowed . imo b .


Question: the average of 13 result is 60 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th result ?

<gadget id="calculator">7 * 57</gadget>
<output>399</output>

<gadget id="calculator">7 * 61</gadget>
<output>427</output>

<gadget id="calculator">399 + 427</gadget>
<output>826</output>

<gadget id="calculator">13 * 60</gadget>
<output>780</output>

<gadget id="calculator">826 - 780</gadget>
<output>46</output>
<result>46</result>

Choices:
A. 35
B. 37
C. 46
D. 48
E. 50

subtract(add(multiply(7, 57), multiply(7, 61)), multiply(13, 60))

Explanation: sum of all the 13 results = 13 * 60 = 780 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 780 = 46 . c


Question: after decreasing 25 % in the price of an article costs rs . 1500 . find the actual cost of an article ?

<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_500 / (3/4)</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. 1400
B. 1300
C. 1200
D. 2000
E. 1500

divide(1500, subtract(const_1, divide(25, const_100)))

Explanation: "cp * ( 75 / 100 ) = 1500 cp = 20 * 100 = > cp = 2000 answer : d"


Question: if the sides of a triangle are 52 cm , 48 cm and 20 cm , what is its area ?

<gadget id="calculator">48 * 20</gadget>
<output>960</output>

<gadget id="calculator">960 / 2</gadget>
<output>480</output>
<result>480</result>

Choices:
A. 480 cm 2
B. 765 cm 2
C. 216 cm 2
D. 197 cm 2
E. 275 cm 2

Explanation: "the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a"


Question: 5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3443 , how much was it in the beginning ?

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

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

<gadget id="calculator">100 - 15</gadget>
<output>85</output>

<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">(19/20) * (17/20)</gadget>
<output>323/400 = around 0.8075</output>

<gadget id="calculator">3_443 / (323/400)</gadget>
<output>1_377_200/323 = around 4_263.77709</output>

<gadget id="calculator">floor(1_377_200/323)</gadget>
<output>4_263</output>
<result>4_263</result>

Choices:
A. 4264
B. 2776
C. 4400
D. 2871
E. 881

floor(divide(3443, multiply(divide(subtract(const_100, 5), const_100), divide(subtract(const_100, 15), const_100))))

Explanation: "x * ( 95 / 100 ) * ( 85 / 100 ) = 3443 x = 4264 answer : a"


Question: 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 6 men , 4 women and 10 children together complete the piece of work ?

<gadget id="calculator">24 * 10</gadget>
<output>240</output>

<gadget id="calculator">1 / 240</gadget>
<output>1/240 = around 0.004167</output>

<gadget id="calculator">10 * (1/240)</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">12 * 8</gadget>
<output>96</output>

<gadget id="calculator">1 / 96</gadget>
<output>1/96 = around 0.010417</output>

<gadget id="calculator">(1/96) * 6</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">48 * 4</gadget>
<output>192</output>

<gadget id="calculator">1 / 192</gadget>
<output>1/192 = around 0.005208</output>

<gadget id="calculator">(1/192) * 4</gadget>
<output>1/48 = around 0.020833</output>

<gadget id="calculator">(1/16) + (1/48)</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/24) + (1/12)</gadget>
<output>1/8 = around 0.125</output>

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

Choices:
A. 5 days
B. 15 days
C. 28 days
D. 8 days
E. 7 days

inverse(add(multiply(10, inverse(multiply(24, 10))), add(multiply(inverse(multiply(12, 8)), 6), multiply(inverse(multiply(48, 4)), 4))))

Explanation: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 6 men ’ s 1 day ’ s work = 1 × 6 / 96 = 1 / 16 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 6 men + 4 women + 10 children ) ’ s 1 day ’ s work = 1 / 16 + 1 / 48 + 1 / 24 = 1 / 8 the required no . of days = 8 days answer : option d"


Question: if henry were to add 6 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?

<gadget id="calculator">7 / 8</gadget>
<output>7/8 = around 0.875</output>

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

<gadget id="calculator">(7/8) - (3/4)</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">1 / (1/8)</gadget>
<output>8</output>

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

Choices:
A. 25
B. 48
C. 64
D. 80
E. 96

multiply(6, divide(const_1, subtract(divide(7, 8), divide(3, 4))))

Explanation: "7 / 8 x - 3 / 4 x = 6 galls 1 / 8 * x = 6 gallons x = 48 gallons answer b"


Question: in what time will a railway train 120 m long moving at the rate of 70 kmph pass a telegraph post on its way ?

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

<gadget id="calculator">70 * (5/18)</gadget>
<output>175/9 = around 19.444444</output>

<gadget id="calculator">120 / (175/9)</gadget>
<output>216/35 = around 6.171429</output>
<result>216/35 = around 6.171429</result>

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

Explanation: "t = 120 / 70 * 18 / 5 = 6 sec answer : d"


Question: there are 400 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?

<gadget id="calculator">99 / 100</gadget>
<output>99/100 = around 0.99</output>

<gadget id="calculator">400 * (99/100)</gadget>
<output>396</output>

<gadget id="calculator">98 / 100</gadget>
<output>49/50 = around 0.98</output>

<gadget id="calculator">400 * (49/50)</gadget>
<output>392</output>

<gadget id="calculator">396 - 392</gadget>
<output>4</output>

<gadget id="calculator">1 - (49/50)</gadget>
<output>1/50 = around 0.02</output>

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

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

divide(subtract(multiply(400, divide(99, const_100)), multiply(400, divide(98, const_100))), subtract(const_1, divide(98, const_100)))

Explanation: "there are 396 managers and 4 others . the 4 others would compose 2 % of the total number of people if there were 200 people in the room . thus 200 managers must leave . the answer is d ."


Question: each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 97 % water by weight . what is the new weight of the cucumbers , in pounds ?

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

<gadget id="calculator">100 - 97</gadget>
<output>3</output>

<gadget id="calculator">1 / 3</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. 2
B. 33
C. 92
D. 96
E. 98

multiply(divide(subtract(100, 99), subtract(100, 97)), 100)

Explanation: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 97 % water and 3 % of non - water , so now 1 pound of non - water composes 3 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.03 = 34 pounds . answer : b ."


Question: a light flashes every 5 seconds , how many times will it flash in ? of an hour ?

<gadget id="calculator">3_600 / 5</gadget>
<output>720</output>
<result>720</result>

Choices:
A. 720
B. 600
C. 650
D. 700
E. 750

Explanation: "1 flash = 5 sec for 1 min = 12 flashes so for 1 hour = 12 * 60 = 720 flashes . answer : a"


Question: a 6 litre sol is 40 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?

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

<gadget id="calculator">(2/5) * 6</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">2 * (12/5)</gadget>
<output>24/5 = around 4.8</output>

<gadget id="calculator">6 - (24/5)</gadget>
<output>6/5 = around 1.2</output>
<result>6/5 = around 1.2</result>

Choices:
A. a . 0.6
B. b . 1.2
C. c . 2.1
D. d . 3
E. e . 5.4

subtract(6, multiply(const_2, multiply(divide(40, const_100), 6)))

Explanation: "40 % of 6 = 2.4 50 % of 6 = 3 shortage is 0.6 so we need to have 0.6 / 50 % to get 50 % alcohol content . = 1.2 b"


Question: in arun ' s opinion , his weight is greater than 63 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 66 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?

<gadget id="calculator">63 + 1</gadget>
<output>64</output>

<gadget id="calculator">66 + 64</gadget>
<output>130</output>

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

Choices:
A. 86.5 kg
B. 64.5 kg
C. 46.5 kg
D. 26.5 kg
E. 16.5 kg

divide(add(66, add(63, const_1)), const_2)

Explanation: "let arun ' s weight be x kg . according to arun , 63 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 66 . the values satisfying all the above conditions are 64 and 65 . required average = ( 64 + 65 ) / 2 = 64.5 kg answer : b"


Question: a cat leaps 5 leaps for every 4 leaps of a dog , but 2 leaps of the dog are equal to 3 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?

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

<gadget id="calculator">(2/3) * 5</gadget>
<output>10/3 = around 3.333333</output>

<gadget id="calculator">(10/3) / 4</gadget>
<output>5/6 = around 0.833333</output>
<result>5/6 = around 0.833333</result>

Choices:
A. 5 : 6
B. 3 : 2
C. 4 : 8
D. 1 : 2
E. 7 : 8

Explanation: given ; 2 dog = 3 cat ; or , dog / cat = 3 / 2 ; let cat ' s 1 leap = 2 meter and dogs 1 leap = 3 meter . then , ratio of speed of cat and dog = 2 * 5 / 3 * 4 = 5 : 6 . ' ' answer : 5 : 6 ;


Question: the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 15 % profit ?

<gadget id="calculator">100 + 15</gadget>
<output>115</output>

<gadget id="calculator">115 / 100</gadget>
<output>23/20 = around 1.15</output>

<gadget id="calculator">1_920 + 1_280</gadget>
<output>3_200</output>

<gadget id="calculator">3_200 / 2</gadget>
<output>1_600</output>

<gadget id="calculator">(23/20) * 1_600</gadget>
<output>1_840</output>
<result>1_840</result>

Choices:
A. 2000
B. 2778
C. 1840
D. 2778
E. 2771

multiply(divide(add(const_100, 15), const_100), divide(add(1920, 1280), const_2))

Explanation: "let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 115 % of rs . 1600 = 115 / 100 * 1600 = rs . 1840 . answer : c"


Question: rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 125 . how much was lent at 5 % ?

<gadget id="calculator">6 * 2_500</gadget>
<output>15_000</output>

<gadget id="calculator">15_000 / 100</gadget>
<output>150</output>

<gadget id="calculator">125 - 150</gadget>
<output>-25</output>

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

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

<gadget id="calculator">(1/20) - (3/50)</gadget>
<output>-1/100 = around -0.01</output>

<gadget id="calculator">(-25) / (-1/100)</gadget>
<output>2_500</output>
<result>2_500</result>

Choices:
A. 2333
B. 2777
C. 2688
D. 1000
E. 2500

divide(subtract(125, divide(multiply(6, 2500), const_100)), subtract(divide(5, const_100), divide(6, const_100)))

Explanation: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 125 x = 2500 answer : e"


Question: surface area of two spheres are in the ratio 1 : 4 what is the ratio of their volumes ?

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

<gadget id="calculator">(1/4) ** (1/2)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) ** 3</gadget>
<output>1/8 = around 0.125</output>
<result>1/8 = around 0.125</result>

Choices:
A. 1 : 9
B. 1 : 8
C. 1 : 3
D. 1 : 4
E. 1 : 5

Explanation: 1 : 8 answer : b


Question: if the area of a circle decreases by 30 % , then the radius of a circle decreases by

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

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">(7/10) ** (1/2)</gadget>
<output>sqrt(70)/10 = around 0.83666</output>

<gadget id="calculator">1 - (sqrt(70)/10)</gadget>
<output>1 - sqrt(70)/10 = around 0.16334</output>

<gadget id="calculator">(1 - sqrt(70)/10) * 100</gadget>
<output>100 - 10*sqrt(70) = around 16.333997</output>
<result>100 - 10*sqrt(70) = around 16.333997</result>

Choices:
A. 20 %
B. 16 %
C. 36 %
D. 64 %
E. none of these

multiply(subtract(const_1, sqrt(divide(subtract(const_100, 30), const_100))), const_100)

Explanation: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 30 ) % = ( 100 − 10 √ 70 ) % = 100 - 84 = 16 % answer b"


Question: the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 25 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?

<gadget id="calculator">24 / 10</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">25 * 6</gadget>
<output>150</output>

<gadget id="calculator">150 / 2</gadget>
<output>75</output>

<gadget id="calculator">(12/5) * 75</gadget>
<output>180</output>

<gadget id="calculator">4 * 180</gadget>
<output>720</output>

<gadget id="calculator">3 * 75</gadget>
<output>225</output>

<gadget id="calculator">720 + 225</gadget>
<output>945</output>

<gadget id="calculator">5 * 25</gadget>
<output>125</output>

<gadget id="calculator">945 + 125</gadget>
<output>1_070</output>
<result>1_070</result>

Choices:
A. 347
B. 987
C. 1070
D. 1371
E. 1667

add(add(multiply(4, multiply(divide(24, 10), divide(multiply(25, 6), 2))), multiply(3, divide(multiply(25, 6), 2))), multiply(5, 25))

Explanation: "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 25 = 2 r a = 12 / 5 r and r = 75 a = 180 required total cost = 4 * 180 + 3 * 75 + 5 * 25 = 720 + 225 + 125 = $ 1070 c"


Question: in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?

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

<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">(2/5) * (4/5)</gadget>
<output>8/25 = around 0.32</output>

<gadget id="calculator">1 - (8/25)</gadget>
<output>17/25 = around 0.68</output>
<result>17/25 = around 0.68</result>

Choices:
A. 0.9
B. 0.7
C. 0.45
D. 0.3
E. 0.25

subtract(const_1, multiply(divide(40, const_100), divide(subtract(const_100, 20), const_100)))

Explanation: "percent of students who are 25 years old or older is 0.4 * 48 + 0.2 * 52 = ~ 30 , so percent of people who are less than 25 years old is 100 - 30 = 70 . answer : b ."


Question: a train 300 m long , running with a speed of 54 km / hr will pass a tree in ?

<gadget id="calculator">54 * 1_000</gadget>
<output>54_000</output>

<gadget id="calculator">300 / 54_000</gadget>
<output>1/180 = around 0.005556</output>

<gadget id="calculator">(1/180) * 3_600</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 17 sec
B. 16 sec
C. 20 sec
D. 14 sec
E. 12 sec

multiply(divide(300, multiply(54, const_1000)), const_3600)

Explanation: "speed = 54 * 5 / 18 = 15 m / sec time taken = 300 * 1 / 15 = 20 sec answer : c"


Question: a student got twice as many sums wrong as he got right . if he attempted 27 sums in all , how many did he solve correctly ?

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

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

Choices:
A. 12
B. 16
C. 18
D. 9
E. 12

Explanation: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 27 3 x = 27 x = 9 . answer : d"


Question: the compound interest on a sum for 2 years is rs . 832 and the simple interest on the same sum for the same period is rs . 800 . the difference between the compound and simple interest for 3 years will be

<gadget id="calculator">832 - 800</gadget>
<output>32</output>

<gadget id="calculator">800 / 2</gadget>
<output>400</output>

<gadget id="calculator">32 / 400</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">832 * (2/25)</gadget>
<output>1_664/25 = around 66.56</output>

<gadget id="calculator">32 + (1_664/25)</gadget>
<output>2_464/25 = around 98.56</output>
<result>2_464/25 = around 98.56</result>

Choices:
A. rs . 48
B. rs . 98.56
C. rs . 66.56
D. rs . 66.58
E. none of these

add(subtract(832, 800), multiply(832, divide(subtract(832, 800), divide(800, 2))))

Explanation: explanation : given that simple interest for 2 years is rs . 800 i . e . , simple interest for 1 st year is rs . 400 and simple interest for 2 nd year is also rs . 400 compound interest for 1 st year will be 400 and compound interest for 2 nd year will be 832 - 400 = 432 you can see that compound interest for 2 nd year is more than simple interest for 2 nd year by 432 - 400 = rs . 32 i . e , rs . 32 is the interest obtained for rs . 400 for 1 year rate , r = 100 × si / pt = ( 100 × 32 ) / ( 400 × 1 ) = 8 % difference between compound and simple interest for the 3 rd year = simple interest obtained for rs . 832 = prt / 100 = ( 832 × 8 × 1 ) / 100 = rs . 66.56 total difference between the compound and simple interest for 3 years = 32 + 66.56 = rs . 98.56 answer : option b


Question: the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8463 for a computer table , then what was the cost price of the computer table ?

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

<gadget id="calculator">1 + (6/25)</gadget>
<output>31/25 = around 1.24</output>

<gadget id="calculator">8_463 / (31/25)</gadget>
<output>6_825</output>
<result>6_825</result>

Choices:
A. 6727
B. 6825
C. 6728
D. 6725
E. 2871

divide(8463, add(const_1, divide(24, const_100)))

Explanation: ": cp = sp * ( 100 / ( 100 + profit % ) ) = 8463 ( 100 / 124 ) = rs . 6825 . answer : b"


Question: 15 beavers , working together in a constant pace , can build a dam in 4 hours . how many hours will it take 20 beavers that work at the same pace , to build the same dam ?

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

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

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

Explanation: "total work = 15 * 4 = 60 beaver hours 20 beaver * x = 60 beaver hours x = 60 / 20 = 3 answer : e"


Question: the sum q of prime numbers that are greater than 60 but less than 70 is

<gadget id="calculator">60 + 1</gadget>
<output>61</output>

<gadget id="calculator">70 - 3</gadget>
<output>67</output>

<gadget id="calculator">61 + 67</gadget>
<output>128</output>
<result>128</result>

Choices:
A. 67
B. 128
C. 191
D. 197
E. 260

add(add(60, const_1), subtract(70, const_3))

Explanation: a prime number is a number that has only two factors : 1 and itself . therefore , a prime number is divisible by two numbers only . let ' s list the numbers from 61 to 69 . 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 immediately we can eliminate the even numbers because they are divisible by 2 and thus are not prime . we are now left with : 61 , 63 , 65 , 67 , 69 we can next eliminate 65 because 65 is a multiple of 5 . we are now left with 61 , 63 , 67 , 69 . to eliminate any remaining values , we would look at those that are multiples of 3 . if you don ’ t know an easy way to do this , just start with a number that is an obvious multiple of 3 , such as 60 , and then keep adding 3 . we see that 60 , 63 , 66 , 69 are all multiples of 3 and therefore are not prime . thus , we can eliminate 63 and 69 from the list because they are not prime . finally , we are left with 61 and 67 , and we must determine whether they are divisible by 7 . they are not , and therefore they must be both prime . thus , the sum q of 61 and 67 is 128 . answer b .


Question: the probability that a man will be alive for 10 more yrs is 1 / 2 & the probability that his wife will alive for 10 more yrs is 1 / 3 . the probability that none of them will be alive for 10 more yrs , is

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

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

<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">(1/2) * (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>

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

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

Explanation: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 3 ans . ( c )"


Question: if a * b = 2 a - 3 b + ab , then 3 * 5 + 5 * 3 is equal to

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

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

<gadget id="calculator">6 + 15</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 22
B. 25
C. 26
D. 28
E. 23

Explanation: 3 * 5 + 5 * 3 = ( 2 x 3 - 3 x 5 + 3 x 5 ) + ( 2 x 5 - 3 x 3 + 5 x 3 ) = 22 answer a 22


Question: if 25 ^ 5 × 5 ^ ( - 1 ) = ( 125 ) ^ x , then what is the value of x ?

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

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

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

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

divide(subtract(multiply(const_2, 5), 1), const_3)

Explanation: 25 ^ 5 × 5 ^ ( - 1 ) = ( 125 ) ^ x ( 5 ^ 2 ) ^ 5 × 5 ^ ( - 1 ) = 5 ^ 3 x 5 ^ 10 x 5 ^ ( - 1 ) = 5 ^ 3 x ; since all of the bases are the same now , we can equate the exponents in the next step 10 - 1 = 3 x 9 = 3 x x = 3 ans . b ) 3


Question: a lady starts from p towards q and realizes that at a point r , if he walks 50 km further he will be at a point s , which is as far away from r as it is from q . what is the distance between p and q if the distance between p and r is half the distance from r to q ? ( assume that p , q , r and s are all on the same straight line )

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

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

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

Choices:
A. 150 km
B. 200 km
C. 250 km
D. 125 km
E. 155 km

add(multiply(50, const_2), divide(multiply(50, const_2), const_2))

Explanation: p ___ 50 _____ r ___ 50 _____ s ____ 50 ___ q the above figure gives the locations of p , r , s & q in relation to each other . answer : a


Question: in kaya ' s teacher ' s desk there are 24 pink highlighters , 28 yellow highlighters , and 25 blue highlighters . how many highlighters are there in all ?

<gadget id="calculator">24 + 28</gadget>
<output>52</output>

<gadget id="calculator">52 + 25</gadget>
<output>77</output>
<result>77</result>

Choices:
A. 11
B. 22
C. 77
D. 33
E. 88

Explanation: "add the numbers of highlighters . 24 + 28 + 25 = 77 . answer is c ."


Question: a train speeds past a pole in 10 seconds and a platform 50 m long in 20 seconds . its length is :

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

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

Choices:
A. 30 m .
B. 40 m .
C. 60 m .
D. 50 m .
E. 70 m .

Explanation: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 10 = > y = x / 10 x + 50 / 20 = x / 10 x = 50 m . answer : option d"


Question: the denominator of a fraction is 6 greater than the numerator . if the numerator and the denominator are increased by 1 , the resulting fraction is equal to 4 â  „ 5 . what is the value of the original fraction ?

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

<gadget id="calculator">4 * 7</gadget>
<output>28</output>

<gadget id="calculator">28 - 5</gadget>
<output>23</output>

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

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

<gadget id="calculator">23 + 6</gadget>
<output>29</output>

<gadget id="calculator">23 / 29</gadget>
<output>23/29 = around 0.793103</output>
<result>23/29 = around 0.793103</result>

Choices:
A. 17 / 23
B. 23 / 29
C. 29 / 35
D. 31 / 37
E. 33 / 39

divide(divide(subtract(multiply(4, add(1, 6)), 5), subtract(5, 4)), add(divide(subtract(multiply(4, add(1, 6)), 5), subtract(5, 4)), 6))

Explanation: "let the numerator be x . then the denominator is x + 6 . x + 1 / x + 7 = 4 / 5 . 5 x + 5 = 4 x + 28 . x = 23 . the original fraction is 23 / 29 . the answer is b ."


Question: consider the sets tn = { n , n + 1 , n + 2 , n + 3 , n + 4 ) , where n = 1 , 2 , 3 , … , 96 . how many of these sets contain 6 or any integral multiple thereof ( i . e . , any one of the numbers 6 , 12 , 18 , … ) ?

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

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

<gadget id="calculator">(5/6) * 96</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 80
B. 81
C. 82
D. 83
E. 84

multiply(divide(add(const_2, const_3), 6), 96)

Explanation: explanation : if n = 1 , then the set t 1 = { 1 , 23 , 45 } , and it does not have 6 or any multiples . n = 2 to n = 6 has 6 in the set . n = 7 , has the set t 7 = { 7 , 89 , 1011 } , and no 6 or multiples . so 1 in every 6 members do not have 6 or multiples of 6 . so , till n = 96 , there are 16 sets of “ 6 members ” ( 16 * 6 = 96 ) and 16 sets do not have 6 or its multiples , while the remaining 80 sets have . answer : a


Question: car z travels 55 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?

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

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

<gadget id="calculator">(4/5) * 55</gadget>
<output>44</output>

<gadget id="calculator">44 * 10</gadget>
<output>440</output>
<result>440</result>

Choices:
A. 320
B. 375.2
C. 400
D. 408.3
E. 440

multiply(multiply(subtract(const_1, divide(20, const_100)), 55), 10)

Explanation: the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 55 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 44 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 44 miles / gallon * 10 gallons = 440 miles . answer e .


Question: a clock shows the time as 9 a . m . if the minute hand gains 6 minutes every hour , how many minutes will the clock gain by 6 p . m . ?

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

<gadget id="calculator">9 * 6</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 30 min
B. 35 min
C. 45 min
D. 50 min
E. 54 min

Explanation: "there are 9 hours in between 9 a . m . to 6 p . m . 9 * 6 = 54 minutes . answer : e"


Question: 20 people went to a hotel for combine dinner party 12 of them spent rs . 70 each on their dinner and rest spent 4 more than the average expenditure of all the 20 . what was the total money spent by them .

<gadget id="calculator">12 * 70</gadget>
<output>840</output>

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

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

<gadget id="calculator">840 + 32</gadget>
<output>872</output>

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

<gadget id="calculator">872 / 12</gadget>
<output>218/3 = around 72.666667</output>

<gadget id="calculator">(218/3) * 20</gadget>
<output>4_360/3 = around 1_453.333333</output>
<result>4_360/3 = around 1_453.333333</result>

Choices:
A. 1628.4
B. 1534
C. 1453
D. 1496
E. none of these

multiply(divide(add(multiply(12, 70), multiply(subtract(20, 12), 4)), subtract(20, subtract(20, 12))), 20)

Explanation: "solution : let average expenditure of 20 people be x . then , 20 x = 12 * 70 + 8 * ( x + 4 ) ; or , 20 x = 12 * 70 + 8 x + 32 ; or , x = 72.667 ; so , total money spent = 72.67 * 20 = rs . 1453.4 . answer : option c"


Question: what annual payment will discharge a debt of rs . 1060 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_060</gadget>
<output>23_373/20 = around 1_168.65</output>

<gadget id="calculator">(23_373/20) / 2</gadget>
<output>23_373/40 = around 584.325</output>
<result>23_373/40 = around 584.325</result>

Choices:
A. 993.2
B. 551.25
C. 570.07
D. 543.33
E. 646.33

divide(multiply(power(add(divide(5, const_100), const_1), 2), 1060), 2)

Explanation: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1060 820 x + 1060 * 441 x = 570.07 so , value of each installment = rs . 570.07 answer : option c"


Question: 50 % of the population of a village is 23040 . the total population of the village is ?

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

<gadget id="calculator">2 * 23_040</gadget>
<output>46_080</output>
<result>46_080</result>

Choices:
A. 32256
B. 24000
C. 44936
D. 46080
E. none

Explanation: "answer ∵ 50 % of p = 23040 ∴ p = ( 23040 x 100 ) / 50 = 46080 correct option : d"


Question: if the perimeter of a rectangular house is 1400 m , its length when its breadth is 300 m is ?

<gadget id="calculator">1_400 / 2</gadget>
<output>700</output>

<gadget id="calculator">700 - 300</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 300
B. 400
C. 500
D. 600
E. 700

Explanation: 2 ( l + 300 ) = 1400 = > l = 400 m answer : b


Question: if a # b = ab – b + b ^ 2 , then 3 # 4 =

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

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

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

<gadget id="calculator">8 + 16</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 2
B. 8
C. 15
D. 24
E. 35

add(subtract(multiply(3, 4), 4), power(4, 2))

Explanation: "solution - simply substitute 3 and 4 in equation in the place of a and b respectively . 3 # 4 = 3 * 4 - 4 + 4 ^ 2 = 12 - 4 + 16 = 24 . ans d"


Question: what number has a 4 : 1 ratio to the number 100 ?

<gadget id="calculator">100 * 4</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 40
B. 200
C. 400
D. 800
E. 4000

Explanation: "4 : 1 = x : 100 x = 4 * 100 x = 400 answer : c"


Question: after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 5535 . what was the number of original inhabitants ?

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

<gadget id="calculator">(9/10) * (1/4)</gadget>
<output>9/40 = around 0.225</output>

<gadget id="calculator">(9/10) - (9/40)</gadget>
<output>27/40 = around 0.675</output>

<gadget id="calculator">5_535 / (27/40)</gadget>
<output>8_200</output>
<result>8_200</result>

Choices:
A. 7900
B. 8200
C. 8500
D. 8800
E. 9100

divide(5535, subtract(subtract(const_1, divide(10, const_100)), multiply(subtract(const_1, divide(10, const_100)), divide(25, const_100))))

Explanation: "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5535 ( 27 / 40 ) * x = 5535 x = 5535 * 40 / 27 = 8200 the answer is b ."


Question: is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 42 , then how old is b ?

<gadget id="calculator">42 - 2</gadget>
<output>40</output>

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

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

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

Choices:
A. 16
B. 8
C. 9
D. 10
E. 11

multiply(divide(subtract(42, const_2), add(const_3, const_2)), const_2)

Explanation: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 42 5 x = 40 = > x = 8 hence , b ' s age = 2 x = 16 years . answer : a"


Question: last year the range of the annual bonus of the 100 employees at company x was $ 20000 . if the annual bonus of each of the 100 employees this year is 10 percent greater than it was last year , what is the range of the annual bonus of the 100 employees this year ?

<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">20_000 * (11/10)</gadget>
<output>22_000</output>
<result>22_000</result>

Choices:
A. $ 27000
B. $ 22000
C. $ 33000
D. $ 16000
E. $ 43000

multiply(20000, add(const_1, divide(10, const_100)))

Explanation: let the lowest bonus be x . therefore , highest bonus is x + 20000 . now bonus of each employee is increased by 10 % . therefore the bonus will remain arranged in the same order as before . or lowest bonus = 1.1 x and highest = 1.1 * ( x + 20000 ) or range = highest - lowest = 1.1 * ( x + 20000 ) - 1.1 x = 22000 , hence , b


Question: the list price of an article is rs . 65 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?

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

<gadget id="calculator">65 * (1/10)</gadget>
<output>13/2 = around 6.5</output>

<gadget id="calculator">65 - (13/2)</gadget>
<output>117/2 = around 58.5</output>

<gadget id="calculator">(117/2) - 56.16</gadget>
<output>2.34</output>

<gadget id="calculator">2.34 / (117/2)</gadget>
<output>0.04</output>

<gadget id="calculator">0.04 * 100</gadget>
<output>4</output>
<result>4</result>

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

multiply(divide(subtract(subtract(65, multiply(65, divide(10, const_100))), 56.16), subtract(65, multiply(65, divide(10, const_100)))), const_100)

Explanation: "explanation : 65 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 4 % answer : option b"


Question: a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 50 cents . how many cents does a solution of 1 liter of spirit and 3 liters of water cost ?

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

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

<gadget id="calculator">50 * (1/4)</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) * 4</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 13
B. 33
C. 56
D. 50
E. 52

multiply(multiply(50, divide(1, add(1, 3))), add(1, 3))

Explanation: c . 50 cents yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 50 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 25 cents . fraction of spirit is 1 / 2 . 25 = k * ( 1 / 2 ) k = 50 cost per liter = 50 * ( 1 / 4 ) ( 1 part spirit , 3 parts water ) cost for 4 liters = 50 * ( 1 / 4 ) * 4 = 50 cents d . 50 cents


Question: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1004 in total compensation , how many total hours did he work that week ?

<gadget id="calculator">16 * 40</gadget>
<output>640</output>

<gadget id="calculator">1_004 - 640</gadget>
<output>364</output>

<gadget id="calculator">100 + 75</gadget>
<output>175</output>

<gadget id="calculator">16 * 175</gadget>
<output>2_800</output>

<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>

<gadget id="calculator">364 / 28</gadget>
<output>13</output>

<gadget id="calculator">40 + 13</gadget>
<output>53</output>
<result>53</result>

Choices:
A. 36
B. 40
C. 44
D. 48
E. 53

add(40, divide(subtract(1004, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100)))

Explanation: "for 40 hrs = 40 * 16 = 640 excess = 1004 - 640 = 364 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 364 / 28 = 13 total hrs = 40 + 13 = 53 answer e 53"


Question: you have to send 3000 grapes 1000 kilometers from grapecity to appleland . your truck can carry 1000 grapes at a time . every time you travel a kilometer towards appleland you must pay a tax of 1 grape but you pay nothing when going in the other direction ( towards grapecity ) . what is highest number of grapes you can get to appleland ?

<gadget id="calculator">1_000 / 3</gadget>
<output>1_000/3 = around 333.333333</output>

<gadget id="calculator">floor(1_000/3)</gadget>
<output>333</output>

<gadget id="calculator">1_000 - 333</gadget>
<output>667</output>

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

<gadget id="calculator">667 - 500</gadget>
<output>167</output>

<gadget id="calculator">1_000 - 167</gadget>
<output>833</output>
<result>833</result>

Choices:
A. 833
B. 765
C. 665
D. 679
E. 874

subtract(1000, subtract(subtract(1000, floor(divide(1000, const_3))), divide(1000, const_2)))

Explanation: step one : first you want to make 3 trips of 1,000 grapes 333 kilometers . you will be left with 2,001 grapes and 667 kilometers to go . step two : next you want to take 2 trips of 1,000 grapes 500 kilometers . you will be left with 1,000 grapes and 167 kilometers to go ( you have to leave a grape behind ) . step three : finally , you travel the last 167 kilometers with one load of 1,000 grapes and are left with 833 grapes in appleland . correct answer is a ) 833


Question: the contents of a certain box consist of 14 apples and 25 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?

<gadget id="calculator">14 + 25</gadget>
<output>39</output>

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">14 / (7/10)</gadget>
<output>20</output>

<gadget id="calculator">39 - 20</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 3
B. 6
C. 14
D. 19
E. 20

subtract(add(14, 25), divide(14, divide(70, const_100)))

Explanation: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 25 oranges , so to get to 6 oranges , we should remove 25 - 6 = 19 oranges . answer d"


Question: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 7 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?

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

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

<gadget id="calculator">35 / 2</gadget>
<output>35/2 = around 17.5</output>
<result>35/2 = around 17.5</result>

Choices:
A. 5 : 1
B. 10 : 5
C. 15 : 2
D. 20 : 2
E. 35 : 2

Explanation: u / i = 7 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 35 : 21 : 2 i . e . u : b = 35 : 2 answer : option e


Question: how many prime numbers are between 13 / 3 and 83 / 6 ?

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

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

Explanation: "13 / 3 = 4 . xxx 83 / 6 = 13 . xxx so we need to find prime numbers between 4 ( exclusive ) - 12 ( inclusive ) there are 2 prime numbers 7 11 hence answer will be ( b ) 2 b"


Question: john makes $ 60 a week from his job . he earns a raise andnow makes $ 80 a week . what is the % increase ?

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

<gadget id="calculator">20 / 60</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. 15 %
B. 33.33 %
C. 17.8 %
D. 19 %
E. 21 %

multiply(divide(subtract(80, 60), 60), const_100)

Explanation: "increase = ( 20 / 60 ) * 100 = ( 1 / 3 ) * 100 = 33.33 % . b"


Question: a boat takes 19 hours for travelling downstream from point a to point b and coming back to a point c which is at midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?

<gadget id="calculator">14 + 4</gadget>
<output>18</output>

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

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

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

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

<gadget id="calculator">(1/18) + (1/20)</gadget>
<output>19/180 = around 0.105556</output>

<gadget id="calculator">19 / (19/180)</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 180 km
B. 127 km
C. 178 km
D. 188 km
E. 111 km

divide(19, add(divide(const_1, add(14, 4)), divide(const_1, multiply(subtract(14, 4), const_2))))

Explanation: "explanation : speed in downstream = ( 14 + 4 ) km / hr = 18 km / hr ; speed in upstream = ( 14 â € “ 4 ) km / hr = 10 km / hr . let the distance between a and b be x km . then , x / 18 + ( x / 2 ) / 10 = 19 â ‡ ” x / 18 + x / 20 = 19 â ‡ ’ x = 180 km . answer : a"


Question: in a division sum , the quotient is 18 , the divisor 43 and the remainder 12 , find the dividend ?

<gadget id="calculator">18 * 43</gadget>
<output>774</output>

<gadget id="calculator">774 + 12</gadget>
<output>786</output>
<result>786</result>

Choices:
A. 586
B. 766
C. 796
D. 786
E. 686

Explanation: "explanation : 18 * 43 + 12 = 786 answer : d"


Question: niall ' s income is 60 % less than rex ' s income , and sam ' s income is 25 % less than niall ' s income . if rex gave 60 % of his income to sam and 40 % of his income to niall , niall ' s new income would be what fraction of sam ' s new income ?

<gadget id="calculator">40 + 40</gadget>
<output>80</output>

<gadget id="calculator">80 + 10</gadget>
<output>90</output>

<gadget id="calculator">80 / 90</gadget>
<output>8/9 = around 0.888889</output>
<result>8/9 = around 0.888889</result>

Choices:
A. 8 / 9
B. 11 / 12
C. 8 / 13
D. 11 / 13
E. 12 / 13

Explanation: we can take some easy numbers and make calculations simpler . let r ( rex ' s income ) = 100 q ( niall ' s income ) = 40 % r = 40 s ( sam ' s income ) = 75 % q = ( 3 / 4 ) * 40 = 30 now , if rex gives 40 % to niall - - > q = 40 + 40 = 80 60 % given to sam - - > s = 30 + 60 = 90 the ratio is : q / s = 80 / 90 = 8 / 9 = a


Question: if 2 a = 4 b = 10 , then 40 ab =

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

<gadget id="calculator">10 / 4</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">5 * (5/2)</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">40 * (25/2)</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 50
B. 100
C. 250
D. 450
E. 500

multiply(40, multiply(divide(10, 2), divide(10, 4)))

Explanation: 2 a * 4 b = 10 * 10 = 100 8 ab = 100 i . e . 40 ab = 500 answer : option e


Question: rahim bought 52 books for rs . 1200 from one shop and 32 books for rs . 480 from another . what is the average price he paid per book ?

<gadget id="calculator">1_200 + 480</gadget>
<output>1_680</output>

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

<gadget id="calculator">1_680 / 84</gadget>
<output>20</output>
<result>20</result>

Choices:
A. s . 17
B. s . 18
C. s . 12
D. s . 20
E. s . 10

Explanation: "average price per book = ( 1200 + 480 ) / ( 52 + 32 ) = 1680 / 84 = rs . 20 answer : d"


Question: if 2 ^ 5 , 4 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?

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

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

<gadget id="calculator">13 / 2</gadget>
<output>13/2 = around 6.5</output>

<gadget id="calculator">16 * (13/2)</gadget>
<output>104</output>

<gadget id="calculator">104 * 2</gadget>
<output>208</output>
<result>208</result>

Choices:
A. 26
B. 39
C. 42
D. 208
E. 156

multiply(multiply(multiply(power(2, 2), 4), divide(13, 2)), 2)

Explanation: "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 4 * 4 = 208 smash d"


Question: if 3 < x < 6 < y < 11 , then what is the greatest possible positive integer difference of x and y ?

<gadget id="calculator">11 - 3</gadget>
<output>8</output>

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

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

Explanation: "3 < x < 6 < y < 11 ; 3 < x y < 11 3 + y < x + 11 y - x < 8 . positive integer difference is 7 ( for example y = 10.5 and x = 3.5 ) answer : e ."


Question: chris age after 20 years will be 5 times his age 5 years back . what is the present age of chris ?

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

<gadget id="calculator">25 + 20</gadget>
<output>45</output>

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

<gadget id="calculator">45 / 4</gadget>
<output>45/4 = around 11.25</output>

<gadget id="calculator">(45/4) - 5</gadget>
<output>25/4 = around 6.25</output>

<gadget id="calculator">(45/4) - (25/4)</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 20
B. 25
C. 15
D. 22
E. 5

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

Explanation: chris present age = x after 20 years = x + 20 5 years back = x - 5 x + 20 = 5 ( x - 5 ) x = 5 answer is e


Question: the weight of a glass of jar is 30 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?

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

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

<gadget id="calculator">30 / 70</gadget>
<output>3/7 = around 0.428571</output>
<result>3/7 = around 0.428571</result>

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

divide(subtract(60, 30), subtract(const_100, 30))

Explanation: let weight of jar filled with beans = 100 g weight of jar = 30 g weight of coffee beans = 70 g weight of jar and remaining beans = 60 g weight of remaining beans = 30 g fraction remaining = 30 / 70 = 3 / 7 answer is e .


Question: a number increased by 15 % gives 1150 . the number is

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

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

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

Choices:
A. 250
B. 1000
C. 450
D. 500
E. 520

divide(1150, add(const_1, divide(15, const_100)))

Explanation: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 15 % = 115 % 115 % - - - - - - - > 1150 ( 115 × 100 = 1150 ) 100 % - - - - - - - > 1000 ( 100 × 100 = 1000 ) b )"


Question: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 390 m long platform ?

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

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

<gadget id="calculator">10 * 12</gadget>
<output>120</output>

<gadget id="calculator">390 + 120</gadget>
<output>510</output>

<gadget id="calculator">510 / 10</gadget>
<output>51</output>
<result>51</result>

Choices:
A. 19
B. 27
C. 51
D. 47
E. 28

divide(add(390, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36))

Explanation: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 390 ) / 36 * 5 / 18 = 51 min . answer : c"


Question: the average of 7 numbers is 23 . if each number be multiplied by 5 . find the average of new set of numbers ?

<gadget id="calculator">23 * 5</gadget>
<output>115</output>
<result>115</result>

Choices:
A. 110
B. 122
C. 120
D. 115
E. 145

Explanation: "explanation : average of new numbers = 23 * 5 = 115 answer : option d"


Question: if 8 men or 12 women can do a piece of work in 35 days , in how many days can the same work be done by 6 men and 11 women ?

<gadget id="calculator">8 * 35</gadget>
<output>280</output>

<gadget id="calculator">6 / 280</gadget>
<output>3/140 = around 0.021429</output>

<gadget id="calculator">12 * 35</gadget>
<output>420</output>

<gadget id="calculator">11 / 420</gadget>
<output>11/420 = around 0.02619</output>

<gadget id="calculator">(3/140) + (11/420)</gadget>
<output>1/21 = around 0.047619</output>

<gadget id="calculator">1 / (1/21)</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 10 days
B. 11 days
C. 13 days
D. 15 days
E. 21 days

inverse(add(divide(6, multiply(8, 35)), divide(11, multiply(12, 35))))

Explanation: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 35 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 35 = 1 / 420 so , 20 women work = 20 / 420 = 1 / 21 ans : 21 days answer : e"


Question: the total age of a and b is 18 years more than the total age of b and c . c is how many year younger than

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

Choices:
A. 14 years
B. 12 years
C. 56 years
D. 66 years
E. 18 years

Explanation: "given that a + b = 182 + b + c = > a â € “ c = 18 + b â € “ b = 18 = > c is younger than a by 18 years answer : e"


Question: the greatest number which on dividing 1657 and 2037 leaves remainders 9 and 5 respectively , is :

<gadget id="calculator">2_037 - 5</gadget>
<output>2_032</output>

<gadget id="calculator">1_657 - 9</gadget>
<output>1_648</output>

<gadget id="calculator">gcd(2_032, 1_648)</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 16
B. 127
C. 235
D. 305
E. 505

gcd(subtract(2037, 5), subtract(1657, 9))

Explanation: "explanation : required number = h . c . f . of ( 1657 - 9 ) and ( 2037 - 5 ) = h . c . f . of 1648 and 2032 = 16 . answer : a"