Question: if an investor puts $ 700 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?

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

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

<gadget id="calculator">1 + (1/20)</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">700 * (441/400)</gadget>
<output>3_087/4 = around 771.75</output>
<result>3_087/4 = around 771.75</result>

Choices:
A. $ 769.75
B. $ 771.75
C. $ 773.75
D. $ 775.75
E. $ 777.75

multiply(700, power(add(const_1, divide(divide(10, const_2), const_100)), const_2))

Explanation: "1.05 * 1.05 * 700 = $ 771.75 the answer is b ."


Question: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?

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

<gadget id="calculator">600 / (1/20)</gadget>
<output>12_000</output>
<result>12_000</result>

Choices:
A. 12002
B. 12000
C. 12028
D. 12020
E. 12013

Explanation: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 12000 answer : b"


Question: to deliver an order on time , a company has to make 25 parts a day . after making 25 parts per day for 3 days , the company started to produce 5 more parts per day , and by the last day of work 100 more parts than planned were produced . find how many parts the company made and how many days this took .

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

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

<gadget id="calculator">90 + 100</gadget>
<output>190</output>

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

<gadget id="calculator">190 - 75</gadget>
<output>115</output>

<gadget id="calculator">115 / 5</gadget>
<output>23</output>

<gadget id="calculator">23 * 25</gadget>
<output>575</output>

<gadget id="calculator">575 + 100</gadget>
<output>675</output>
<result>675</result>

Choices:
A. 600
B. 500
C. 575
D. 655
E. 675

add(multiply(divide(subtract(add(multiply(add(25, 5), 3), 100), multiply(25, 3)), 5), 25), 100)

Explanation: let x be the number of days the company worked . then 25 x is the number of parts they planned to make . at the new production rate they made : 3 ⋅ 25 + ( x − 3 ) ⋅ 30 = 75 + 30 ( x − 3 ) therefore : 25 x = 75 + 30 ( x − 3 ) − 100 25 x = 75 + 30 x − 90 − 100 190 − 75 = 30 x − 25 115 = 5 x x = 23 so the company worked 23 days and they made 23 ⋅ 25 + 100 = 675 pieces . so answer is e .


Question: a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weights 8 g / cm cube , then find the weight of the pipe .

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

<gadget id="calculator">pi * (4 ** 2) * 21</gadget>
<output>336*pi = around 1_055.575132</output>

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

<gadget id="calculator">pi * (3 ** 2) * 21</gadget>
<output>189*pi = around 593.761012</output>

<gadget id="calculator">(336*pi) - (189*pi)</gadget>
<output>147*pi = around 461.81412</output>

<gadget id="calculator">(147*pi) * 8</gadget>
<output>1176*pi = around 3_694.512961</output>

<gadget id="calculator">(1176*pi) / 1_000</gadget>
<output>147*pi/125 = around 3.694513</output>
<result>147*pi/125 = around 3.694513</result>

Choices:
A. 3.696 kg
B. 3.686 kg
C. 2.696 kg
D. 2.686 kg
E. none of these

divide(multiply(subtract(volume_cylinder(divide(8, const_2), 21), volume_cylinder(subtract(divide(8, const_2), const_1), 21)), 8), const_1000)

Explanation: explanation : in this type of question , we need to subtract external radius and internal radius to get the answer using the volume formula as the pipe is hollow . oh ! line become a bit complicated , sorry for that , lets solve it . external radius = 4 cm internal radius = 3 cm [ because thickness of pipe is 1 cm ] volume of iron = π r 2 h = 22 / 7 ∗ [ 42 − 32 ] ∗ 21 cm 3 = 22 / 7 ∗ 1 ∗ 21 cm 3 = 462 cm 3 weight of iron = 462 * 8 = 3696 gm = 3.696 kg option a


Question: village x has a population of 72000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?

<gadget id="calculator">72_000 - 42_000</gadget>
<output>30_000</output>

<gadget id="calculator">800 + 1_200</gadget>
<output>2_000</output>

<gadget id="calculator">30_000 / 2_000</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 15
B. 19
C. 11
D. 18
E. 13

Explanation: "let the population of two villages be equal after p years then , 72000 - 1200 p = 42000 + 800 p 2000 p = 30000 p = 15 answer is a ."


Question: a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is :

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

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

<gadget id="calculator">40 * (11/10)</gadget>
<output>44</output>

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

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

<gadget id="calculator">50 * (6/5)</gadget>
<output>60</output>

<gadget id="calculator">44 + 60</gadget>
<output>104</output>

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

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

<gadget id="calculator">90 * (23/20)</gadget>
<output>207/2 = around 103.5</output>

<gadget id="calculator">104 - (207/2)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">40 / (1/2)</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 50
B. 90
C. 80
D. 28
E. 93

divide(40, subtract(add(multiply(40, add(const_1, divide(10, const_100))), multiply(50, add(const_1, divide(20, const_100)))), multiply(90, add(const_1, divide(15, const_100)))))

Explanation: let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : option c


Question: find the remainder of the division ( 3 ^ 33 ) / 7 .

<gadget id="calculator">3 ** 33</gadget>
<output>5_559_060_566_555_523</output>

<gadget id="calculator">5_559_060_566_555_523 % 7</gadget>
<output>6</output>
<result>6</result>

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

Explanation: find the pattern of the remainders after each power : ( 3 ^ 1 ) / 7 remainder 3 ( 3 ^ 2 ) / 7 remainder 2 ( 3 ^ 3 ) / 7 remainder 6 ( 3 ^ 4 ) / 7 remainder 4 ( 3 ^ 5 ) / 7 remainder 5 ( 3 ^ 6 ) / 7 remainder 1 - - > this is where the cycle ends ( 3 ^ 7 ) / 7 remainder 3 - - > this is where the cycle begins again ( 3 ^ 8 ) / 7 remainder 2 continuing the pattern to ( 3 ^ 33 ) / 7 gives us a remainder of 6 final answer : e ) 6


Question: an inspector rejects 0.05 % of the meters as defective . how many will he examine to reject 4 ?

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

<gadget id="calculator">400 / 0.05</gadget>
<output>8_000</output>
<result>8_000</result>

Choices:
A. 4000
B. 8000
C. 5000
D. 4500
E. 6000

Explanation: "let the number of meters to be examined be x then , 0.05 % of x = 4 ( 5 / 100 ) * ( ( 1 / 100 ) * x = 4 x = 8000 answer is b"


Question: a train passes a platform in 34 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">34 - 20</gadget>
<output>14</output>

<gadget id="calculator">15 * 14</gadget>
<output>210</output>
<result>210</result>

Choices:
A. 280 meter
B. 240 meter
C. 210 meter
D. 200 meter
E. none of these

multiply(multiply(const_0_2778, 54), subtract(34, 20))

Explanation: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 34 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 = 34 = > 300 + l = 15 × 34 = 510 = > l = 510 - 300 = 210 meter answer : option c"


Question: the average age of 15 students of a class is 15 years . out of these , the average age of 3 students is 14 years and that of the other 11 students is 16 years . the age of the 15 th student is

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

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

<gadget id="calculator">11 * 16</gadget>
<output>176</output>

<gadget id="calculator">42 + 176</gadget>
<output>218</output>

<gadget id="calculator">225 - 218</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 9 years
B. 11 years
C. 14 years
D. 7 years
E. 25 years

subtract(multiply(15, 15), add(multiply(3, 14), multiply(11, 16)))

Explanation: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 3 + 16 x 11 ) ] = ( 225 - 218 ) = 7 years . answer d"


Question: a number x is 6 times another number y . the percentage that y is less than x is

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

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

<gadget id="calculator">(5/6) * 100</gadget>
<output>250/3 = around 83.333333</output>
<result>250/3 = around 83.333333</result>

Choices:
A. 12.5 %
B. 83.3 %
C. 80 %
D. 11 %
E. 1 %

multiply(divide(subtract(6, const_1), 6), const_100)

Explanation: say y = 1 and x = 6 . then y = 1 is less than x = 6 by ( 6 - 1 ) / 6 * 100 = 5 / 6 * 100 = 83.3 % . answer : b .


Question: liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 10 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )

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

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

Choices:
A. 50 mph
B. 45 mph
C. 48 mph
D. 30 mph
E. 60 mph

Explanation: "let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 30 where s is the speed and 30 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 30 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 30 mph therefore answer is d"


Question: what is the compound interest paid on a sum of rs . 3000 for the period of 2 years at 10 % per annum .

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

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

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

<gadget id="calculator">3_000 * (121/100)</gadget>
<output>3_630</output>

<gadget id="calculator">3_630 - 3_000</gadget>
<output>630</output>
<result>630</result>

Choices:
A. 630
B. 620
C. 610
D. 600
E. none of these

subtract(multiply(3000, power(add(const_1, divide(10, const_100)), 2)), 3000)

Explanation: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 3000 = 3000 * ( 21 / 100 ) = 630 answer a"


Question: a boy perform 5 times a reaction and his reading are 2 , 2.1 , 2 , 2.2 but unfortunately 5 th reading clearly not visible because a drop of chemical fall onto it . but luckily he have mean of all reading which is 2 . please help him in finding 5 th reading .

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

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

<gadget id="calculator">8 - 2.1</gadget>
<output>5.9</output>

<gadget id="calculator">5.9 - 2</gadget>
<output>3.9</output>

<gadget id="calculator">3.9 - 2.2</gadget>
<output>1.7</output>
<result>1.7</result>

Choices:
A. 2
B. 1.7
C. 1.9
D. 1.8
E. 2.1

subtract(subtract(subtract(subtract(multiply(2, 5), 2), 2.1), 2), 2.2)

Explanation: solution let 5 th reading be x ( 2 + 2.1 + 2 + 2.2 + x ) / 5 = 2 8.3 + x = 10 x = 1.7 answer b


Question: thirty percent of the members of a swim club have passed the lifesaving test . among the members who have not passed the test , 12 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?

<gadget id="calculator">12 + 30</gadget>
<output>42</output>

<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">42 / (7/10)</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 60
B. 80
C. 100
D. 120
E. 140

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

Explanation: 30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 12 = 42 members have not passed the test , thus 0.7 * total = 42 - - > total = 60 . answer : a .


Question: a certain rectangular window is ( 1 / 3 ) times as long as it is wide . if its perimeter is 28 feet , what are its dimensions in terms of length by width ?

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

Choices:
A. 12 by 2
B. 11 by 3
C. 10.5 by 3.5
D. 10 by 4
E. 9 by 3

Explanation: 2 x + 2 y = 28 x + y = 14 x + ( 1 / 3 ) x = 14 4 x = 14 * 3 x = 10.5 answer c


Question: there are 8 teams in a certain league and each team plays each of the other teams exactly once . if each game is played by 2 teams , what is the total number of games played ?

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

<gadget id="calculator">8 * 7</gadget>
<output>56</output>

<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 15
B. 16
C. 28
D. 56
E. 64

divide(multiply(8, subtract(8, const_1)), const_2)

Explanation: "number of ways 2 teams can be selected out of 8 teams : c 8 / 2 = 8 ∗ 7 / 2 = 28 ans : ' ' c ' '"


Question: 3 candidates in an election and received 1136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?

<gadget id="calculator">1_136 + 7_636</gadget>
<output>8_772</output>

<gadget id="calculator">8_772 + 11_628</gadget>
<output>20_400</output>

<gadget id="calculator">11_628 / 20_400</gadget>
<output>57/100 = around 0.57</output>

<gadget id="calculator">(57/100) * 100</gadget>
<output>57</output>
<result>57</result>

Choices:
A. 40 %
B. 55 %
C. 57 %
D. 60 %
E. 62 %

Explanation: "total number of votes polled = ( 1136 + 7636 + 11628 ) = 20400 so , required percentage = 11628 / 20400 * 100 = 57 % c"


Question: at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 3 years ?

<gadget id="calculator">2_000 - 1_750</gadget>
<output>250</output>

<gadget id="calculator">250 / 1_750</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">(1/7) / 3</gadget>
<output>1/21 = around 0.047619</output>

<gadget id="calculator">(1/21) * 100</gadget>
<output>100/21 = around 4.761905</output>
<result>100/21 = around 4.761905</result>

Choices:
A. 4 %
B. 3 6 / 7 %
C. 4.76 %
D. 5 %
E. 6 %

multiply(divide(divide(subtract(2000, 1750), 1750), 3), const_100)

Explanation: "explanation : 250 = ( 1750 x 3 xr ) / 100 r = 4.76 % answer : option c"


Question: the perimeter of a square is equal to the perimeter of a rectangle of length 19 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )

<gadget id="calculator">14 + 19</gadget>
<output>33</output>

<gadget id="calculator">2 * 33</gadget>
<output>66</output>

<gadget id="calculator">66 / 4</gadget>
<output>33/2 = around 16.5</output>

<gadget id="calculator">(33/2) / 2</gadget>
<output>33/4 = around 8.25</output>

<gadget id="calculator">2 * pi * (33/4)</gadget>
<output>33*pi/2 = around 51.836279</output>

<gadget id="calculator">(33*pi/2) / 2</gadget>
<output>33*pi/4 = around 25.918139</output>

<gadget id="calculator">floor(33*pi/4)</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 22.78
B. 23.54
C. 23.5
D. 24.55
E. 25.93

floor(divide(circumface(divide(divide(multiply(const_2, add(14, 19)), const_4), const_2)), const_2))

Explanation: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 19 + 14 ) = 66 cm perimeter of the square = 66 cm i . e . 4 a = 66 a = 16.5 diameter of the semicircle = 16.5 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 16.5 ) = 1 / 2 ( 22 / 7 ) ( 16.5 ) = 25.93 cm to two decimal places answer : e"


Question: john and steve are speed walkers in a race . john is 15 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?

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

<gadget id="calculator">3.7 * 17</gadget>
<output>62.9</output>

<gadget id="calculator">4.2 - 3.7</gadget>
<output>0.5</output>

<gadget id="calculator">62.9 / 0.5</gadget>
<output>125.8</output>

<gadget id="calculator">125.8 + 17</gadget>
<output>142.8</output>

<gadget id="calculator">142.8 / 4.2</gadget>
<output>34</output>
<result>34</result>

Choices:
A. 13 seconds
B. 17 seconds
C. 26 seconds
D. 34 seconds
E. 51 seconds

Explanation: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 15 + 2 - - - > 0.5 t = 17 - - - > t = 34 seconds . d is the correct answer ."


Question: a ratio between two numbers is 3 : 4 and their l . c . m . is 84 . the first number is

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

<gadget id="calculator">84 / 12</gadget>
<output>7</output>

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

Choices:
A. 60
B. 45
C. 21
D. 15
E. none

Explanation: "sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . ∴ 12 x = 84 ⇔ x = 7 . hence , the first number is 21 . answer c"


Question: the principal that amounts to rs . 4813 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?

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

<gadget id="calculator">6 + (1/4)</gadget>
<output>25/4 = around 6.25</output>

<gadget id="calculator">(25/4) / 100</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">1 + (1/16)</gadget>
<output>17/16 = around 1.0625</output>

<gadget id="calculator">(17/16) ** 3</gadget>
<output>4_913/4_096 = around 1.199463</output>

<gadget id="calculator">4_813 / (4_913/4_096)</gadget>
<output>19_714_048/4_913 = around 4_012.629351</output>
<result>19_714_048/4_913 = around 4_012.629351</result>

Choices:
A. s . 3096
B. s . 4036
C. s . 4085
D. s . 4096
E. s . 5096

divide(4813, power(add(1, divide(add(6, divide(1, 4)), const_100)), 3))

Explanation: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4813 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4036 . answer : b"


Question: the area of a rectangular plot is 18 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?

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

Choices:
A. 10 metres
B. 8 metres
C. 7.5 metres
D. data inadequate
E. none of these

Explanation: "l × b = 18 × b ∴ l = 18 m and l – b = 10 ∴ b = 18 – 10 = 8 m answer b"


Question: in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 38500 . how many times did he participate in the competition ?

<gadget id="calculator">11 * 7</gadget>
<output>77</output>

<gadget id="calculator">77 * 5</gadget>
<output>385</output>

<gadget id="calculator">385 * 2</gadget>
<output>770</output>

<gadget id="calculator">38_500 / 770</gadget>
<output>50</output>

<gadget id="calculator">50 ** (1/2)</gadget>
<output>5*sqrt(2) = around 7.071068</output>

<gadget id="calculator">floor(5*sqrt(2))</gadget>
<output>7</output>
<result>7</result>

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

floor(sqrt(divide(38500, multiply(multiply(multiply(11, 7), 5), 2))))

Explanation: 38500 = 2 * 2 * 5 * 5 * 5 * 7 * 11 john participated 7 times . the answer is b .


Question: the first flight out of phoenix airport had a late departure . if the next 3 flights departed on - time , how many subsequent flights need to depart from phoenix on - time , for the airport ' s on - time departure rate to be higher than 40 % ?

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

<gadget id="calculator">(2/5) * 3</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">floor(6/5)</gadget>
<output>1</output>

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

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

add(floor(multiply(divide(40, const_100), 3)), const_1)

Explanation: we need on - time departure rate to be higher than 4 / 10 , so it should be at least 5 / 11 , which means that 5 out of 11 flights must depart on time . since for now 3 out of 4 flights departed on time then 5 - 3 = 2 subsequent flights need to depart on - time . answer : d


Question: two years ago , ram put $ 500 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 600 . the next year , his account balance increased by 10 % . at the end of the two years , by what percent has ram ' s account balance increased from his initial deposit of $ 500 ?

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

<gadget id="calculator">(1/10) * 600</gadget>
<output>60</output>

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

<gadget id="calculator">160 / 500</gadget>
<output>8/25 = around 0.32</output>

<gadget id="calculator">(8/25) * 100</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 19 %
B. 28 %
C. 30 %
D. 32 %
E. 25 %

multiply(divide(add(multiply(divide(10, const_100), 600), 100), 500), const_100)

Explanation: investment 500 dollars 1 st year total gained = 100 total amount end of first year = 600 second year account increased by 10 % = 600 * 0.1 = 60 therefore total amount by second year end = 660 so total percentage increase in money = ( 660 - 500 ) * 100 / 500 = 32 % correct answer d = 32 %


Question: if the sum of two numbers is 45 and the h . c . f and l . c . m of these numbers are 3 and 100 respectively , then the sum of the reciprocal of the numbers is equal to :

<gadget id="calculator">3 + 100</gadget>
<output>103</output>

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

<gadget id="calculator">103 / 300</gadget>
<output>103/300 = around 0.343333</output>
<result>103/300 = around 0.343333</result>

Choices:
A. 103 / 300
B. 103 / 200
C. 112 / 300
D. 154 / 140
E. 100 / 300

Explanation: let the numbers be a and b . then , a + b = 45 and ab = 3 * 100 = 300 . required sum = 1 / a + 1 / b = ( a + b ) / ab = 103 / 300 answer : a


Question: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 45 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?

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

<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">(1/2) - (9/20)</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">1 - (9/20)</gadget>
<output>11/20 = around 0.55</output>

<gadget id="calculator">(1/20) / (11/20)</gadget>
<output>1/11 = around 0.090909</output>

<gadget id="calculator">(1/11) * 100</gadget>
<output>100/11 = around 9.090909</output>
<result>100/11 = around 9.090909</result>

Choices:
A. 9 %
B. 12 %
C. 15 %
D. 17 %
E. 20 %

multiply(divide(subtract(divide(50, const_100), divide(45, const_100)), subtract(const_1, divide(45, const_100))), const_100)

Explanation: "let me try a simpler one . lets assume that candidate got 45 % votes and total votes is 100 . candidate won = 45 remaining = 55 to get 50 % , candidate requires 5 votes from 100 which is 5 % and 5 votes from 55 . 5 / 55 = 1 / 11 = . 09 = 9 % which is approx 9 % . hence the answer is a ."


Question: pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 12 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?

<gadget id="calculator">12 * 6</gadget>
<output>72</output>

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

<gadget id="calculator">72 / 6</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 13
B. 17
C. 18
D. 19
E. 12

divide(multiply(12, 6), subtract(12, 6))

Explanation: "let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 12 = > 1 / x = 1 / 6 - 1 / 12 = ( 2 - 1 ) / 12 = 1 / 12 = > x = 12 . answer : e"


Question: w and x start a business with rs . 5000 and rs . 20000 respectively . hoe should they share their profits at the end of one year ?

<gadget id="calculator">5_000 * 12</gadget>
<output>60_000</output>

<gadget id="calculator">20_000 * 12</gadget>
<output>240_000</output>

<gadget id="calculator">60_000 / 240_000</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>

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

divide(multiply(5000, const_12), multiply(20000, const_12))

Explanation: they should share the profits in the ratio of their investments . the ratio of the investments made by w and x = 5000 : 20000 = > 1 : 4 . answer : c


Question: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 130 marks , the no of questions he attempts correctly is :

<gadget id="calculator">130 + 80</gadget>
<output>210</output>

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

<gadget id="calculator">210 / 5</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 35
B. 38
C. 90
D. 88
E. 42

Explanation: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 80 – x ) = 130 = > 5 x = 210 = > x = 42 answer : e"


Question: what is the least number should be added to 1056 , so the sum of the number is completely divisible by 29 ?

<gadget id="calculator">1_056 / 29</gadget>
<output>1_056/29 = around 36.413793</output>

<gadget id="calculator">floor(1_056/29)</gadget>
<output>36</output>

<gadget id="calculator">36 + 1</gadget>
<output>37</output>

<gadget id="calculator">37 * 29</gadget>
<output>1_073</output>

<gadget id="calculator">1_073 - 1_056</gadget>
<output>17</output>
<result>17</result>

Choices:
A. 17
B. 27
C. 37
D. 47
E. 57

subtract(multiply(add(floor(divide(1056, 29)), const_1), 29), 1056)

Explanation: ( 1056 / 29 ) gives remainder 12 17 + 12 = 29 , so we need to add 17 a


Question: an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1455 , what was the total number of pairs of contact lenses that she sold ?

<gadget id="calculator">150 * 5</gadget>
<output>750</output>

<gadget id="calculator">1_455 - 750</gadget>
<output>705</output>

<gadget id="calculator">150 + 85</gadget>
<output>235</output>

<gadget id="calculator">705 / 235</gadget>
<output>3</output>

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

<gadget id="calculator">8 + 3</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 11
B. 13
C. 15
D. 17
E. 19

Explanation: ( x + 5 ) * 150 + x * 85 = 1455 = > x = 3 total lens = 3 + ( 3 + 5 ) = 11 answer a


Question: if the price of an article went up by 30 % , then by what percent should it be brought down to bring it back to its original price ?

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

<gadget id="calculator">30 / 130</gadget>
<output>3/13 = around 0.230769</output>

<gadget id="calculator">(3/13) * 100</gadget>
<output>300/13 = around 23.076923</output>
<result>300/13 = around 23.076923</result>

Choices:
A. 25 %
B. 23 1 / 13 %
C. 16 7 / 3 %
D. 16 6 / 3 %
E. 16 2 / 3 %

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

Explanation: "let the price of the article be rs . 100 . 30 % of 100 = 30 . new price = 100 + 30 = rs . 130 required percentage = ( 130 - 100 ) / 130 * 100 = 30 / 130 * 100 = 23 1 / 13 % answer : b"


Question: if n is the product of all the integers from 5 to 20 , inclusive , what is the greatest integer k for which 2 ^ k is a factor of n ?

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

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

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

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

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

<gadget id="calculator">12 + 1</gadget>
<output>13</output>

<gadget id="calculator">13 + 2</gadget>
<output>15</output>
<result>15</result>

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

add(add(add(add(add(add(add(const_1, const_3), const_1), 2), const_1), const_4), const_1), 2)

Explanation: 20 / 2 = 10 10 / 2 = 5 ans : 10 + 5 = 15 answer : e


Question: the perimeter of an isosceles right triangle is 14 + 14 sq rt 2 . what is the length of the hypotenuse of the triangle ?

<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>

<gadget id="calculator">14 * (sqrt(2))</gadget>
<output>14*sqrt(2) = around 19.79899</output>

<gadget id="calculator">(14*sqrt(2)) / 2</gadget>
<output>7*sqrt(2) = around 9.899495</output>
<result>7*sqrt(2) = around 9.899495</result>

Choices:
A. 5
B. 6
C. 7
D. 8
E. 9.899

Explanation: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 14 + 14 sqrt 2 or , a . ( 2 + sqrt 2 ) = 14 ( 1 + sqrt 2 ) , a = 14 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 14 * 2.414 / 3.414 = then hypotenuse = 9.899 e"


Question: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?

<gadget id="calculator">9 / 100</gadget>
<output>9/100 = around 0.09</output>

<gadget id="calculator">(9/100) * 18_000</gadget>
<output>1_620</output>

<gadget id="calculator">1_950 - 1_620</gadget>
<output>330</output>

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">(3/25) - (9/100)</gadget>
<output>3/100 = around 0.03</output>

<gadget id="calculator">330 / (3/100)</gadget>
<output>11_000</output>
<result>11_000</result>

Choices:
A. $ 11500
B. $ 11000
C. $ 12000
D. $ 12100
E. $ 12500

divide(subtract(1950, multiply(divide(9, const_100), 18000)), subtract(divide(12, const_100), divide(9, const_100)))

Explanation: let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b


Question: a 90 cm long wire is to be cut into two pieces so that one piece will be 2 / 7 th of the other , how many centimeters will the shorter piece be ?

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

<gadget id="calculator">(2/7) + 1</gadget>
<output>9/7 = around 1.285714</output>

<gadget id="calculator">90 / (9/7)</gadget>
<output>70</output>

<gadget id="calculator">90 - 70</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 73
B. 20
C. 83
D. 21
E. 52

subtract(90, divide(90, add(divide(2, 7), const_1)))

Explanation: "explanation : 1 : 2 / 7 = 7 : 2 2 / 9 * 90 = 20 answer : option b"


Question: the sum of 3 integers is 33 . the largest integer is 3 times the middle integer , and the smallest integer is 23 less than the largest integer . what is the product of the 3 integers ?

<gadget id="calculator">33 + 23</gadget>
<output>56</output>

<gadget id="calculator">56 * 3</gadget>
<output>168</output>

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

<gadget id="calculator">168 / 7</gadget>
<output>24</output>

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

<gadget id="calculator">24 * 8</gadget>
<output>192</output>

<gadget id="calculator">24 - 23</gadget>
<output>1</output>

<gadget id="calculator">192 * 1</gadget>
<output>192</output>
<result>192</result>

Choices:
A. 192
B. 203
C. 214
D. 225
E. 236

multiply(multiply(divide(multiply(add(33, 23), 3), add(const_3, const_4)), divide(divide(multiply(add(33, 23), 3), add(const_3, const_4)), 3)), subtract(divide(multiply(add(33, 23), 3), add(const_3, const_4)), 23))

Explanation: let x be the middle integer . then the largest is 3 x and the smallest is 3 x - 23 . 3 x - 23 + x + 3 x = 33 x = 8 the three integers are 1 , 8 , and 24 . the product is 1 * 8 * 24 = 192 the answer is a .


Question: joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 70 . he was allowed to drop his lowest score . after doing so , his average test score improved to 75 . what is the lowest test score that was dropped ?

<gadget id="calculator">70 * 4</gadget>
<output>280</output>

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

<gadget id="calculator">280 - 225</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 20
B. 25
C. 55
D. 65
E. 80

subtract(multiply(70, 4), multiply(75, const_3))

Explanation: "the arithmetic mean of 4 equally weighted tests was 70 . so what we can assume is that we have 4 test scores , each 70 . he dropped his lowest score and the avg went to 75 . this means that the lowest score was not 70 and other three scores had given the lowest score 5 each to make it up to 70 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 70 . so the lowest score = 70 - 15 = 55 answer ( c )"


Question: an error 2 % in excess is made while measuring the sideofa square . the % of error in the calculated area of the square is ?

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

<gadget id="calculator">102 ** 2</gadget>
<output>10_404</output>

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

<gadget id="calculator">10_404 - 10_000</gadget>
<output>404</output>

<gadget id="calculator">404 * 100</gadget>
<output>40_400</output>

<gadget id="calculator">40_400 / 10_000</gadget>
<output>101/25 = around 4.04</output>
<result>101/25 = around 4.04</result>

Choices:
A. 4 %
B. 4.04 %
C. 4.15 %
D. 5 %
E. 5.24 %

divide(multiply(subtract(square_area(add(const_100, 2)), square_area(const_100)), const_100), square_area(const_100))

Explanation: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b"


Question: what is the normal price of an article sold at $ 144 after two successive discounts of 10 % and 20 % ?

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

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

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

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

<gadget id="calculator">(9/10) * (4/5)</gadget>
<output>18/25 = around 0.72</output>

<gadget id="calculator">144 / (18/25)</gadget>
<output>200</output>
<result>200</result>

Choices:
A. $ 184
B. $ 192
C. $ 200
D. $ 208
E. $ 216

divide(144, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 20), const_100)))

Explanation: "0.8 * 0.9 * cost price = $ 144 cost price = $ 200 the answer is c ."


Question: the length of a room is 6.5 m and width is 2.75 m . what is the cost of paying the floor by slabs at the rate of rs . 600 per sq . metre .

<gadget id="calculator">6.5 * 2.75</gadget>
<output>17.875</output>

<gadget id="calculator">600 * 17.875</gadget>
<output>10_725</output>
<result>10_725</result>

Choices:
A. rs . 18725
B. rs . 16725
C. rs . 30725
D. rs . 10725
E. rs . 20725

Explanation: "area = 6.5 * 2.75 sq . metre . cost for sq . metre . = rs . 600 hence , total cost = 6.5 * 2.75 * 600 = rs . 10725 answer : d"


Question: the number of diagonals of a polygon of n sides is given by the formula v = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?

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

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

Explanation: "v = n ( n - 3 ) v = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"


Question: if 15 % of 30 % of 50 % of a number is 108 , then what is the number ?

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

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

<gadget id="calculator">(1/2) * (3/10)</gadget>
<output>3/20 = around 0.15</output>

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

<gadget id="calculator">(3/20) * (3/20)</gadget>
<output>9/400 = around 0.0225</output>

<gadget id="calculator">108 / (9/400)</gadget>
<output>4_800</output>
<result>4_800</result>

Choices:
A. 4000
B. 3050
C. 4400
D. 4800
E. none of these

divide(108, multiply(multiply(divide(50, const_100), divide(30, const_100)), divide(15, const_100)))

Explanation: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 108 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 108 = > a = 10 * 20 * 10 * 2 = 4800 . answer : d"


Question: andy solves problems 75 to 125 inclusive in a math exercise . how many problems does he solve ?

<gadget id="calculator">125 - 75</gadget>
<output>50</output>

<gadget id="calculator">50 + 1</gadget>
<output>51</output>
<result>51</result>

Choices:
A. 53
B. 52
C. 51
D. 50
E. 49

Explanation: "125 - 75 + 1 = 51 ' c ' is the answer"


Question: 6 ) a marketing firm determined that , of 260 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?

<gadget id="calculator">260 - 80</gadget>
<output>180</output>

<gadget id="calculator">180 - 60</gadget>
<output>120</output>

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

Choices:
A. 15
B. 20
C. 30
D. 40
E. 45

divide(subtract(subtract(260, 80), 60), const_4)

Explanation: "180 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 180 = > 4 x = 120 = > x = 30 answer - c"


Question: 26 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?

<gadget id="calculator">13.5 * 26</gadget>
<output>351</output>

<gadget id="calculator">351 / 9</gadget>
<output>39</output>
<result>39</result>

Choices:
A. 30
B. 39
C. 60
D. data inadequate
E. none of these

Explanation: "capacity of the tank = 26 ã — 13.5 = 351 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 351 â  „ 9 = 39 answer b"


Question: a train is running at a speed of 40 km / hr and it crosses a post in 22.5 seconds . what is the length of the train ?

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

<gadget id="calculator">40 * (5/18)</gadget>
<output>100/9 = around 11.111111</output>

<gadget id="calculator">22.5 * (100/9)</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 190 metres
B. 160 metres
C. 200 metres
D. 120 metres
E. 250 metres

Explanation: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 22.5 s distance covered , d = vt = ( 400 / 36 ) ã — 22.5 = 250 m distance covered is equal to the length of the train = 250 m correct answer is 250 metres e"


Question: a 70 kg metal bar made of alloy of tin and silver lost 7 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?

<gadget id="calculator">0.375 / 5</gadget>
<output>0.075</output>

<gadget id="calculator">0.075 * 70</gadget>
<output>5.25</output>

<gadget id="calculator">7 - 5.25</gadget>
<output>1.75</output>

<gadget id="calculator">1.375 / 10</gadget>
<output>0.1375</output>

<gadget id="calculator">0.1375 - 0.075</gadget>
<output>0.0625</output>

<gadget id="calculator">1.75 / 0.0625</gadget>
<output>28</output>

<gadget id="calculator">70 - 28</gadget>
<output>42</output>

<gadget id="calculator">28 / 42</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>

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

divide(divide(subtract(7, multiply(divide(0.375, 5), 70)), subtract(divide(1.375, 10), divide(0.375, 5))), subtract(70, divide(subtract(7, multiply(divide(0.375, 5), 70)), subtract(divide(1.375, 10), divide(0.375, 5)))))

Explanation: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 7 kg when 70 kg alloy is immersed . this is a loss of ( 7 / 70 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"


Question: what is the rate percent when the simple interest on rs . 720 amount to rs . 180 in 4 years ?

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

<gadget id="calculator">720 * 4</gadget>
<output>2_880</output>

<gadget id="calculator">18_000 / 2_880</gadget>
<output>25/4 = around 6.25</output>
<result>25/4 = around 6.25</result>

Choices:
A. 6.25
B. 7.25
C. 8.25
D. 9.25
E. 10.25

divide(multiply(const_100, 180), multiply(720, 4))

Explanation: "180 = ( 720 * 4 * r ) / 100 r = 6.25 % answer : a"


Question: when 242 is divided by a certain divisor the remainder obtained is 15 . when 698 is divided by the same divisor the remainder obtained is 27 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 5 . what is the value of the divisor ?

<gadget id="calculator">15 + 27</gadget>
<output>42</output>

<gadget id="calculator">42 - 5</gadget>
<output>37</output>
<result>37</result>

Choices:
A. 11
B. 17
C. 13
D. 23
E. 37

Explanation: let that divisor be x since remainder is 15 or 27 it means divisor is greater than 27 . now 242 - 15 = 227 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 27 = 671 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 227 + 671 ) + 15 + 27 = x ( k + l ) + 42 when we divide this number by x then remainder will be equal to remainder of ( 42 divided by x ) = 5 hence x = 42 - 5 = 37 hence e


Question: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 15 times as heavy as water ?

<gadget id="calculator">15 - 9</gadget>
<output>6</output>

<gadget id="calculator">19 - 15</gadget>
<output>4</output>

<gadget id="calculator">6 / 4</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>

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

divide(subtract(15, 9), subtract(19, 15))

Explanation: "let us say , water weighs 1 kg / 1 liter . then gold weighs 19 kgs and copper weighs 9 kgs . assume x kgs of gold and y kgs of copper required to get the required alloy . we use weighted average formula = ax = n 1 . a 1 + n 2 . a 2 n 1 + n 2 ax = n 1 . a 1 + n 2 . a 2 n 1 + n 2 therefore , 15 = x . 19 + y . 9 x + y 15 = x . 19 + y . 9 x + y 15 x + 15 y = 19 x + 9 y 4 x = 6 y ⇒ x / y = 3 : 2 so gold and copper should be mixed in the ratio 3 : 2 . answer : a"


Question: find the cost of fencing around a circular field of diameter 32 m at the rate of rs . 2 a meter ?

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

<gadget id="calculator">2 * pi * 16</gadget>
<output>32*pi = around 100.530965</output>

<gadget id="calculator">(32*pi) * 2</gadget>
<output>64*pi = around 201.06193</output>
<result>64*pi = around 201.06193</result>

Choices:
A. 201
B. 132
C. 772
D. 592
E. 261

Explanation: "2 * 22 / 7 * 16 = 100.5 100.5 * 2 = rs . 201 answer : a"


Question: a bookseller has two display windows . she plans to display 3 new fiction books in the left window , and 3 new non - fiction books in the right window . assuming she can put the 4 fiction books in any order , and separately , the 3 non - fiction books in any order , how many total configurations will there be for the two display windows ?

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

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

Choices:
A. 24
B. 72
C. 144
D. 36
E. 420

Explanation: the left window will have permutations of the 3 fiction books , so the number of possibilities for that window is permutations = 3 ! = ( 3 ) ( 2 ) ( 1 ) = 6 the right window will have permutations of the 3 non - fiction books , so the number of possibilities for that window is permutations = 3 ! = ( 3 ) ( 2 ) ( 1 ) = 6 any of the 24 displays of the left window could be combined with any of the 6 displays of the right window , so the total number of configurations is 6 * 6 = 36 answer : d .


Question: if julie rows 32 km upstream and 72 km down steam taking 4 hours each , then the speed of the stream

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

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

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

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

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

<gadget id="calculator">(5/2) - 2</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

Choices:
A. 1.5 kmph
B. 0.5 kmph
C. 0.4 kmph
D. 1.6 kmph
E. 2.5 kmph

subtract(divide(divide(subtract(divide(72, 4), divide(32, 4)), const_2), const_2), const_2)

Explanation: speed upstream = 32 / 4 = 8 kmph speed down stream = 72 / 8 = 9 kmph speed of stream = ½ ( 9 - 8 ) = 0.5 kmph answer : b


Question: sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 7 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?

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

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

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

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

<gadget id="calculator">(1/6) + (1/7)</gadget>
<output>13/42 = around 0.309524</output>

<gadget id="calculator">1 - (13/42)</gadget>
<output>29/42 = around 0.690476</output>
<result>29/42 = around 0.690476</result>

Choices:
A. 11 / 30
B. 29 / 42
C. 17 / 30
D. 19 / 30
E. 11 / 15

subtract(1, add(multiply(inverse(3), inverse(const_2)), inverse(7)))

Explanation: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 7 x = 6 / 7 x so if gold card balance is transferred then the rest unspent will be 6 / 7 x - x / 6 = 29 / 42 x so the ans is b"


Question: of all the homes on gotham street , 1 / 3 are termite - ridden , and 4 / 7 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?

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

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

<gadget id="calculator">3 / 21</gadget>
<output>1/7 = around 0.142857</output>
<result>1/7 = around 0.142857</result>

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

divide(add(1, const_2.0), multiply(3, 7))

Explanation: "the fraction of homes which are termite - infested but not collapsing is 3 / 7 * 1 / 3 = 1 / 7 the answer is e ."


Question: what is the minimum value of | x - 4 | + | x + 5 | + | x - 5 | ?

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

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

Explanation: "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 5 | > = 0 - - > minimum occurs at x = - 5 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 5 - - > result = 9 + 0 + 10 = 19 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 9 + 1 = 10 x = 5 - - > result = 1 + 10 + 0 = 11 so minimum value of the expression occurs at x = 4 and the resultant value = 10 answer : e"


Question: sravan travelled for 15 hours . he covered the first half of the distance at 45 kmph and remaining half of the distance at 30 kmph . find the distance travelled by sravan ?

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

<gadget id="calculator">45 * 900</gadget>
<output>40_500</output>

<gadget id="calculator">45 + 30</gadget>
<output>75</output>

<gadget id="calculator">40_500 / 75</gadget>
<output>540</output>
<result>540</result>

Choices:
A. 520
B. 540
C. 550
D. 560
E. 440

divide(multiply(45, multiply(30, 30)), add(45, 30))

Explanation: let the distance travelled be x km . total time = ( x / 2 ) / 45 + ( x / 2 ) / 30 = 15 = > x / 90 + x / 60 = 15 = > ( 2 x + 3 x ) / 180 = 15 = > x = 540 km answer : b


Question: 50 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?

<gadget id="calculator">800 * 600</gadget>
<output>480_000</output>

<gadget id="calculator">50 / 480_000</gadget>
<output>1/9_600 = around 0.000104</output>

<gadget id="calculator">800 * (1/9_600)</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1_200 * (1/12)</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 80 litres
B. 90 litres
C. 100 litres
D. 170 litres
E. none of these

multiply(1200, multiply(800, divide(50, multiply(800, 600))))

Explanation: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 50 = 66.67 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 66.67 = 100 litres . answer c"


Question: a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 4 - inch increase in the length of the shoe . if the largest size of this shoe is 10 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?

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

<gadget id="calculator">17 - 8</gadget>
<output>9</output>

<gadget id="calculator">(1/4) * 9</gadget>
<output>9/4 = around 2.25</output>

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

<gadget id="calculator">(9/4) / (1/10)</gadget>
<output>45/2 = around 22.5</output>

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

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

<gadget id="calculator">(45/2) + (7/4)</gadget>
<output>97/4 = around 24.25</output>
<result>97/4 = around 24.25</result>

Choices:
A. 18.25
B. 20.75
C. 22.25
D. 24.25
E. 26.75

add(divide(multiply(divide(1, 4), subtract(17, 8)), divide(10, const_100)), multiply(subtract(15, 8), divide(1, 4)))

Explanation: "let x be the length of the size 8 shoe . then 0.1 x = 9 / 4 x = 90 / 4 inches the size 15 shoe has a length of 90 / 4 + 7 / 4 = 97 / 4 = 24.25 inches the answer is d ."


Question: excluding stoppages , the average speed of a bus is 75 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?

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

<gadget id="calculator">40 / 75</gadget>
<output>8/15 = around 0.533333</output>

<gadget id="calculator">(8/15) * 60</gadget>
<output>32</output>

<gadget id="calculator">60 - 32</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 15 min
B. 18 min
C. 16 min
D. 20 min
E. 28 min

subtract(multiply(const_1, const_60), multiply(divide(40, 75), const_60))

Explanation: "in 1 hr , the bus covers 75 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 75 - 40 ) km i . e 35 km at 75 km / hr . stoppage time = 35 / 75 hrs = 28 min answer : e"


Question: find the area of a parallelogram with base 26 cm and height 16 cm ?

<gadget id="calculator">26 * 16</gadget>
<output>416</output>
<result>416</result>

Choices:
A. 297 cm 2
B. 384 cm 2
C. 672 cm 2
D. 416 cm 2
E. 286 cm 2

Explanation: "area of a parallelogram = base * height = 26 * 16 = 416 cm 2 answer : d"


Question: by selling an article at rs . 600 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?

<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>

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

<gadget id="calculator">60_000 / 125</gadget>
<output>480</output>

<gadget id="calculator">480 * 25</gadget>
<output>12_000</output>

<gadget id="calculator">12_000 / 100</gadget>
<output>120</output>

<gadget id="calculator">480 - 120</gadget>
<output>360</output>
<result>360</result>

Choices:
A. s . 360
B. s . 480
C. s . 500
D. s . 450
E. s . 550

subtract(divide(multiply(600, const_100), add(25, const_100)), divide(multiply(divide(multiply(600, const_100), add(25, const_100)), 25), const_100))

Explanation: "sp = 600 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / 125 ] = 480 loss = 25 % = 25 % of 480 = rs . 120 sp = cp - loss = 480 - 120 = rs . 360 answer : a"


Question: the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 600 per sq . metre .

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

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

Choices:
A. rs . 12375
B. rs . 15550
C. rs . 15600
D. rs . 16500
E. none of these

Explanation: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 600 × 20.625 ) = 12375 . answer a"


Question: if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 14 ?

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

<gadget id="calculator">14 / 4</gadget>
<output>7/2 = around 3.5</output>

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

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

Explanation: @ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 14 . then 4 n < 14 and n < 3.5 . the largest possible integer is n = 3 . the answer is c .


Question: if 9 workers can build 9 cars in 9 days , then how many days would it take 7 workers to build 7 cars ?

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

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

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

<gadget id="calculator">9 * 1</gadget>
<output>9</output>
<result>9</result>

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

multiply(divide(multiply(9, 9), 9), divide(7, 7))

Explanation: "9 workers can build 1 car per day on average . 1 worker can build 1 / 9 of a car per day . 7 workers can build 7 / 9 car per day . the time required to build 7 cars is 7 / ( 7 / 9 ) = 9 days the answer is d ."


Question: the probability of two events a and b are 0.25 and 0.40 respectively . the probability that both a and b occur is 0.20 . the probability that neither a nor b occur is _________

<gadget id="calculator">0.25 + 0.4</gadget>
<output>0.65</output>

<gadget id="calculator">0.65 - 0.2</gadget>
<output>0.45</output>

<gadget id="calculator">1 - 0.45</gadget>
<output>0.55</output>
<result>0.55</result>

Choices:
A. 0.45
B. 0.4
C. 0.55
D. 0.05
E. 0.6

subtract(const_1, subtract(add(0.25, 0.40), 0.20))

Explanation: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 40 - . 20 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : c"


Question: the length of a rectangular floor is more than its breadth by 200 % . if rs . 300 is required to paint the floor at the rate of rs . 5 per sq m , then what would be the length of the floor ?

<gadget id="calculator">300 / 5</gadget>
<output>60</output>

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

<gadget id="calculator">20 ** (1/2)</gadget>
<output>2*sqrt(5) = around 4.472136</output>

<gadget id="calculator">(2*sqrt(5)) * 3</gadget>
<output>6*sqrt(5) = around 13.416408</output>
<result>6*sqrt(5) = around 13.416408</result>

Choices:
A. 65
B. 13.42
C. 18
D. 16
E. 14

multiply(sqrt(divide(divide(300, 5), 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 = 300 / 5 = 60 sq m l b = 60 i . e . , l * l / 3 = 60 l 2 = 180 = > l = 13.42 answer : b"


Question: the s . i . on a certain sum of money for 5 years at 10 % per annum is half the c . i . on rs . 5000 for 2 years at 12 % per annum . the sum placed on s . i . is ?

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">1 + (3/25)</gadget>
<output>28/25 = around 1.12</output>

<gadget id="calculator">(28/25) ** 2</gadget>
<output>784/625 = around 1.2544</output>

<gadget id="calculator">5_000 * (784/625)</gadget>
<output>6_272</output>

<gadget id="calculator">6_272 - 5_000</gadget>
<output>1_272</output>

<gadget id="calculator">1_272 / 2</gadget>
<output>636</output>

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

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

<gadget id="calculator">636 / (1/2)</gadget>
<output>1_272</output>
<result>1_272</result>

Choices:
A. 1585
B. 1454
C. 1656
D. 2458
E. 1272

divide(divide(subtract(multiply(5000, power(add(const_1, divide(12, const_100)), 2)), 5000), 2), multiply(5, divide(10, const_100)))

Explanation: c . i . = [ 5000 * ( 1 + 12 / 100 ) 2 - 5000 ] = ( 5000 * 28 / 25 * 28 / 25 - 5000 ) = rs . 1272 . sum = ( 636 * 100 ) / ( 5 * 10 ) = rs . 1272 answer : e


Question: dropbox charges $ 3.10 for first 1 / 5 of a month for 500 gb storage , plus $ 0.40 for each additional 1 / 5 of a month . what would dropbox charge for a data storage of 500 gb for 8 months ?

<gadget id="calculator">500 * 0.4</gadget>
<output>200</output>

<gadget id="calculator">200 / 8</gadget>
<output>25</output>

<gadget id="calculator">25 - 8</gadget>
<output>17</output>

<gadget id="calculator">17 + 1</gadget>
<output>18</output>
<result>18</result>

Choices:
A. $ 15.60
B. $ 16.00
C. $ 17.80
D. $ 18.70
E. $ 19.10

add(subtract(divide(multiply(500, 0.4), 8), 8), 1)

Explanation: first 1 / 5 month charge = $ 3.10 rest of the months = 8 - ( 1 / 5 ) = 39 / 5 charge for the rest of the months = 39 * 0.4 = 15.6 total charge = 3.10 + 15.6 = 18.7 answer is d .


Question: find the simple interest on rs . 72,000 at 16 2 / 3 % per year for 9 months .

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

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

<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>

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

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

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

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

<gadget id="calculator">900 * 10</gadget>
<output>9_000</output>

<gadget id="calculator">60_000 + 9_000</gadget>
<output>69_000</output>

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

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

<gadget id="calculator">50 / 3</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">69_000 * (50/3)</gadget>
<output>1_150_000</output>

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

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

<gadget id="calculator">1_150_000 * (3/4)</gadget>
<output>862_500</output>

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

<gadget id="calculator">862_500 * (1/100)</gadget>
<output>8_625</output>
<result>8_625</result>

Choices:
A. 7500
B. 6500
C. 9000
D. 9500
E. none of them

multiply(multiply(multiply(add(multiply(multiply(multiply(2, 3), const_100), const_100), multiply(multiply(multiply(3, 3), const_100), multiply(add(3, 2), 2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(3, 3), multiply(2, multiply(2, 3)))), divide(const_1, const_100))

Explanation: "p = rs . 72000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 72,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 9000 answer is c ."


Question: if it would take one machine 20 minutes to fill a large production order and another machine 30 minutes to fill the same order , how many minutes would it take both machines working together , at their respective rates , to fill the order ?

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

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">(1/20) + (1/30)</gadget>
<output>1/12 = around 0.083333</output>

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

Choices:
A. 10 min
B. 12 min
C. 15 min
D. 20 min
E. 18 min

inverse(add(divide(const_1, 20), divide(const_1, 30)))

Explanation: this question can be solved using the work formula : work = ( a ) ( b ) / ( a + b ) where a and b are the individual completion rates of the respective entities ( for the same job ) . we ' re told that one machine takes 10 minutes to complete a job and another machine takes 12 minutes to complete the same job . plugging in those values gets us . . . ( 20 ) ( 30 ) / ( 20 + 30 ) = 600 / 50 = 12 minutes answer is b


Question: how many digits are required to number a book containing 220 pages ?

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

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

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

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

<gadget id="calculator">220 - 100</gadget>
<output>120</output>

<gadget id="calculator">120 + 1</gadget>
<output>121</output>

<gadget id="calculator">121 * 3</gadget>
<output>363</output>

<gadget id="calculator">189 + 363</gadget>
<output>552</output>
<result>552</result>

Choices:
A. 674
B. 604
C. 552
D. 372
E. 250

add(add(subtract(const_10, const_1), multiply(multiply(subtract(const_10, const_1), const_10), const_2)), multiply(add(subtract(220, const_100), const_1), const_3))

Explanation: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 220 - ( 90 + 9 ) = 121 pages will require 121 * 3 = 363 digits . the total number of digits is 9 + 180 + 363 = 552 . the answer is c ."


Question: a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent w of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?

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

<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>

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

Choices:
A. 9 %
B. 11 %
C. 15 %
D. 25 %
E. 90 %

subtract(const_100, multiply(divide(9, 12), const_100))

Explanation: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is w = . 25 / 1 * 100 = 25 % d is the answer ."


Question: the ratio between the number of sheep and the number of horses at the stewart farm is 5 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?

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

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

<gadget id="calculator">8 * 100</gadget>
<output>800</output>

<gadget id="calculator">80 + 800</gadget>
<output>880</output>

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

<gadget id="calculator">880 + 12_000</gadget>
<output>12_880</output>

<gadget id="calculator">12_880 / 230</gadget>
<output>56</output>

<gadget id="calculator">56 / 7</gadget>
<output>8</output>

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

Choices:
A. 18
B. 28
C. 40
D. 56
E. 60

multiply(divide(divide(add(add(multiply(multiply(const_4, const_2), const_10), multiply(multiply(const_4, const_2), const_100)), multiply(const_12, const_1000)), 230), 7), 5)

Explanation: "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 5 x = 5 * 8 = 40 . hence c ."


Question: calculate the amount that an investor needs to be invest to earn $ 1005 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 11 % compounded semi - annually ?

Choices:
A. 8000
B. 8100
C. 8900
D. 8600
E. 8400

Explanation: "the approach is substitution , our interest requirement is $ 1005 after 12 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields 460 in 12 months 8900 yielded $ 1005 using the formula a = p ( 1 + r / n ) nt hence answer is c"


Question: a reduction of 42 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?

<gadget id="calculator">42 / 100</gadget>
<output>21/50 = around 0.42</output>

<gadget id="calculator">42 * (21/50)</gadget>
<output>441/25 = around 17.64</output>

<gadget id="calculator">(441/25) / 64</gadget>
<output>441/1_600 = around 0.275625</output>

<gadget id="calculator">12 * (441/1_600)</gadget>
<output>1_323/400 = around 3.3075</output>
<result>1_323/400 = around 3.3075</result>

Choices:
A. 2.15
B. 8.15
C. 7.15
D. 3.15
E. 1.15

multiply(const_12, divide(multiply(42, divide(42, const_100)), 64))

Explanation: "explanation : 40 * ( 42 / 100 ) = 16.8 - - - 64 ? - - - 12 = > rs . 3.15 answer : d"


Question: a train crosses a bridge of length 1500 m in 70 seconds and a lamp post on the bridge in 20 seconds . what is the length of the train in metres ?

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

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

<gadget id="calculator">30 * 20</gadget>
<output>600</output>
<result>600</result>

Choices:
A. 375 m
B. 750 m
C. 250 m
D. 600 m
E. 300 m

multiply(divide(1500, subtract(70, 20)), 20)

Explanation: "let length of train = l case - 1 : distance = 1500 + l ( while crossing the bridge ) time = 70 seconds i . e . speed = distance / time = ( 1500 + l ) / 70 case - 2 : distance = l ( while passing the lamp post ) time = 20 seconds i . e . speed = distance / time = ( l ) / 20 but since speed has to be same in both cases so ( 1500 + l ) / 70 = ( l ) / 20 i . e . 1500 + l = 3.5 l i . e . 2.5 l = 1500 i . e . l = 600 answer : option d"


Question: what will be the cost of building a fence around a square plot with area equal to 289 square feet , if the price per foot of building the fence is rs . 58 ?

<gadget id="calculator">289 ** (1/2)</gadget>
<output>17</output>

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

<gadget id="calculator">68 * 58</gadget>
<output>3_944</output>
<result>3_944</result>

Choices:
A. 3944
B. 3932
C. 3929
D. 3926
E. 3902

Explanation: "let the side of the square plot be a foot a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 foot cost of building the fence = 68 * 58 = rs . 3944 . answer : a"


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

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

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

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

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

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

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

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

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

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


Question: the dimensions of a field are 20 m by 10 m . a pit 8 m long , 5 m wide and 2 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?

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

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

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

<gadget id="calculator">200 - 40</gadget>
<output>160</output>

<gadget id="calculator">80 / 160</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

Choices:
A. 1 m
B. 2 m
C. 0.5 m
D. 0.75 m
E. 1.5 m

divide(multiply(10, 8), subtract(rectangle_area(20, 10), rectangle_area(5, 8)))

Explanation: the volume of the earth removed is 8 * 5 * 2 = 80 m ^ 3 . the remaining area of the field is 20 * 10 - 8 * 5 = 160 m ^ 2 . 80 m ^ 3 of the earth evenly spread over the area of 160 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 80 / 160 = 0.5 m . answer : c


Question: the grade point average of the entire class is 90 . if the average of one third of the class is 96 , what is the average of the rest ?

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

<gadget id="calculator">360 - 96</gadget>
<output>264</output>

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

<gadget id="calculator">264 / 3</gadget>
<output>88</output>
<result>88</result>

Choices:
A. 92
B. 89
C. 88
D. 87
E. 86

divide(subtract(multiply(90, const_4), 96), subtract(const_4, const_1))

Explanation: "let us take number of students on the class as ' x ' . avg grade point = sum of all grade points / x sum of all grade points = avg grade point * x = 90 x average of one third of the class = 96 = sum of one third grade points of the class / ( x / 3 ) sum of one third grade points of the class = 96 * ( x / 3 ) = 32 x sum of rest two third grade points of the class = sum of all grade points - sum of one third grade points of the class sum of rest two third grade points of the class = 90 x - 32 x = 58 x avg of two third of the class = sum of rest two third grade points of the class / ( x * 2 / 3 ) = 58 x / ( 2 x / 3 ) = 29 * 3 = 87 . hence , answer is d"


Question: last year department store x had a sales total for december that was 6 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?

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

<gadget id="calculator">11 + 6</gadget>
<output>17</output>

<gadget id="calculator">6 / 17</gadget>
<output>6/17 = around 0.352941</output>
<result>6/17 = around 0.352941</result>

Choices:
A. 6 / 17
B. 4 / 15
C. 1 / 3
D. 4 / 11
E. 4 / 5

divide(6, add(subtract(const_12, const_1), 6))

Explanation: "let avg for 11 mos . = 10 therefore , dec = 60 year total = 11 * 10 + 60 = 170 answer = 60 / 170 = 6 / 17 = a"


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

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

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

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

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

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

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

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

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

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


Question: if x is the median of the set { 9 / 2 , 11 / 3 , x , 28 / 9 , 21 / 5 } , x could be

<gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>

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

<gadget id="calculator">(9/2) + (11/3)</gadget>
<output>49/6 = around 8.166667</output>

<gadget id="calculator">28 / 9</gadget>
<output>28/9 = around 3.111111</output>

<gadget id="calculator">(49/6) + (28/9)</gadget>
<output>203/18 = around 11.277778</output>

<gadget id="calculator">21 / 5</gadget>
<output>21/5 = around 4.2</output>

<gadget id="calculator">(203/18) + (21/5)</gadget>
<output>1_393/90 = around 15.477778</output>

<gadget id="calculator">(1_393/90) / 4</gadget>
<output>1_393/360 = around 3.869444</output>

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

<gadget id="calculator">(1_393/360) + (1/10)</gadget>
<output>1_429/360 = around 3.969444</output>

<gadget id="calculator">(1_429/360) + (1/10)</gadget>
<output>293/72 = around 4.069444</output>
<result>293/72 = around 4.069444</result>

Choices:
A. 16 / 5
B. 17 / 5
C. 4 / 7
D. 30 / 7
E. 4

add(add(divide(add(add(add(divide(9, 2), divide(11, 3)), divide(28, 9)), divide(21, 5)), const_4), divide(const_10, const_100)), divide(const_10, const_100))

Explanation: "the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 11 / 3 = 3 . something , 28 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( e )"


Question: a can do a piece of work in 4 days . b can do it in 7 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?

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

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

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

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

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

<gadget id="calculator">28 - 22</gadget>
<output>6</output>

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

<gadget id="calculator">28 / 3</gadget>
<output>28/3 = around 9.333333</output>
<result>28/3 = around 9.333333</result>

Choices:
A. 22 days
B. 28 / 3 days
C. 67 days
D. 17 / 5 days
E. 18 days

divide(multiply(4, 7), divide(subtract(multiply(4, 7), multiply(add(divide(multiply(4, 7), 4), divide(multiply(4, 7), 7)), 2)), 2))

Explanation: "c = 1 / 2 - 1 / 4 - 1 / 7 = 3 / 28 = > 28 / 3 days answer : b"


Question: what least no . must be subtracted from 101054 so that remaining no . is divisible by 10 ?

<gadget id="calculator">101_054 / 10</gadget>
<output>50_527/5 = around 10_105.4</output>

<gadget id="calculator">floor(50_527/5)</gadget>
<output>10_105</output>

<gadget id="calculator">10_105 * 10</gadget>
<output>101_050</output>

<gadget id="calculator">101_054 - 101_050</gadget>
<output>4</output>
<result>4</result>

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

subtract(101054, multiply(floor(divide(101054, 10)), 10))

Explanation: "explanation : on dividing 101054 by 10 we get the remainder 4 , so 4 should be subtracted option b"


Question: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 8 years ?

<gadget id="calculator">900 - 750</gadget>
<output>150</output>

<gadget id="calculator">150 / 750</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) / 8</gadget>
<output>1/40 = around 0.025</output>

<gadget id="calculator">(1/40) * 100</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>

Choices:
A. 6 %
B. 2.5 %
C. 4 %
D. 5 %
E. 3.5 %

multiply(divide(divide(subtract(900, 750), 750), 8), const_100)

Explanation: 150 = ( 750 * 8 * r ) / 100 r = 2.5 % answer : b


Question: machine – x produces 50 % of the total output and machine - y produces 75 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - x and two unit of 500 units produced by machine - x prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ?

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

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

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

<gadget id="calculator">9 + 6</gadget>
<output>15</output>

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

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

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

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

<gadget id="calculator">15 / 2_500</gadget>
<output>3/500 = around 0.006</output>
<result>3/500 = around 0.006</result>

Choices:
A. 0.008
B. 0.1
C. 0.12
D. 0.006
E. 0.007

divide(add(9, divide(divide(9, divide(75, const_100)), const_2)), add(add(1000, multiply(1000, divide(50, const_100))), 1000))

Explanation: suppose machine x produce 1000 units total defective = 9 machine y then produces = 1500 units total defective = 6 probability = 15 / 2500 = 0.006 answer : d


Question: find the cost of fencing around a circular field of diameter 22 m at the rate of rs . 2.50 a meter ?

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

<gadget id="calculator">2 * pi * 11</gadget>
<output>22*pi = around 69.115038</output>

<gadget id="calculator">(22*pi) * 2.5</gadget>
<output>55.0*pi = around 172.787596</output>
<result>55.0*pi = around 172.787596</result>

Choices:
A. 188
B. 172
C. 278
D. 279
E. 222

Explanation: "2 * 22 / 7 * 11 = 69 69 * 2 1 / 2 = rs . 172 answer : b"


Question: two cycles are standing side - by - side . one cycle , which is 2.5 feets tall , casts a shadow that is 5 feets long . the other cycle is 2 feets tall . compute , in feets , the length of the shadow that the shorter cycle casts .

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

<gadget id="calculator">10 / 2.5</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 3
B. 4
C. 6
D. 8
E. 10

Explanation: the ratio of shadow to height is constant , so if x is the length of the shadow , then 2.5 / 5 = 2 / x and x = 4 . correct answer b


Question: stacy has a 12 page history paper due in 12 days . how many pages per day would she have to write to finish on time ?

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

Choices:
A. 9
B. 8
C. 10
D. 1
E. 6

Explanation: "12 / 12 = 1 answer : d"


Question: on a two - dimensional coordinate plane , the line a = x ^ 2 - x ^ 3 touches the x - axis in how many places ?

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

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

Choices:
A. 0
B. 1
C. 2
D. 3
E. 4

Explanation: "apparently it ' s a = x ^ 2 - x ^ 3 instead of a = x ^ 2 - a ^ 3 . in this case : the x - intercept is the value ( s ) of x for a = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ."


Question: if the wages of 6 men for 15 days be rs . 2100 , then find the wages of for 12 days .

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

<gadget id="calculator">2_100 / 15</gadget>
<output>140</output>

<gadget id="calculator">140 / 6</gadget>
<output>70/3 = around 23.333333</output>

<gadget id="calculator">12 * (70/3)</gadget>
<output>280</output>

<gadget id="calculator">9 * 280</gadget>
<output>2_520</output>
<result>2_520</result>

Choices:
A. rs . 2420
B. rs . 2500
C. rs . 2520
D. rs . 2020
E. rs . 2650

multiply(multiply(const_3, const_3), multiply(12, divide(divide(2100, 15), 6)))

Explanation: . let the required wages be rs . x . more men , more wages ( direct proportion ) less days , less wages ( direct proportion ) men 6 : 9 : : 2100 : x days 15 : 12 therefore ( 6 x 15 x x ) = ( 9 x 12 x 2100 )  x = ( 9 x 12 x 2100 ) / ( 6 x 15 ) = 2520 hence the required wages are rs . 2520 . answer is c


Question: a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 40 percent of the drive from the center , what percent of the round - trip has the technician completed ?

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

<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>

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

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

Choices:
A. 5 %
B. 70 %
C. 25 %
D. 40 %
E. 55 %

add(divide(const_100, const_2), divide(multiply(40, divide(const_100, const_2)), const_100))

Explanation: "the complete round trip consists of driving to the service center and then back home again . so , once the technician drives to the service center he / she has already competed 50 % of the entire trip . since the technician completes a portion of the trip back home , the correct answer must be greater than 50 % so 0.5 + 0.5 * 0.4 = 0.70 answer : b"


Question: what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 35 ?

Choices:
A. 884
B. 890
C. 892
D. 910
E. 945

subtract(1000, subtract(add(divide(1000, 11), divide(1000, 35)), divide(1000, multiply(11, 35))))

Explanation: "number divisible by 11 : - 1000 / 11 = 90 numbers divisible by 35 : - 1000 / 35 = 28 numbers divisible by both 11 and 35 = 2 total numbers divisible by both 11 and 28 = 90 + 28 - 2 = 116 ( because we counted 2 in both 90 and 28 ) total numbers not divisible by 11 or 35 = 1000 - 116 = 884 answer : a"


Question: 3 positive integers a , b , and c are such that their average is 20 and a ≤ b ≤ c . if the median is ( a + 13 ) , what is the least possible value of c ?

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

<gadget id="calculator">13 + 1</gadget>
<output>14</output>

<gadget id="calculator">13 + 14</gadget>
<output>27</output>

<gadget id="calculator">60 - 27</gadget>
<output>33</output>

<gadget id="calculator">33 / 3</gadget>
<output>11</output>

<gadget id="calculator">11 + 14</gadget>
<output>25</output>
<result>25</result>

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

add(divide(subtract(multiply(20, 3), add(13, add(13, const_1))), 3), add(13, const_1))

Explanation: solution : we know that the average value is 20 therefore ( a + b + c ) / 3 = 20 so a + b + c = 60 and b = a + 13 therefore a + ( a + 13 ) + c = 60 the least value of c is when c = b so take c = a + 13 hence , a + ( a + 13 ) + ( a + 13 ) = 60 i . e . , a = 34 / 3 a non integer therefore c is not equal to b so take c = b + 1 therefore c = a + 14 a + ( a + 13 ) + ( a + 14 ) = 60 i . e . , a = 33 / 3 = 11 hence , a = 11 , b = 24 , and c = 25 answer : e


Question: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips ?

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

<gadget id="calculator">(1/2) ** 6</gadget>
<output>1/64 = around 0.015625</output>
<result>1/64 = around 0.015625</result>

Choices:
A. 1 / 8
B. 1 / 16
C. 1 / 32
D. 1 / 64
E. 1 / 128

Explanation: "p ( hhhhtt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 64 the answer is d ."


Question: a man goes downstream at 10 kmph , and upstream 8 kmph . the speed of the stream is

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

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

Choices:
A. 0 kmph
B. 4 kmph
C. 1 kmph
D. 2.5 kmph
E. 26 kmph

Explanation: "speed of the stream = 1 / 2 ( 10 - 8 ) kmph = 1 kmph . correct option : c"


Question: if shares of two persons in profits are rs . 600 and rs . 1000 then ratio of their capitals is

<gadget id="calculator">600 / 1_000</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>

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

Explanation: "profit = time * capital so 600 : 1000 = 3 : 5 answer : a"


Question: if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 22 , then n =

<gadget id="calculator">22 * 2</gadget>
<output>44</output>

<gadget id="calculator">44 - 2</gadget>
<output>42</output>

<gadget id="calculator">42 / 2</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 3
B. 6
C. 12
D. 23
E. 21

Explanation: 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 22 = > 4 x 2 ^ 2 n = 4 ^ 22 = 2 ^ 44 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 44 = > 2 ^ ( 2 n + 2 ) = 2 ^ 44 = > 2 n + 2 = 44 = > n = 21 so . answer will be e .


Question: a is the average ( arithmetic mean ) of the first 7 positive multiples of 5 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?

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

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

Choices:
A. 5
B. 6
C. 10
D. 15
E. 20

Explanation: "if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 20 , which also equals b . b is the second positive multiple of n , thus n = 20 / 2 = 10 . the answer is c ."


Question: length of a rectangular plot is 10 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?

<gadget id="calculator">5_300 / 26.5</gadget>
<output>200</output>

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

<gadget id="calculator">200 + 20</gadget>
<output>220</output>

<gadget id="calculator">220 / 4</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 46 m
B. 55 m
C. 58 m
D. 78 m
E. 80 m

divide(add(divide(5300, 26.50), multiply(const_2, 10)), const_4)

Explanation: "let breadth = x metres . then , length = ( x + 10 ) metres . perimeter = 5300 / 26.5 = 200 m . 2 [ ( x + 10 ) + x ] = 200 2 x + 10 = 100 2 x = 90 x = 45 . hence , length = x + 10 = 55 m b"


Question: 2 men and 4 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )

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

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

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

Choices:
A. 12
B. 15
C. 18
D. 21
E. 48

Explanation: the list should be wmwmw . hence , from women 4 ! and men 2 ! , we get ( 4 ! ) ( 2 ! ) = 48 . therefore , the correct answer is e .


Question: each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 40 minutes earlier than usual . how much time did the man spend walking ?

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

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

Choices:
A. 45 minutes
B. 50 minutes
C. 40 minutes
D. 55 minutes
E. 35 minutes

Explanation: "as they arrived 40 minutes earlier than usual , they saved 40 minutes on round trip from home to station ( home - station - home ) - - > 20 minutes in each direction ( home - station ) - - > wife meets husband 20 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 20 minutes = 40 minutes . answer : c"


Question: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio a of men to women ?

<gadget id="calculator">180 - 170</gadget>
<output>10</output>

<gadget id="calculator">184 - 180</gadget>
<output>4</output>

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

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

divide(subtract(180, 170), subtract(184, 180))

Explanation: ( a ) a = 184 x 5 + 170 x 2 = 1260 . a


Question: if ( 8000 ) ( 6000 ) = ( 480 ) ( 10 ^ y ) , what is the value of y ?

<gadget id="calculator">8_000 * 6_000</gadget>
<output>48_000_000</output>

<gadget id="calculator">48_000_000 / 480</gadget>
<output>100_000</output>

<gadget id="calculator">log(100_000)</gadget>
<output>log(100000) = around 11.512925</output>

<gadget id="calculator">log(10)</gadget>
<output>log(10) = around 2.302585</output>

<gadget id="calculator">log(100000) / log(10)</gadget>
<output>log(100000)/log(10) = around 5</output>
<result>log(100000)/log(10) = around 5</result>

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

divide(log(divide(multiply(8000, 6000), 480)), log(const_10))

Explanation: ( 8000 ) ( 6000 ) = ( 480 ) ( 10 ^ y ) = > ( 8000 ) ( 6000 ) / 480 = 10 ^ y = > 100000 = 100 ^ y = > 10 ^ 5 = 10 ^ y since , base is same so powers will be same too . so , y = 5 answer will be a


Question: if ( 5 + k ) ( 5 - k ) = ( 5 ^ 2 ) - ( 2 ^ 3 ) , then what is the value of k ?

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

<gadget id="calculator">3 + 10</gadget>
<output>13</output>

<gadget id="calculator">15 - 13</gadget>
<output>2</output>
<result>2</result>

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

subtract(multiply(5, 3), add(3, const_10))

Explanation: obviously , it is in the formula a ^ 2 - b ^ 2 = ( a + b ) ( a - b ) so k is 2 option d


Question: a train consists of 48 boxcars pulled by 2 engines . the boxcars are 15 meters long and the two engines are each 20 meters long . it crosses over a highway 24 meters wide at a speed of 14 m / s . how long does it take for the entire train to cross ?

<gadget id="calculator">48 * 15</gadget>
<output>720</output>

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

<gadget id="calculator">720 + 40</gadget>
<output>760</output>

<gadget id="calculator">760 / 14</gadget>
<output>380/7 = around 54.285714</output>
<result>380/7 = around 54.285714</result>

Choices:
A. 56 sec
B. 63 sec
C. 72 sec
D. 81 sec
E. 88 sec

divide(add(multiply(48, 15), multiply(20, 2)), 14)

Explanation: a 56 sec d = 48 * 15 m + 2 * 20 m + 24 m = 784 m t = 784 m / 14 m / s = 56 s


Question: a store reported total sales of $ 416 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?

<gadget id="calculator">416 - 320</gadget>
<output>96</output>

<gadget id="calculator">96 / 320</gadget>
<output>3/10 = around 0.3</output>

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

Choices:
A. 2 %
B. 17 %
C. 30 %
D. 65 %
E. 83 %

multiply(divide(subtract(416, 320), 320), const_100)

Explanation: "new value – old value ) / old value x 100 we are given : february sales this year = 416 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 416 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 416 – 320 ) / 320 ] x 100 = 30 % the answer is c ."


Question: the ratio of the radius of two circles is 2 : 5 , and then the ratio of their areas is ?

<gadget id="calculator">pi * (2 ** 2)</gadget>
<output>4*pi = around 12.566371</output>

<gadget id="calculator">pi * (5 ** 2)</gadget>
<output>25*pi = around 78.539816</output>

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

Choices:
A. 4 : 25
B. 2 : 9
C. 1 : 9
D. 3 : 7
E. 3 : 4

Explanation: "r 1 : r 2 = 2 : 5 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 4 : 25 answer : a"


Question: of the families in city x in 2000 , 30 percent owned a personal computer . the number of families in city x owning a computer in 2004 was 20 percent greater than it was in 1994 , and the total number of families in city x was 10 percent greater in 2004 than it was in 2000 . what percent of the families in city x owned a personal computer in 1998 ?

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

<gadget id="calculator">120 * 30</gadget>
<output>3_600</output>

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

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

<gadget id="calculator">36 / 110</gadget>
<output>18/55 = around 0.327273</output>

<gadget id="calculator">100 * (18/55)</gadget>
<output>360/11 = around 32.727273</output>
<result>360/11 = around 32.727273</result>

Choices:
A. 55.42 %
B. 52.25 %
C. 56.23 %
D. 30.70 %
E. 32.72 %

multiply(const_100, divide(divide(multiply(add(20, const_100), 30), const_100), add(const_100, 10)))

Explanation: "say a 100 families existed in 2000 then the number of families owning a computer in 2000 - 30 number of families owning computer in 2000 = 30 * 120 / 100 = 36 number of families in 2004 = 110 the percentage = 36 / 110 * 100 = 32.72 % . option : e"


Question: raman mixed 48 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?

<gadget id="calculator">48 * 150</gadget>
<output>7_200</output>

<gadget id="calculator">36 * 125</gadget>
<output>4_500</output>

<gadget id="calculator">7_200 + 4_500</gadget>
<output>11_700</output>

<gadget id="calculator">36 + 48</gadget>
<output>84</output>

<gadget id="calculator">11_700 / 84</gadget>
<output>975/7 = around 139.285714</output>

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

<gadget id="calculator">(975/7) * (2/5)</gadget>
<output>390/7 = around 55.714286</output>

<gadget id="calculator">(975/7) + (390/7)</gadget>
<output>195</output>
<result>195</result>

Choices:
A. 129
B. 287
C. 195
D. 188
E. 112

add(divide(add(multiply(48, 150), multiply(36, 125)), add(36, 48)), multiply(divide(add(multiply(48, 150), multiply(36, 125)), add(36, 48)), divide(40, const_100)))

Explanation: "explanation : cp per kg of mixture = [ 48 ( 150 ) + 36 ( 125 ) ] / ( 48 + 36 ) = rs . 139.28 sp = cp [ ( 100 + profit % ) / 100 ] = 139.28 * [ ( 100 + 40 ) / 100 ] = rs . 195 answer : c"