Question: tough and tricky questions : ratios 4 / 5 of a certain class left on a field trip . 1 / 3 of the students who stayed behind did not want to go on the field trip ( all the others did want to go ) . when another vehicle was located , 1 / 2 of the students who did want to go on the field trip but had been left behind were able to join . what fraction of the class ended up going on the field trip ?

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

<gadget id="calculator">lcm(3, 5)</gadget>
<output>15</output>

<gadget id="calculator">lcm(15, 2)</gadget>
<output>30</output>

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

<gadget id="calculator">(4/5) * 30</gadget>
<output>24</output>

<gadget id="calculator">30 - 24</gadget>
<output>6</output>

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

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

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

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

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

<gadget id="calculator">26 / 30</gadget>
<output>13/15 = around 0.866667</output>
<result>13/15 = around 0.866667</result>

Choices:
A. 1 / 2
B. 2 / 3
C. 13 / 15
D. 23 / 30
E. 4 / 5

divide(add(multiply(divide(1, 2), subtract(subtract(lcm(lcm(3, 5), 2), multiply(divide(4, 5), lcm(lcm(3, 5), 2))), multiply(divide(1, 3), subtract(lcm(lcm(3, 5), 2), multiply(divide(4, 5), lcm(lcm(3, 5), 2)))))), multiply(divide(4, 5), lcm(lcm(3, 5), 2))), lcm(lcm(3, 5), 2))

Explanation: let total no . of students be 30 students left on a field trip = 4 / 5 ( 30 ) = 24 thus 6 students left behind 1 / 3 ( 6 ) = 2 students did not want to go . thus 4 students want to go on the trip 1 / 2 ( 4 ) = 2 were able to join the other students on the field trip . thus total number of students that went on a field trip = 24 + 2 = 26 thus required fraction = 26 / 30 = 13 / 15 c


Question: if x ^ 2 + 9 / x ^ 2 = 10 , what is the value of x - 3 / x

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

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

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

Choices:
A. 36
B. 25
C. 2
D. 5
E. 3

Explanation: to find : x - 3 / x . let it be t . = > x - 3 / x = t = > ( x ^ 2 + 9 / x ^ 2 ) - 2 * x * 3 / x = t ^ 2 ( squaring both sides ) . = > ( 10 ) - 2 * 3 = 4 = > t ^ 2 = 4 . thus t = 2 or t = - 2 . answer c


Question: the average salary / head of all the workers in a workshop is rs . 1100 , if the average salary / head of 9 technician is rs . 1300 and the average salary / head of the rest is rs . 880 , the total no . of workers in the work - shop is ?

<gadget id="calculator">9 * 1_300</gadget>
<output>11_700</output>

<gadget id="calculator">880 * 9</gadget>
<output>7_920</output>

<gadget id="calculator">11_700 - 7_920</gadget>
<output>3_780</output>

<gadget id="calculator">1_100 - 880</gadget>
<output>220</output>

<gadget id="calculator">3_780 / 220</gadget>
<output>189/11 = around 17.181818</output>
<result>189/11 = around 17.181818</result>

Choices:
A. 18
B. 20
C. 22
D. 17
E. 26

divide(subtract(multiply(9, 1300), multiply(880, 9)), subtract(1100, 880))

Explanation: let the total number of workers be y . so sum of salary for all workers = sum of salary of 9 technician + sum of salary for other y - 9 workers . 9 x 1300 + 880 ( y - 9 ) = 1100 y ⇒ 11700 + 880 y - 7920 = 1100 y ⇒ 220 y = 3780 ∴ y = 17 so total number of workers = 17 d


Question: joe invested a certain sum of money in a simple interest bond whose value grew to $ 310 at the end of 3 years and to $ 410 at the end of another 5 years . what was the rate of interest in which he invested his sum ?

<gadget id="calculator">410 - 310</gadget>
<output>100</output>

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

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

<gadget id="calculator">310 - 60</gadget>
<output>250</output>

<gadget id="calculator">20 / 250</gadget>
<output>2/25 = around 0.08</output>

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

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

multiply(divide(divide(subtract(410, 310), 5), subtract(310, multiply(divide(subtract(410, 310), 5), 3))), const_100)

Explanation: "in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 310 - $ 60 = 250 . the interest rate is $ 20 / $ 250 = 8 % the answer is c ."


Question: a rhombus has area 432 sq m , one diagonal is 36 cm . find other diagonal ?

<gadget id="calculator">432 * 2</gadget>
<output>864</output>

<gadget id="calculator">36 / 100</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">864 / (9/25)</gadget>
<output>2_400</output>
<result>2_400</result>

Choices:
A. 2400 m
B. 2500 m
C. 2600 m
D. 2700 m
E. 2900 m

divide(multiply(432, const_2), divide(36, const_100))

Explanation: area of rhombus = 1 / 2 * d 1 * d 2 432 = 1 / 2 * d 1 * . 36 d 1 = 2400 m answer : a


Question: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 12 } + { 10 } ?

<gadget id="calculator">12 + 10</gadget>
<output>22</output>

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

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

<gadget id="calculator">11 + 2</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 23
B. 20
C. 13
D. 5
E. 2

add(divide(add(12, 10), const_2), multiply(1, const_2))

Explanation: "soln : { 12 } + { 10 } = 12 * { 10 } + { 10 } = 13 * { 10 } answer : c"


Question: a , b and c invested rs . 2400 , rs . 7200 and rs . 9600 respectively , in a partnership business . find the share of a in profit of rs . 9000 after a year ?

<gadget id="calculator">2_400 + 7_200</gadget>
<output>9_600</output>

<gadget id="calculator">9_600 + 9_600</gadget>
<output>19_200</output>

<gadget id="calculator">2_400 / 19_200</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/8) * 9_000</gadget>
<output>1_125</output>
<result>1_125</result>

Choices:
A. 1125
B. 2400
C. 7200
D. 2500
E. 2511

Explanation: "explanation : 2400 : 7200 : 9600 1 : 3 : 4 1 / 8 * 9000 = 1125 answer : a"


Question: a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 165 . find the unknown rate of two towels ?

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

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

<gadget id="calculator">10 * 165</gadget>
<output>1_650</output>

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

<gadget id="calculator">1_650 - 750</gadget>
<output>900</output>

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

<gadget id="calculator">900 - 300</gadget>
<output>600</output>
<result>600</result>

Choices:
A. 400
B. 450
C. 500
D. 550
E. 600

subtract(subtract(multiply(add(add(3, 5), const_2), 165), multiply(5, 150)), multiply(3, 100))

Explanation: "10 * 150 = 1650 3 * 100 + 5 * 150 = 1050 1650 – 1050 = 600 e"


Question: aaron will jog from home at 2 miles per hour and then walk back home by the same route at 4 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?

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

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

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

Choices:
A. 5
B. 7
C. 3
D. 9
E. 10

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

Explanation: xyt / ( x + y ) x = 2 , y = 4 t = 3 2 * 4 * 3 / 2 + 4 = 18 / 6 = 3 answer : c


Question: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 57600 ?

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

<gadget id="calculator">(1/8) * 57_600</gadget>
<output>7_200</output>

<gadget id="calculator">57_600 + 7_200</gadget>
<output>64_800</output>

<gadget id="calculator">(1/8) * 64_800</gadget>
<output>8_100</output>

<gadget id="calculator">64_800 + 8_100</gadget>
<output>72_900</output>
<result>72_900</result>

Choices:
A. 81000
B. 81028
C. 27772
D. 72900
E. 22312

Explanation: 57600 * 9 / 8 * 9 / 8 = 72900 . answer : d


Question: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 35 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?

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

<gadget id="calculator">(1/5) * 500</gadget>
<output>100</output>

<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>

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

<gadget id="calculator">(7/20) * 300</gadget>
<output>105</output>

<gadget id="calculator">100 + 105</gadget>
<output>205</output>

<gadget id="calculator">205 / 800</gadget>
<output>41/160 = around 0.25625</output>

<gadget id="calculator">(41/160) * 100</gadget>
<output>205/8 = around 25.625</output>
<result>205/8 = around 25.625</result>

Choices:
A. 22 %
B. 24 %
C. 25 %
D. 26 %
E. 28 %

multiply(divide(add(multiply(divide(20, const_100), 500), multiply(divide(35, const_100), subtract(800, 500))), 800), const_100)

Explanation: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 35 / 100 ) * 300 = 100 + 105 = 205 % comission = ( 205 / 800 ) * 100 = 25.6 ~ 26 % answer is d"


Question: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 135 km downstream

<gadget id="calculator">22 + 5</gadget>
<output>27</output>

<gadget id="calculator">135 / 27</gadget>
<output>5</output>
<result>5</result>

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

Explanation: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 135 km time taken = distance / speed = 135 / 27 = 5 hours . answer : option a"


Question: a bag contains 5 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is

<gadget id="calculator">5 + 8</gadget>
<output>13</output>

<gadget id="calculator">8 / 13</gadget>
<output>8/13 = around 0.615385</output>

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

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

<gadget id="calculator">7 / 12</gadget>
<output>7/12 = around 0.583333</output>

<gadget id="calculator">(8/13) * (7/12)</gadget>
<output>14/39 = around 0.358974</output>

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

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

<gadget id="calculator">4 / 12</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(5/13) * (1/3)</gadget>
<output>5/39 = around 0.128205</output>

<gadget id="calculator">(14/39) + (5/39)</gadget>
<output>19/39 = around 0.487179</output>
<result>19/39 = around 0.487179</result>

Choices:
A. 8 / 15
B. 2 / 5
C. 3 / 5
D. 11 / 15
E. 19 / 39

add(multiply(divide(8, add(5, 8)), divide(subtract(8, const_1), subtract(add(5, 8), const_1))), multiply(divide(5, add(5, 8)), divide(subtract(5, const_1), subtract(add(5, 8), const_1))))

Explanation: "drawing two balls of same color from five green balls can be done in 5 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 5 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 19 / 39 answer : e"


Question: find the 10 th term of an arithmetic progression whose first term is 8 and the common difference is 2 .

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

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

<gadget id="calculator">18 + 8</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 45
B. 26
C. 44
D. 40
E. 46

add(multiply(subtract(10, const_1), 2), 8)

Explanation: "n th term of a . p = a + ( n - 1 ) * d = 8 + ( 10 - 1 ) * 2 , = 8 + 18 = 26 . answer : b"


Question: if ( 10 x + 2 ) / 4 - ( 3 x - 6 ) / 18 = ( 2 x + 4 ) / 3 , then what is the value of x ?

<gadget id="calculator">lcm(4, 18)</gadget>
<output>36</output>

<gadget id="calculator">lcm(36, 3)</gadget>
<output>36</output>

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

<gadget id="calculator">12 * 4</gadget>
<output>48</output>

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

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

<gadget id="calculator">48 - 18</gadget>
<output>30</output>

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

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

<gadget id="calculator">30 - 12</gadget>
<output>18</output>

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

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

<gadget id="calculator">90 - 6</gadget>
<output>84</output>

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

<gadget id="calculator">84 - 24</gadget>
<output>60</output>

<gadget id="calculator">18 / 60</gadget>
<output>3/10 = around 0.3</output>
<result>3/10 = around 0.3</result>

Choices:
A. 3
B. - 3
C. 10 / 3
D. 3 / 10
E. - 10 / 3

divide(subtract(subtract(multiply(divide(lcm(lcm(4, 18), 3), 3), 4), multiply(divide(lcm(lcm(4, 18), 3), 4), 2)), multiply(divide(lcm(lcm(4, 18), 3), 18), 6)), subtract(subtract(multiply(divide(lcm(lcm(4, 18), 3), 4), 10), multiply(divide(lcm(lcm(4, 18), 3), 18), 3)), multiply(divide(lcm(lcm(4, 18), 3), 3), 2)))

Explanation: ( 10 x + 2 ) / 4 - ( 3 x - 6 ) / 18 = ( 2 x + 4 ) / 3 = > 18 ( 10 x + 2 ) / 4 - ( 3 x - 6 ) = 18 ( 2 x + 4 ) / 3 = > 4.5 ( 10 x + 2 ) - 3 x + 6 = 6 ( 2 x + 4 ) = > 45 x + 9 - 3 x + 6 = 12 x + 24 = > 45 x - 3 x - 12 x = 24 - 9 - 6 = > 30 x = 9 = > x = 9 / 30 = > x = 3 / 10 answer : d


Question: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.80 per metre .

Choices:
A. 2399
B. 6336
C. 2999
D. 5808
E. 2888

multiply(circumface(multiply(sqrt(divide(13.86, const_pi)), const_100)), 4.80)

Explanation: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.80 ) = rs . 6336 . answer : b ) 6336"


Question: a train 150 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?

<gadget id="calculator">68 - 8</gadget>
<output>60</output>

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

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

<gadget id="calculator">150 / (50/3)</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 2 sec
B. 6 sec
C. 8 sec
D. 9 sec
E. 5 sec

divide(150, multiply(subtract(68, 8), const_0_2778))

Explanation: "d 9 sec speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 150 m at 50 / 3 m / sec = 150 * 3 / 50 sec = 9 sec"


Question: annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 30 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?

<gadget id="calculator">15 - 12</gadget>
<output>3</output>

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

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

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

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

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

<gadget id="calculator">(4/3) * 60</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 20
B. 40
C. 60
D. 80
E. 100

multiply(divide(subtract(divide(12, multiply(subtract(15, 12), divide(40, const_60))), multiply(subtract(15, 12), divide(40, const_60))), subtract(15, 12)), const_60)

Explanation: annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 30 minutes , sam rides 6 km so sam will be 4 km ahead . it will take annie 80 minutes to catch sam . the answer is d .


Question: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.60 more than jane , what was the original price of the dish ?

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

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

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

<gadget id="calculator">(9/10) * (3/20)</gadget>
<output>27/200 = around 0.135</output>

<gadget id="calculator">(3/20) - (27/200)</gadget>
<output>3/200 = around 0.015</output>

<gadget id="calculator">0.6 / (3/200)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 24
B. 34.8
C. 37.8
D. 40
E. 84

divide(0.60, subtract(divide(15, const_100), multiply(subtract(const_1, divide(10, const_100)), divide(15, const_100))))

Explanation: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.60 - - > 15 p - 13.5 p = 60 - - > p = 40 . answer : d ."


Question: a certain industrial loom weaves 0.126 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?

<gadget id="calculator">15 / 0.126</gadget>
<output>119.047619</output>
<result>119.047619</result>

Choices:
A. 114
B. 115
C. 116
D. 117
E. 119

Explanation: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.126 : 15 : : 1 : x = > 0.126 * x = 15 = > x = 15 / 0.126 = > x = 119 answer : e"


Question: a cistern is normally filled in 8 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?

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

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

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

<gadget id="calculator">(1/8) - (1/10)</gadget>
<output>1/40 = around 0.025</output>

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

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

inverse(subtract(divide(const_1, 8), divide(const_1, add(8, 2))))

Explanation: if leakage / hour = 1 / x , then 1 / 8 - 1 / x = 1 / 10 , solving 1 / x = 1 / 40 so in 40 hours full cistern will be empty . answer : d


Question: oil cans x and y are right circular cylinders and the height and radius of y are each 4 times those of x . if the oil in can x filled to capacity sells for $ 2 , how much does the oil in y sell for if y is only half filled ?

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

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

Choices:
A. $ 60
B. $ 52
C. $ 63
D. $ 64
E. $ 68

Explanation: formula for vol of a cyl is pi * r ^ 2 * h so vy = 64 * vy y when half filled will cost 32 times x so ans is d


Question: how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 15 ?

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

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

Choices:
A. 15
B. 16
C. 17
D. 18
E. 13

Explanation: so i can write this as in - 3 i + 4 < = 15 or in - 3 i < = 11 so n can have - 8 to 14 = 13 true values . . . . e


Question: a man rows his boat 75 km downstream and 45 km upstream , taking 5 hours each time . find the speed of the stream ?

<gadget id="calculator">75 / 5</gadget>
<output>15</output>

<gadget id="calculator">45 / 5</gadget>
<output>9</output>

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

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

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

divide(subtract(divide(75, 5), divide(45, 5)), const_2)

Explanation: "speed downstream = d / t = 75 / ( 5 ) = 15 kmph speed upstream = d / t = 45 / ( 5 ) = 9 kmph the speed of the stream = ( 15 - 9 ) / 2 = 3 kmph answer : d"


Question: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 25 metre of cloth ?

<gadget id="calculator">25 / 0.128</gadget>
<output>195.3125</output>
<result>195.3125</result>

Choices:
A. 194 seconds
B. 195 seconds
C. 196 seconds
D. 197 seconds
E. none of these

Explanation: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 25 : x = > x = 25 ∗ 1 / 0.128 = > x = 195.31 so time will be approx 195 seconds option b"


Question: at what time between 5 and 6 o ' clock are the hands of a 3 minutes apart ?

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

<gadget id="calculator">25 - 3</gadget>
<output>22</output>

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

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

<gadget id="calculator">12 / 11</gadget>
<output>12/11 = around 1.090909</output>

<gadget id="calculator">22 * (12/11)</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 24
B. 55
C. 66
D. 88
E. 21

multiply(subtract(multiply(5, 5), 3), divide(add(6, 6), add(6, 5)))

Explanation: in this type of problems the formuae is ( 5 * x + or - t ) * 12 / 11 here x is replaced by the first interval of given time . here x is 5 . t is spaces apart case 1 : ( 5 * x + t ) * 12 / 11 ( 5 * 5 + 3 ) * 12 / 11 28 * 12 / 11 = 336 / 11 = min therefore the hands will be 3 min apart at 31 5 / 11 min past 5 . case 2 : ( 5 * x - t ) * 12 / 11 ( 5 * 5 - 3 ) * 12 / 11 22 * 12 / 11 = 24 min therefore the hands will be 3 min apart at 24 min past 5 answer : a ) 24 min


Question: the probability is 1 / 2 that a certain coin turns up heads on any given toss . if the coin is tossed 6 times , what is the probability that the coin turns up tails on at least one of the tosses ?

<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>

<gadget id="calculator">1 - (1/64)</gadget>
<output>63/64 = around 0.984375</output>
<result>63/64 = around 0.984375</result>

Choices:
A. 15 / 16
B. 21 / 32
C. 31 / 32
D. 63 / 64
E. 51 / 64

Explanation: p ( 6 heads ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 64 . p ( at least one tail ) = 1 - 1 / 64 = 63 / 64 . the answer is d .


Question: a football field is 8400 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3500 square yards ?

<gadget id="calculator">1_200 / 8_400</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">3_500 * (1/7)</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 450
B. 600
C. 500
D. 2400
E. 3200

Explanation: "answer a ) 4800 yards need 1200 lbs 1 yard will need 1200 / 8400 = 1 / 7 lbs 3600 yards will need 1 / 7 * 3500 yards = 500 lbs c"


Question: the lowest number which should be added to 11390 so that the sum is exactly divisible by 7 , 9 , 10 and 12 is :

Choices:
A. 1010
B. 2210
C. 1250
D. 1210
E. 1110

Explanation: l . c . m . of 7 , 9 , 10 and 12 = 1260 . on dividing 11390 by 1260 , the remainder is 50 . number to be added = ( 1260 - 50 ) = 1210 . answer : option ' d '


Question: a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 3 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?

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

<gadget id="calculator">27 - 1</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 20
B. 26
C. 24
D. 22
E. 30

Explanation: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 333 will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 1 = 26 . answer : b"


Question: 120 students represent x percent of the boys at a school . if the boys at the school make up 30 % of the total school population of x students , what is x ?

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

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

<gadget id="calculator">12_000 / (3/10)</gadget>
<output>40_000</output>

<gadget id="calculator">40_000 ** (1/2)</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 120
B. 150
C. 180
D. 200
E. 250

sqrt(divide(multiply(120, const_100), divide(30, const_100)))

Explanation: "let b be the number of boys in the school . 120 = xb / 100 b = 0.3 x 12000 = 0.3 x ^ 2 x ^ 2 = 40000 x = 200 the answer is d ."


Question: of the diplomats attending a summit conference , 17 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?

<gadget id="calculator">32 - 17</gadget>
<output>15</output>

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

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

<gadget id="calculator">(1/5) - (1/10)</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">15 / (1/10)</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 72
B. 96
C. 108
D. 120
E. 150

divide(subtract(32, 17), subtract(divide(20, const_100), divide(10, const_100)))

Explanation: "{ total } = { french } + { russian } - { both } + { neither } { total } = 17 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 150 . answer : e ."


Question: a lady grows broccoli in her garden that is in the shape of a square . each broccoli takes 1 square foot of area in her garden . this year , she has increased her output by 79 broccoli when compared to last year . the shape of the area used for growing the broccoli has remained a square in both these years . how many broccoli did she produce this year ?

<gadget id="calculator">79 + 1</gadget>
<output>80</output>

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

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

Choices:
A. 1600
B. 1500
C. 1650
D. 1700
E. can not be determined

power(divide(add(79, 1), const_2), const_2)

Explanation: explanatory answer the shape of the area used for growing broccoli has remained a square in both the years . let the side of the square area used for growing broccoli this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing broccoli last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of broccoli grown has increased by 79 , the area would have increased by 79 sq ft because each broccoli takes 1 sq ft space . hence , x 2 - y 2 = 79 ( x + y ) ( x - y ) = 79 . 79 is a prime number and hence it will have only two factors . i . e . , 79 and 1 . therefore , 79 can be expressed as product of 2 numbers in only way = 79 * 1 i . e . , ( x + y ) ( x - y ) = 79 * 1 so , ( x + y ) should be 79 and ( x - y ) should be 1 . solving the two equations we get x = 40 and y = 39 . therefore , number of broccoli produced this year = x 2 = 402 = 1600 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice b , c and d . as 1500,1650 and 1700 are not the square of any number . check choice a : if this year ' s produce is 1600 , last year ' s produce would have been 1600 - 79 = 1521 1521 is the square of 39 . so , 1600 is the answer . choice a


Question: a train 120 m long is running at 60 kmph . in how much time will it pass a platform 240 m long ?

<gadget id="calculator">120 + 240</gadget>
<output>360</output>

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

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

<gadget id="calculator">360 / (50/3)</gadget>
<output>108/5 = around 21.6</output>
<result>108/5 = around 21.6</result>

Choices:
A. 15.6 seconds
B. 24.6 seconds
C. 21.6 seconds
D. 30.6 seconds
E. 35.6 seconds

Explanation: distance travelled = 120 + 240 m = 360 m speed = 60 * 5 / 8 = 50 / 3 m time = 360 * 3 / 50 = 21.6 seconds answer : c .


Question: a is twice as good a workman as b and together they complete a work in 12 days . in how many days a alone can do the work ?

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

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

Choices:
A. 32
B. 33
C. 34
D. 35
E. 36

Explanation: a ’ s one day ’ s work : b ’ s one day ’ s work = 2 : 1 ( a + b ) ’ s one day ’ s work = 1 / 12 b ’ s one day ’ s work = 1 / 12 * 1 / 3 = 1 / 36 b alone can do the work in 36 days answer : e


Question: 10 women can complete a work in 5 days and 10 children take 10 days to complete the work . how many days will 5 women and 10 children take to complete the work ?

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

<gadget id="calculator">5 / 50</gadget>
<output>1/10 = around 0.1</output>

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

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

<gadget id="calculator">(1/10) + (1/10)</gadget>
<output>1/5 = around 0.2</output>

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

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

inverse(add(divide(5, multiply(10, 5)), divide(10, multiply(10, 10))))

Explanation: "1 women ' s 1 day work = 1 / 50 1 child ' s 1 day work = 1 / 100 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 50 + 10 / 100 ) = 1 / 5 5 women and 10 children will complete the work in 5 days . b"


Question: if p # q denotes the least common multiple of p and q , then e = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?

<gadget id="calculator">18 * 24</gadget>
<output>432</output>

<gadget id="calculator">12 * 16</gadget>
<output>192</output>

<gadget id="calculator">432 - 192</gadget>
<output>240</output>

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

<gadget id="calculator">120 + 24</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 216
B. 180
C. 144
D. 108
E. 72

add(divide(subtract(multiply(18, 24), multiply(12, 16)), const_2), 24)

Explanation: there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , e = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c .


Question: if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 6 - m ) then m = ?

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

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

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

Explanation: ( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 6 - m ) = 4 ^ ( ( 6 - m ) / 2 ) therefore , m = ( 6 - m ) / 2 2 m = 6 - m m = 2 answer b


Question: a train passes a platform in 44 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">44 - 20</gadget>
<output>24</output>

<gadget id="calculator">15 * 24</gadget>
<output>360</output>
<result>360</result>

Choices:
A. 240
B. 250
C. 360
D. 230
E. 220

multiply(multiply(const_0_2778, 54), subtract(44, 20))

Explanation: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 36 = > 300 + l = 15 × 44 = 660 = > l = 660 - 300 = 360 meter answer is c ."


Question: exactly 35 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?

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

<gadget id="calculator">35 / 70</gadget>
<output>1/2 = around 0.5</output>

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

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

Choices:
A. 20 %
B. 42 %
C. 44 %
D. 50 %
E. 84 %

multiply(subtract(const_1, divide(35, subtract(const_100, 30))), const_100)

Explanation: "you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 35 % ofall reporters reporters covering politics / all reporters = 35 / 70 = 1 / 2 reporters not covering politics / all reporters = 1 / 2 = 50 % = d"


Question: if rs . 10 be allowed as true discount on a bill of rs . 110 due at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is :

<gadget id="calculator">10 + 110</gadget>
<output>120</output>

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

<gadget id="calculator">20 / 120</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">110 * (1/6)</gadget>
<output>55/3 = around 18.333333</output>
<result>55/3 = around 18.333333</result>

Choices:
A. rs . 20
B. rs . 21.81
C. rs . 22
D. rs . 18.33
E. none

multiply(110, divide(subtract(add(10, 110), const_100), add(10, 110)))

Explanation: "solution s . i . on rs . ( 110 - 10 ) for a certain time = rs . 10 . s . i . on rs . 100 for double the time = rs . 20 . t . d . on rs . 120 = rs . ( 120 - 100 ) = rs . 20 . t . d . on rs . 110 = rs . ( 20 / 120 x 120 ) = rs . 18.33 . answer d"


Question: a shopkeeper gave an additional 20 per cent concession on the reduced price after giving 30 per cent standard concession on an article . if arun bought that article for 1120 , what was the original price ?

<gadget id="calculator">1_120 * 100</gadget>
<output>112_000</output>

<gadget id="calculator">112_000 * 100</gadget>
<output>11_200_000</output>

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

<gadget id="calculator">11_200_000 / 80</gadget>
<output>140_000</output>

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

<gadget id="calculator">140_000 / 70</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. 3000
B. 4000
C. 2400
D. 2000
E. none of these

divide(divide(multiply(multiply(1120, const_100), const_100), subtract(const_100, 20)), subtract(const_100, 30))

Explanation: original price = 1120 × 100 ⁄ 70 × 100 ⁄ 80 = 2000 answer d


Question: if x , y , and z are positive integers and 3 x = 4 y = 7 z , then the least possible value of x - y + z is

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

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

<gadget id="calculator">84 / 3</gadget>
<output>28</output>

<gadget id="calculator">84 / 4</gadget>
<output>21</output>

<gadget id="calculator">28 - 21</gadget>
<output>7</output>

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

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

Choices:
A. 33
B. 40
C. 49
D. 19
E. 61

add(subtract(divide(multiply(multiply(3, 4), 7), 3), divide(multiply(multiply(3, 4), 7), 4)), divide(multiply(multiply(3, 4), 7), 7))

Explanation: x - y + z = - 3 x / 4 + x + 3 x / 7 = ( - 21 + 28 + 12 ) x / 28 = 19 x / 28 19 is not divisible by 28 ( it ' s a prime # ) , so for least value , x = 28 answer - d


Question: a man buys an article for $ 100 . and sells it for $ 130 . find the gain percent ?

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

<gadget id="calculator">130 / 1</gadget>
<output>130</output>

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

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

subtract(divide(130, divide(100, const_100)), const_100)

Explanation: "c . p . = $ 100 s . p . = $ 130 gain = $ 30 gain % = 30 / 100 * 100 = 30 % answer is e"


Question: how many cubes of 20 cm edge can be put in a cubical box of 1 m edge .

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

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

<gadget id="calculator">(1/5) ** 3</gadget>
<output>1/125 = around 0.008</output>

<gadget id="calculator">1 / (1/125)</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 177 cm
B. 125 cm
C. 786 cm
D. 617 cm
E. 187 cm

Explanation: "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 20 â ˆ — 20 â ˆ — 20 = 125 note : 1 m = 100 cm answer : b"


Question: 3 houses are available in a new flat . 3 persons apply for the houses . each applies for 1 house without consulting others . the probability that all the 3 apply for the same house is ?

<gadget id="calculator">binomial(3, 1)</gadget>
<output>3</output>

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

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

Choices:
A. 1 / 7
B. 1 / 9
C. 2 / 7
D. 3 / 7
E. 2 / 9

divide(1, multiply(choose(3, 1), choose(3, 1)))

Explanation: one person can select one house out of 3 = \ inline { \ color { black } 3 c _ { 1 } } ways = 3 . hence , three persons can select one house out of 3 in 3 x 3 x 3 = 9 . therefore , probability that all thre apply for the same house is 1 / 9 b


Question: if log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + 1 , then x is equal to :

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

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

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

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

divide(subtract(10, 1), subtract(5, const_2))

Explanation: log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + 1 log 10 5 + log 10 ( 5 x + 1 ) = log 10 ( x + 5 ) + log 10 10 log 10 [ 5 ( 5 x + 1 ) ] = log 10 [ 10 ( x + 5 ) ] 5 ( 5 x + 1 ) = 10 ( x + 5 ) 5 x + 1 = 2 x + 10 3 x = 9 = > x = 3 answer c


Question: the sum of 4 consecutive even numbers is 140 . what would be the smallest number ?

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

<gadget id="calculator">140 / 8</gadget>
<output>35/2 = around 17.5</output>

<gadget id="calculator">(35/2) * 2</gadget>
<output>35</output>

<gadget id="calculator">35 - 1</gadget>
<output>34</output>

<gadget id="calculator">34 - 1</gadget>
<output>33</output>

<gadget id="calculator">33 - 1</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 32
B. 88
C. 70
D. 123
E. 12

subtract(subtract(subtract(multiply(divide(140, add(4, 4)), const_2), const_1), const_1), const_1)

Explanation: let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x - 2 ) = 32 answer : a


Question: an article is sold at a certain price . by selling it at 2 / 3 of that price one loses 10 % . find the gain percent at original price ?

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

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

<gadget id="calculator">90 / (2/3)</gadget>
<output>135</output>

<gadget id="calculator">135 - 100</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 25 %
B. 20 %
C. 35 %
D. 40 %
E. 50 %

subtract(divide(subtract(const_100, 10), divide(2, 3)), const_100)

Explanation: let the original s . p . be $ x then , new s . p . = $ 2 / 3 x loss = 10 % c . p . = 100 / 90 * 2 / 3 x = 20 x / 27 c . p . = 20 x / 27 gain = x - 20 x / 27 = 7 x / 27 gain % = 7 x / 27 * 27 / 20 x * 100 = 35 % answer is c


Question: in a sports club with 30 members , 17 play badminton and 19 play tennis and 3 do not play either . how many members play both badminton and tennis ?

<gadget id="calculator">17 + 19</gadget>
<output>36</output>

<gadget id="calculator">36 + 3</gadget>
<output>39</output>

<gadget id="calculator">39 - 30</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 7
B. 8
C. 9
D. 10
E. 11

Explanation: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 3 = 30 39 - 2 x + x = 30 39 - x = 30 x = 9 so 9 members play both badminton and tennis . c"


Question: the local recycling plant had a contract requiring anyone who obtained recycled bottles for storage for them , to bring them back to be recycled again . the plant could make one new bottle from every 7 bottles returned . one week , on monday , they got 343 bottles to recycle . assuming that everybody brought back all the empties , how many could they eventually remake from the 343 ?

<gadget id="calculator">343 / 7</gadget>
<output>49</output>

<gadget id="calculator">49 + 7</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 53
B. 54
C. 55
D. 56
E. 57

Explanation: in 1 st level they will make 343 / 7 = 49 bottles . in 2 nd level they will make 49 / 7 = 7 bottles . in 3 rd level they will make 7 / 7 = 1 bottle . totally they can remake 49 + 7 + 1 = 57 bottles answer : e


Question: the difference between the heights of two trees is 20 cm . 10 years ago , the taller one was thrice as taller as the shorter one . the present height of the taller tree is

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

<gadget id="calculator">30 * 10</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 300 cm
B. 15 cm
C. 20 cm
D. 10 cm
E. 40 cm

Explanation: let their heights of x cm and ( x + 20 ) cm respectively . then , ( x + 20 ) - 10 = 3 ( x - 10 ) ⇔ x + 10 = 3 x - 30 ⇔ 2 x = 40 ∴ present height of taller tree = ( 20 + 10 ) = 30 cm . answer : 30 cm


Question: in an examination , 35 % of total students failed in hindi , 45 % failed in english and 20 % in both . the percentage of these who passed in both the subjects is :

<gadget id="calculator">35 + 45</gadget>
<output>80</output>

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

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

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

subtract(const_100, subtract(add(35, 45), 20))

Explanation: "pass percentage = 100 - ( 35 + 45 - 20 ) = 100 - 60 = 40 answer : d"


Question: 8 people went to a restaurant for dinner . 7 of them spent $ 10 each on their meals and the eighth spent $ 7 more than the average expenditure of all 8 people . what was the total amount of money that the 8 people spent ?

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

<gadget id="calculator">70 + 7</gadget>
<output>77</output>

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

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

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

<gadget id="calculator">70 + 18</gadget>
<output>88</output>
<result>88</result>

Choices:
A. $ 85
B. $ 88
C. $ 91
D. $ 94
E. $ 97

add(multiply(7, 10), add(divide(add(multiply(7, 10), 7), subtract(8, const_1)), 7))

Explanation: let t be the total amount of money spent . 7 * 10 + ( t / 8 + 7 ) = t 77 = 7 t / 8 t = ( 8 * 77 ) / 7 = 88 the answer is b .


Question: a person crosses a 1080 m long street in 12 minutes . what is his speed in km per hour ?

<gadget id="calculator">1_080 / 1_000</gadget>
<output>27/25 = around 1.08</output>

<gadget id="calculator">12 * 60</gadget>
<output>720</output>

<gadget id="calculator">720 / 3_600</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(27/25) / (1/5)</gadget>
<output>27/5 = around 5.4</output>
<result>27/5 = around 5.4</result>

Choices:
A. 4.1
B. 4.5
C. 4.8
D. 5.4
E. 5.5

divide(divide(1080, const_1000), divide(multiply(12, const_60), const_3600))

Explanation: "speed = 1080 / ( 12 x 60 ) m / sec = 1.5 m / sec . converting m / sec to km / hr = 1.5 x ( 18 / 5 ) km / hr = 5.4 km / hr . answer : d"


Question: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 384 votes . find the number of votes casted to the winning candidate ?

<gadget id="calculator">100 - 62</gadget>
<output>38</output>

<gadget id="calculator">62 - 38</gadget>
<output>24</output>

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

<gadget id="calculator">384 / (6/25)</gadget>
<output>1_600</output>

<gadget id="calculator">1_600 * 62</gadget>
<output>99_200</output>

<gadget id="calculator">99_200 / 100</gadget>
<output>992</output>
<result>992</result>

Choices:
A. 288
B. 744
C. 992
D. 298
E. 177

divide(multiply(divide(384, divide(subtract(62, subtract(const_100, 62)), const_100)), 62), const_100)

Explanation: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 384 62 % - - - - - - - - ? = > 992 answer : c"


Question: a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 10 inches , then what is the maximum number of soap boxes that can be placed in each carton ?

<gadget id="calculator">25 * 42</gadget>
<output>1_050</output>

<gadget id="calculator">1_050 * 60</gadget>
<output>63_000</output>

<gadget id="calculator">7 * 6</gadget>
<output>42</output>

<gadget id="calculator">42 * 10</gadget>
<output>420</output>

<gadget id="calculator">63_000 / 420</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 210
B. 252
C. 280
D. 150
E. 420

divide(multiply(multiply(25, 42), 60), multiply(multiply(7, 6), 10))

Explanation: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 10 * 6 * 7 we get = 5 x 6 x 5 = 150 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( d )"


Question: selling an kite for rs . 30 , a shop keeper gains 25 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?

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

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

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

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

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

<gadget id="calculator">3_000 / 125</gadget>
<output>24</output>

<gadget id="calculator">27 - 24</gadget>
<output>3</output>

<gadget id="calculator">3 / 24</gadget>
<output>1/8 = around 0.125</output>

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

Choices:
A. 8 %
B. 10 %
C. 11 %
D. 12.5 %
E. 20 %

multiply(divide(subtract(multiply(divide(30, const_100), subtract(const_100, 10)), divide(multiply(30, const_100), add(25, const_100))), divide(multiply(30, const_100), add(25, const_100))), const_100)

Explanation: "explanation : marked price = rs . 30 c . p . = 100 / 125 * 30 = rs . 24 sale price = 90 % of rs . 30 = rs . 27 required gain % = 3 / 24 * 100 = 12.5 % . answer : d"


Question: in a university the average age in an arts class is 21 and average age in technical class is 18 . what is the age average of university if there are 8 arts classes and 5 technical classes ?

<gadget id="calculator">8 * 21</gadget>
<output>168</output>

<gadget id="calculator">5 * 18</gadget>
<output>90</output>

<gadget id="calculator">168 + 90</gadget>
<output>258</output>

<gadget id="calculator">8 + 5</gadget>
<output>13</output>

<gadget id="calculator">258 / 13</gadget>
<output>258/13 = around 19.846154</output>
<result>258/13 = around 19.846154</result>

Choices:
A. 18.75
B. 19.85
C. 20.32
D. 20.9
E. 21.0

divide(add(multiply(8, 21), multiply(5, 18)), add(8, 5))

Explanation: average age of university = ( ( 8 x 21 ) + ( 5 x 18 ) ) / 13 = 19.85 answer : b


Question: a theater box office sold an average ( arithmetic mean ) of 65 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 75 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?

<gadget id="calculator">65 - 60</gadget>
<output>5</output>

<gadget id="calculator">75 - 65</gadget>
<output>10</output>

<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

Choices:
A. 1 : 2
B. 1 : 4
C. 5 : 11
D. 1 : 3
E. 13 : 15

divide(subtract(65, 60), subtract(75, 65))

Explanation: "deviation from the mean for the daytime staff = 75 - 65 = 10 . deviation from the mean for the evening staff = 65 - 60 = 5 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 5 : 10 = 1 : 2 . the answer is a ."


Question: in a kilometer race , if abhishek gives bharti a 40 m start , abhishek wins by 19 sec . but if abhishek gives bharti a 30 sec start , bharti wins by 40 m . find the time taken by bharti to run 5,000 m ?

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

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

<gadget id="calculator">1_000 - 40</gadget>
<output>960</output>

<gadget id="calculator">960 / 1_000</gadget>
<output>24/25 = around 0.96</output>

<gadget id="calculator">30 * (24/25)</gadget>
<output>144/5 = around 28.8</output>

<gadget id="calculator">(144/5) - 19</gadget>
<output>49/5 = around 9.8</output>

<gadget id="calculator">(24/25) ** 2</gadget>
<output>576/625 = around 0.9216</output>

<gadget id="calculator">1 - (576/625)</gadget>
<output>49/625 = around 0.0784</output>

<gadget id="calculator">(49/5) / (49/625)</gadget>
<output>125</output>

<gadget id="calculator">125 * (24/25)</gadget>
<output>120</output>

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

<gadget id="calculator">150 / 1_000</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">5_000 * (3/20)</gadget>
<output>750</output>
<result>750</result>

Choices:
A. 150 sec
B. 750 sec
C. 450 sec
D. 825 sec
E. none of these

multiply(add(multiply(const_1000, const_4), const_1000), divide(add(multiply(divide(subtract(multiply(30, divide(subtract(const_1000, 40), const_1000)), 19), subtract(const_1, power(divide(subtract(const_1000, 40), const_1000), const_2))), divide(subtract(const_1000, 40), const_1000)), 30), const_1000))

Explanation: explanation : if abhishek takes x seconds and bharti takes y seconds to run 1 km , then : = > y = 150 sec and x = 125 sec = > x + 19 = 960 y / 1000 and = ( 960 x / 1000 ) + 30 = y = > y = 150 sec and x = 125 sec answer = ( 150 / 1000 ) × 500 = 750 sec answer : b


Question: every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 144 , how many more green disks than blue disks are in the bag ?

<gadget id="calculator">3 + 7</gadget>
<output>10</output>

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

<gadget id="calculator">144 / 18</gadget>
<output>8</output>

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

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

Choices:
A. 25
B. 28
C. 30
D. 35
E. 40

multiply(divide(144, add(add(3, 7), 8)), subtract(8, 3))

Explanation: "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 144 - - > x = 8 . g - b = 8 x - 3 x = 5 x = 40 . the answer is e ."


Question: if the sum of two numbers is 22 and the sum of their squares is 404 , then the product of the numbers is

<gadget id="calculator">22 ** 2</gadget>
<output>484</output>

<gadget id="calculator">484 - 404</gadget>
<output>80</output>

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

Choices:
A. 40
B. 44
C. 80
D. 88
E. 48

divide(subtract(power(22, const_2), 404), const_2)

Explanation: "according to the given conditions x + y = 22 and x ^ 2 + y ^ 2 = 404 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 22 ^ 2 = 404 + 2 xy so xy = 80 / 2 = 40 answer : a"


Question: there are 200 female managers in a certain company . find the total number w of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .

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

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

Choices:
A. 300
B. w = 400
C. w = 500
D. w = 600
E. none of these

Explanation: "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."


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

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

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

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

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

Choices:
A. 80.0
B. 80.9
C. 81.0
D. 81.1
E. 81.9

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

Explanation: "consider price of the all items as $ 100 after a initial reduction of 10 % price becomes = 0.9 * 100 = $ 90 after the final reduction of 10 % price becomes = 0.9 * 90 = $ 81 price of all items on second day is 81 % of price on first day correct answer option c"


Question: on the first of the year , james invested x dollars at proudstar bank in an account that yields 0.5 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?

<gadget id="calculator">0.5 * 4</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 2.04 %
B. 4.12 %
C. 5 %
D. 8.25 %
E. 10 %

Explanation: per quarter , interest = 0.5 % so for a year , interest = 2 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 2 % answer = 2.04 % = answer : a


Question: the chance of rain on any given day in tel - aviv is 50 % . what is the probability w that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?

<gadget id="calculator">binomial(6, 4)</gadget>
<output>15</output>

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

<gadget id="calculator">(1/2) ** 4</gadget>
<output>1/16 = around 0.0625</output>

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

<gadget id="calculator">(1/16) * (1/4)</gadget>
<output>1/64 = around 0.015625</output>

<gadget id="calculator">1 / (1/64)</gadget>
<output>64</output>

<gadget id="calculator">15 / 64</gadget>
<output>15/64 = around 0.234375</output>
<result>15/64 = around 0.234375</result>

Choices:
A. 15 / 64
B. 30 / 64
C. 1 / 2
D. 1 / 4
E. 52 / 64

divide(choose(6, 4), inverse(multiply(power(divide(const_1, const_2), const_4), power(divide(const_1, const_2), const_2))))

Explanation: chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days w = 15 / 64 ans a it is .


Question: the sum of two numbers is 77 . 5 times one number is equal to 6 times the other . the bigger of the two numbers is

<gadget id="calculator">6 / 5</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) + 1</gadget>
<output>11/5 = around 2.2</output>

<gadget id="calculator">77 / (11/5)</gadget>
<output>35</output>

<gadget id="calculator">77 - 35</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 10
B. 42
C. 14
D. 15
E. 60

subtract(77, divide(77, add(divide(6, 5), const_1)))

Explanation: a : b 5 : 6 a + b = 77 5 x + 6 x = 77 x = 7 then two numbers are 35,42 . the bigger number is 42 answer : b


Question: income and expenditure of a person are in the ratio 7 : 6 . if the income of the person is rs . 14000 , then find his savings ?

<gadget id="calculator">6 / 7</gadget>
<output>6/7 = around 0.857143</output>

<gadget id="calculator">(6/7) * 14_000</gadget>
<output>12_000</output>

<gadget id="calculator">14_000 - 12_000</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. 500
B. 1000
C. 1500
D. 2000
E. 2500

subtract(14000, multiply(divide(6, 7), 14000))

Explanation: "let the income and the expenditure of the person be rs . 7 x and rs . 6 x respectively . income , 7 x = 14000 = > x = 2000 savings = income - expenditure = 7 x - 6 x = x so , savings = rs . 2000 . answer : d"


Question: 3 people took gmat practice tests in which the minimum and maximum possible scores are 200 and 800 , respectively . they each took a test 3 times , and no one scored below 400 or over 700 . if the individual ranges of the 3 people ' s scores in those 3 practice tests were 40 , 70 and 100 , what is the difference between the maximum and minimum possible ranges of all their scores put together .

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

<gadget id="calculator">300 - 100</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 70
B. 80
C. 100
D. 140
E. 200

Explanation: according to the information in the question the maximum range would be between 400 and 700 ( 300 ) . the minimum range would be the greatest range for any one individual , which is listed in the problem as 100 . so the difference between these would be 300 - 100 or 200 . answer : e


Question: if p / q = 3 / 11 , then 2 p + q = ?

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

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

Choices:
A. 12
B. 14
C. 17
D. 15
E. 16

Explanation: let p = 3 , q = 11 then 2 * 3 + 11 = 17 so 2 p + q = 17 . answer : c


Question: what is the probability of rolling a total of 5 with a single roll of two fair 6 - sided dice , each with the distinct numbers 1 through 6 on each side ?

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

<gadget id="calculator">4 / 36</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>

Choices:
A. 1 / 12
B. 1 / 6
C. 2 / 7
D. 1 / 3
E. 1 / 9

Explanation: totalsample spacefrom two fair six - sided dice is 36 . there are six possible ways to be 5 i . e . ( 1 + 4 ) , ( 2 + 3 ) , ( 3 + 2 ) , ( 4 + 1 ) so , total probability is 4 / 36 or 1 / 9 . answer is e .


Question: if the simple interest on a certain sum of money for 6 years is one – fifth of the sum , then the rate of interest per annum is

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

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

<gadget id="calculator">20 / 6</gadget>
<output>10/3 = around 3.333333</output>
<result>10/3 = around 3.333333</result>

Choices:
A. 3.3 %
B. 7.2 %
C. 6.1 %
D. 5.0 %
E. 3.1 %

divide(divide(const_100, add(const_1, const_4)), 6)

Explanation: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 6 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 6 ) = 20 / 6 = 3.3 % answer : option a"


Question: the population of a city is 415600 . it increased by 25 % in the first year and decreased by 30 % in the second year . what is the population of the city at the end of second year ?

<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">25 + 100</gadget>
<output>125</output>

<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) * 415_600</gadget>
<output>519_500</output>

<gadget id="calculator">(7/10) * 519_500</gadget>
<output>363_650</output>
<result>363_650</result>

Choices:
A. 367300
B. 363580
C. 363650
D. 373650
E. 386750

multiply(divide(subtract(const_100, 30), const_100), multiply(divide(add(25, const_100), const_100), 415600))

Explanation: as per given data , p = 415600 , r 1 = 25 % incresed , r 2 = 30 % decreased population of the city at the end of the second year = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) = 415600 ( 1 + 25 / 100 ) ( 1 - 30 / 100 ) = 363650 answer : c


Question: a thief is spotted by a policeman from a distance of 150 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?

<gadget id="calculator">150 * 8</gadget>
<output>1_200</output>

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

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

Choices:
A. 350 m
B. 200 m
C. 400 m
D. 600 m
E. none of them

divide(multiply(150, 8), subtract(10, 8))

Explanation: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 150 m / 1000 ) x 1 / 2 hr = 3 / 40 hr . in 3 / 40 hrs , the thief covers a distance of 8 x 3 / 40 km = 3 / 5 km = 600 m answer is d"


Question: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 70 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?

<gadget id="calculator">72 / 60</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) * 35</gadget>
<output>42</output>

<gadget id="calculator">70 - 35</gadget>
<output>35</output>

<gadget id="calculator">42 / 35</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">35 * (6/5)</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 15
B. 20
C. 40
D. 42
E. 68

multiply(35, divide(multiply(divide(72, const_60), 35), subtract(70, 35)))

Explanation: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 70 t t = 1.2 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 1.2 = 42 miles answer : - d"


Question: a fruit juice company earns $ 150 per 100 gallons of apple juice sold , $ 170 per 100 gallons of guava juice sold , $ 130 per 100 gallons of grape juice sold , $ 100 per 100 gallons of orange juice . if the company manages to sell 230 gallons of apple , 210 gallons of guava , 310 gallons of grape , 270 gallons of orange on a particular day . what is the average earning of the company per 100 gallon of the juice sold ?

<gadget id="calculator">130 + 4</gadget>
<output>134</output>

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

<gadget id="calculator">8 / 10</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">134 + (4/5)</gadget>
<output>674/5 = around 134.8</output>
<result>674/5 = around 134.8</result>

Choices:
A. 134.8
B. 141.2
C. 147.2
D. 152.3
E. 160.1

add(add(130, const_4), divide(add(const_4, const_4), const_10))

Explanation: earning of the company from apple = 150 / 100 x 230 = 345 earning of the company from guava = 170 / 100 x 210 = 357 earning of the company from grape = 130 / 100 x 310 = 403 earning of the company from orange = 100 / 100 x 270 = 270 total earning of the company = 345 + 357 + 403 + 270 = 1375 total juice sold = 1020 average earning per 100 gallon of juice sold = ( 1375 / 1020 ) x 100 = $ 134.8 answer : a


Question: if a mixture is 1 ⁄ 7 alcohol by volume and 2 ⁄ 7 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?

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

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

<gadget id="calculator">(1/7) / (2/7)</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

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

Explanation: "should be a sub - 600 level q . . volume = { 1 / 7 } / { 2 / 7 } = 1 / 2 c"


Question: the average of 10 numbers is 7 . if each number is multiplied by 12 , then the average of new set of numbers is

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

Choices:
A. 28
B. 236
C. 288
D. 84
E. 26

Explanation: explanation : if each number is multiplied by k , then the new average increases by k times . so new average = 84 answer : d


Question: a train 500 m long can cross an electric pole in 50 sec and then find the speed of the train ?

<gadget id="calculator">500 / 1_000</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">50 / 3_600</gadget>
<output>1/72 = around 0.013889</output>

<gadget id="calculator">(1/2) / (1/72)</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 76 kmph
B. 54 kmph
C. 72 kmph
D. 34 kmph
E. 36 kmph

divide(divide(500, const_1000), divide(50, const_3600))

Explanation: "length = speed * time speed = l / t s = 500 / 50 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : e"


Question: the length of a rectangle is increased by 40 % while its width is halved . what is the % change in area ?

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

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

<gadget id="calculator">(2/5) + 1</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">(1/2) * (7/5)</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>

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

Choices:
A. 25 %
B. 30 %
C. 50 %
D. 65 %
E. 70 %

multiply(subtract(const_1, multiply(divide(const_1, const_2), add(divide(40, const_100), const_1))), const_100)

Explanation: the original area is l * w the new area is 1.4 l * 0.5 w = 0.7 * l * w = l * w - 0.3 * l * w the area decreased by 30 % . the answer is b .


Question: if 5 x = 3 y and xy ≠ 0 , what is the ratio of 1 / 5 * x to 1 / 6 * y ?

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

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

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

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

<gadget id="calculator">(6/5) * (3/5)</gadget>
<output>18/25 = around 0.72</output>
<result>18/25 = around 0.72</result>

Choices:
A. 25 / 6
B. 36 / 25
C. 18 / 25
D. 5 / 6
E. 25 / 36

multiply(divide(divide(1, 5), divide(1, 6)), divide(3, 5))

Explanation: "5 x = 3 y = > x / y = 3 / 5 1 / 5 * x to 1 / 6 * y = x / y * 6 / 5 = ( 3 / 5 ) * ( 6 / 5 ) = 18 / 25 ans : c"


Question: for every integer n ≥ 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 101 ) – g ( 99 ) ?

<gadget id="calculator">101 - 1</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 0
B. 98
C. 99
D. 100
E. 90

Explanation: "g ( 101 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 g ( 101 ) - g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 - 1 * 3 * 5 * 7 * 9 * . . . * 99 = 1 * 3 * 5 * 7 * 9 * . . . * 99 * ( 101 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 100 hence : d"


Question: two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 72 seconds . the length of each train is :

<gadget id="calculator">46 - 36</gadget>
<output>10</output>

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

<gadget id="calculator">10_000 / 3_600</gadget>
<output>25/9 = around 2.777778</output>

<gadget id="calculator">(25/9) * 72</gadget>
<output>200</output>

<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 82 m
B. 50 m
C. 72 m
D. 100 m
E. none of these

divide(multiply(divide(multiply(subtract(46, 36), const_1000), const_3600), 72), const_2)

Explanation: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 72 secs the total distance traveled is 72 x 25 / 9 = 200 m . therefore the length of each train is = 200 / 2 = 100 m . answer d"


Question: a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 30 % ?

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

<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>

<gadget id="calculator">6 * (13/10)</gadget>
<output>39/5 = around 7.8</output>
<result>39/5 = around 7.8</result>

Choices:
A. 1 / 2
B. 2 / 6
C. 3 / 6
D. 9 / 6
E. 15 / 2

multiply(6, add(const_1, divide(30, const_100)))

Explanation: c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 180 % of re . 1 = rs . 9 / 5 for rs . 9 / 5 , toffees sold = 6 . for re . 1 , toffees sold = 9 x 5 / 6 = 15 / 2 . answer e


Question: how many seconds will a train 140 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?

<gadget id="calculator">150 + 140</gadget>
<output>290</output>

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

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

<gadget id="calculator">290 / 10</gadget>
<output>29</output>
<result>29</result>

Choices:
A. 28 sec
B. 29 sec
C. 24 sec
D. 25 sec
E. 26 sec

Explanation: "d = 140 + 150 = 290 s = 36 * 5 / 18 = 10 mps t = 290 / 10 = 29 sec b"


Question: sophia finished 2323 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?

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

<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(2/3) - (1/3)</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">90 / (1/3)</gadget>
<output>270</output>
<result>270</result>

Choices:
A. 140
B. 320
C. 745
D. 270
E. 350

divide(90, subtract(divide(const_2, const_3), subtract(const_1, divide(const_2, const_3))))

Explanation: let x be the total number of pages in the book , then she finished 23 ⋅ x pages . then she has x − 23 ⋅ x = 13 ⋅ xpages left . 23 ⋅ x − 13 ⋅ x = 90 13 ⋅ x = 90 x = 270 so the book is 270 pages long . correct answer is d ) 270


Question: on her annual road trip to visit her family in seal beach , california , traci stopped to rest after she traveled 1 ⁄ 3 of the total distance and again after she traveled 1 ⁄ 4 of the distance remaining between her first stop and her destination . she then drove the remaining 300 miles and arrived safely at her destination . what was the total distance , in miles , from traci ’ s starting point to seal beach ?

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

Choices:
A. 600
B. 300
C. 350
D. 400
E. 550

Explanation: let d = total distance traci traveled 1 / 3 = d / 3 i . e . remaining distance = 2 d / 3 she traveled 1 / 4 th of 2 d / 3 = d / 6 thus : d = ( d / 3 ) + ( d / 6 ) + 300 d = 600 answer : a


Question: the marks obtained by vijay and amith are in the ratio 4 : 5 and those obtained by amith and abhishek in the ratio of 3 : 4 . the marks obtained by vijay and abhishek are in the ratio of ?

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

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

<gadget id="calculator">12 / 20</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>

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

Explanation: "4 : 5 3 : 4 - - - - - - - 12 : 15 : 20 12 : 20 - - - - - - > 6 : 10 3 : 5 answer : b"


Question: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 1200 per sq . metre .

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

<gadget id="calculator">1_200 * 20.625</gadget>
<output>24_750</output>
<result>24_750</result>

Choices:
A. rs . 15,000
B. rs . 24,750
C. rs . 15,600
D. rs . 16,500
E. none

Explanation: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 1200 x 20.625 ) = rs . 24,750 . answer b"


Question: how many zeroes are there at the end of the number n , if n = 70 ! + 140 ! ?

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

<gadget id="calculator">70 / 5</gadget>
<output>14</output>

<gadget id="calculator">14 + 2</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 8
B. 12
C. 16
D. 20
E. 24

add(divide(70, add(const_4, const_1)), const_2)

Explanation: "the number of zeroes at the end of 70 ! will be less than the number of zeroes at the end of 140 ! hence it is sufficient to calculate the number of zeroes at the end of 70 ! the number of zeroes = [ 70 / 5 ] + [ 70 / 25 ] + [ 70 / 125 ] = 14 + 2 + 0 = 16 the answer is c ."


Question: if 15 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?

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

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

<gadget id="calculator">15 / (1/4)</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 95
B. 90
C. 85
D. 80
E. 60

divide(15, divide(subtract(100, 75), 100))

Explanation: "let x be the number of students in the school . 0.15 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.15 x / 0.25 = 0.6 x students went to the camping which is 60 % . the answer is e"


Question: an object thrown directly upward is at a height of h feet after t seconds , where h = - 14 ( t - 3 ) ^ 2 + 150 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?

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

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

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

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

<gadget id="calculator">(-14) * 4</gadget>
<output>-56</output>

<gadget id="calculator">(-56) + 150</gadget>
<output>94</output>
<result>94</result>

Choices:
A. 80
B. 88
C. 94
D. 112
E. 124

add(multiply(negate(14), power(subtract(add(3, 2), 3), 2)), 150)

Explanation: "we see that h will be a maximum h = 150 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 14 ( 5 - 3 ) ^ 2 + 150 = - 14 ( 4 ) + 150 = 94 the answer is c ."


Question: how many cones of radius 4 m , height 2 m can be formed from a cylinder of 12 m radius , 10 m height :

<gadget id="calculator">pi * (12 ** 2) * 10</gadget>
<output>1440*pi = around 4_523.893421</output>

<gadget id="calculator">pi * (4 ** 2) * 2 / 3</gadget>
<output>32*pi/3 = around 33.510322</output>

<gadget id="calculator">(1440*pi) / (32*pi/3)</gadget>
<output>135</output>
<result>135</result>

Choices:
A. 135
B. 125
C. 145
D. 115
E. 155

divide(volume_cylinder(12, 10), volume_cone(4, 2))

Explanation: ( cylinder volume ) / ( cone volume ) ( π r ( power 2 ) h ) / ( 1 / 3 π r ( power 2 ) h ) = ( π × 12 × 12 × 10 ) / ( 1 / 3 π × 4 × 4 × 2 ) = 135 answer is a .


Question: 70 is increased by 50 % . find the final number .

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

<gadget id="calculator">70 * (1/2)</gadget>
<output>35</output>

<gadget id="calculator">70 + 35</gadget>
<output>105</output>
<result>105</result>

Choices:
A. 100
B. 110
C. 105
D. 30
E. 160

add(70, multiply(70, divide(50, const_100)))

Explanation: "final number = initial number + 50 % ( original number ) = 70 + 50 % ( 70 ) = 70 + 35 = 105 . answer c"


Question: in a group of 8 semifinalists , all but 2 will advance to the final round . if in the final round only the top 3 will be awarded medals , then how many groups of medal winners are possible ?

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

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

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

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

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

<gadget id="calculator">factorial(3)</gadget>
<output>6</output>

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

<gadget id="calculator">720 / 36</gadget>
<output>20</output>

<gadget id="calculator">28 * 20</gadget>
<output>560</output>

<gadget id="calculator">560 / 10</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 20
B. 56
C. 120
D. 560
E. 720

divide(multiply(divide(factorial(8), multiply(factorial(subtract(8, 2)), 2)), divide(factorial(subtract(8, 2)), multiply(factorial(3), factorial(3)))), const_10)

Explanation: 1 ) is it important here that how many go into finals . . . no . . . . what is important is how many get medals . . 3 finally these 3 can be any of the 8 - 8 c 3 = 8 ! 5 ! 3 ! = 8 ∗ 7 ∗ 63 ∗ 2 = 568 c 3 = 8 ! 5 ! 3 ! = 8 ∗ 7 ∗ 63 ∗ 2 = 56 2 ) is order important . . . no we are looking for groups only . . ans 56 answer : b


Question: martha has the unique talent of being able to guess other people ’ s height and weight . for every 6 people that martha meets , she consistently guesses the people ’ s correct height 5 times , and for every 8 people that she meets , she consistently guesses the people ’ s correct weight 6 times . if martha meets 3 people and her success rate remains constant , what is the probability that martha correctly guesses a person ’ s weight and height at least once ?

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

<gadget id="calculator">6 / 8</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(5/6) * (3/4)</gadget>
<output>5/8 = around 0.625</output>

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

<gadget id="calculator">(3/8) ** 3</gadget>
<output>27/512 = around 0.052734</output>

<gadget id="calculator">1 - (27/512)</gadget>
<output>485/512 = around 0.947266</output>
<result>485/512 = around 0.947266</result>

Choices:
A. 8 / 27
B. 2 / 5
C. 485 / 512
D. 98 / 125
E. 625 / 952

subtract(const_1, power(subtract(const_1, multiply(divide(5, 6), divide(6, 8))), const_3))

Explanation: probability that she guesses the height correctly p ( h ) = 5 / 6 probability that she guesses the weight correctlyp ( w ) = 6 / 8 probability that she guesses both weight and height correctly ( p ( h ) * p ( w ) ) = 5 / 6 * 6 / 8 = 30 / 48 now the q asks about the probability of this happening atleast once . we calculate it by finding the probability of not being able to guess in any of the three occasions . probability of not being able to guess any no . of times = 1 - 30 / 48 = 18 / 48 = 3 / 8 for all three occasions p ( a ) = 3 / 8 * 3 / 8 * 3 / 8 = 27 / 512 probability of the event happening atleast once = 1 - p ( a ) = 1 - 27 / 512 = 485 / 512 ans should be c


Question: the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 90 black cars in the lot , how many red cars are there in the lot ?

<gadget id="calculator">3 / 8</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">(3/8) * 90</gadget>
<output>135/4 = around 33.75</output>

<gadget id="calculator">floor(135/4)</gadget>
<output>33</output>
<result>33</result>

Choices:
A. 11
B. 33
C. 24
D. 27
E. 32

Explanation: b is correct r / b = 3 / 8 and b = 90 r = 90 * 3 / 8 = 33


Question: a bowl was filled with 10 ounces of water , and 0.004 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?

<gadget id="calculator">50 * 0.004</gadget>
<output>0.2</output>

<gadget id="calculator">0.2 / 10</gadget>
<output>0.02</output>

<gadget id="calculator">0.02 * 100</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 0.004 %
B. 0.04 %
C. 0.40 %
D. 2 %
E. 40 %

multiply(divide(multiply(50, 0.004), 10), const_100)

Explanation: "total amount of water evaporated each day during a 50 - day period = . 004 * 50 = . 004 * 100 / 2 = . 4 / 2 = . 2 percent of the original amount of water evaporated during this period = ( . 2 / 10 ) * 100 % = 2 % answer d"


Question: of the families in city x in 1994 , 35 percent owned a personal computer . the number of families in city x owning a computer in 1998 was 20 percent greater than it was in 1994 , and the total number of families in city x was 4 percent greater in 1998 than it was in 1994 . 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 * 35</gadget>
<output>4_200</output>

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

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

<gadget id="calculator">42 / 104</gadget>
<output>21/52 = around 0.403846</output>

<gadget id="calculator">100 * (21/52)</gadget>
<output>525/13 = around 40.384615</output>
<result>525/13 = around 40.384615</result>

Choices:
A. 50.12 %
B. 40.52 %
C. 40.56 %
D. 40.38 %
E. 40.14 %

multiply(const_100, divide(divide(multiply(add(20, const_100), 35), const_100), add(const_100, 4)))

Explanation: "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40 number of families owning computer in 1998 = 35 * 120 / 100 = 42 number of families in 1998 = 104 the percentage = 42 / 104 * 100 = 40.38 % . option : d"


Question: the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each . the radius of the sphere is

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

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

<gadget id="calculator">pi * 72</gadget>
<output>72*pi = around 226.194671</output>

<gadget id="calculator">(72*pi) * 2</gadget>
<output>144*pi = around 452.389342</output>

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

<gadget id="calculator">(144*pi) / (4*pi)</gadget>
<output>36</output>

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

Choices:
A. 3 cm
B. 4 cm
C. 6 cm
D. 8 cm
E. none

sqrt(divide(multiply(multiply(const_pi, multiply(12, divide(12, const_2))), const_2), multiply(const_pi, const_4)))

Explanation: "solution 4 π r 2 = 2 π 6 x 12 ⇒ r 2 = ( 6 x 12 / 2 ) ⇒ 36 ⇒ r = 6 cm . answer c"


Question: the area of a parallelogram is 72 sq m and its base is 12 m . then the length of the height is ?

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

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

Choices:
A. 6 m
B. 7 m
C. 60 m
D. 13 m
E. none

Explanation: b * h = 72 . h * 12 = 72 = > h = 6 m . answer : ( a )


Question: a set of pictures of butterflies contains 10 pictures . jim bought 3 of the pictures . if 2 pictures are to be picked out from the 10 pictures , what is the probability that both pictures are not those that were already bought by jim ?

<gadget id="calculator">10 - 3</gadget>
<output>7</output>

<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>

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

<gadget id="calculator">factorial(5)</gadget>
<output>120</output>

<gadget id="calculator">5_040 / 120</gadget>
<output>42</output>

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

<gadget id="calculator">42 / 2</gadget>
<output>21</output>

<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>

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

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

<gadget id="calculator">3_628_800 / 40_320</gadget>
<output>90</output>

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

<gadget id="calculator">21 / 45</gadget>
<output>7/15 = around 0.466667</output>
<result>7/15 = around 0.466667</result>

Choices:
A. 14 / 15
B. 3 / 5
C. 6 / 13
D. 7 / 15
E. 7 / 10

divide(divide(divide(factorial(subtract(10, 3)), factorial(subtract(subtract(10, 3), 2))), factorial(2)), divide(divide(factorial(10), factorial(subtract(10, 2))), factorial(2)))

Explanation: probability of first pick not one of the jim ' s picture is = 7 / 10 ( except for 3 which jim purchased ) probability of second pick not one of the jim ' s picture is = 6 / 9 total = 7 / 10 ∗ 6 / 9 = 7 / 15 answer is d option d


Question: maths , physics and chemistry books are stored on a library shelf that can accommodate 25 books . currently , 20 % of the shelf spots remain empty . there are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books . among all the books , 12 books are soft cover and the remaining are hard - cover . if there are a total of 7 hard - cover books among the maths and physics books . what is the probability q , that a book selected at random is either a hard cover book or a chemistry book ?

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

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

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

<gadget id="calculator">2 / 20</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>

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

<gadget id="calculator">(1/10) * (2/5)</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">(1/2) - (1/25)</gadget>
<output>23/50 = around 0.46</output>
<result>23/50 = around 0.46</result>

Choices:
A. 1 / 10
B. 3 / 20
C. 1 / 5
D. 1 / 4
E. 9 / 20

subtract(add(divide(const_2, add(add(const_2, add(const_2, 4)), 12)), divide(add(const_2, add(const_2, 4)), add(add(const_2, add(const_2, 4)), 12))), multiply(divide(const_2, add(add(const_2, add(const_2, 4)), 12)), divide(add(const_2, add(const_2, 4)), add(add(const_2, add(const_2, 4)), 12))))

Explanation: first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , q = 9 provide the desired outcome , making the answer e .


Question: a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 15 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )

<gadget id="calculator">330 * 15</gadget>
<output>4_950</output>
<result>4_950</result>

Choices:
A. 1650
B. 2750
C. 3850
D. 4950
E. 6050

Explanation: "the distance the sound traveled to the man is 15 * 330 = 4950 meters the answer is d ."


Question: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 510 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )

<gadget id="calculator">510 / 3</gadget>
<output>170</output>

<gadget id="calculator">300 / 4</gadget>
<output>75</output>

<gadget id="calculator">170 / 75</gadget>
<output>34/15 = around 2.266667</output>
<result>34/15 = around 2.266667</result>

Choices:
A. 8 / 3
B. 3 / 8
C. 8 / 5
D. 5 / 8
E. 34 / 15

Explanation: distance traveled by eddy = 510 km time taken by eddy = 3 hours average speed of eddy = 510 / 3 = 170 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 170 / 75 = 34 / 15 answer e


Question: two brothers ram and ravi appeared for an exam . the probability of selection of ram is 4 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .

<gadget id="calculator">4 / 7</gadget>
<output>4/7 = around 0.571429</output>

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

<gadget id="calculator">(4/7) * (1/5)</gadget>
<output>4/35 = around 0.114286</output>
<result>4/35 = around 0.114286</result>

Choices:
A. 4 / 35
B. 2 / 3
C. 7 / 35
D. 5 / 7
E. 7 / 5

Explanation: let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 4 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 4 / 7 x 1 / 5 = 4 / 35 answer : a


Question: 120 kg of an alloy a is mixed with 180 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 5 , then the amount of tin in the new alloy is ?

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

<gadget id="calculator">120 / 5</gadget>
<output>24</output>

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

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

<gadget id="calculator">180 / 8</gadget>
<output>45/2 = around 22.5</output>

<gadget id="calculator">(45/2) * 3</gadget>
<output>135/2 = around 67.5</output>

<gadget id="calculator">72 + (135/2)</gadget>
<output>279/2 = around 139.5</output>
<result>279/2 = around 139.5</result>

Choices:
A. 100.6 kg
B. 120.3 kg
C. 139.5 kg
D. 140.8 kg
E. 114.5 kg

add(multiply(divide(120, add(2, 3)), 3), multiply(divide(180, add(3, 5)), 3))

Explanation: "quantity of tin in 120 kg of a = 120 * 3 / 5 = 72 kg quantity of tin in 180 kg of b = 180 * 3 / 8 = 67.5 kg quantity of tin in the new alloy = 72 + 67.5 = 139.5 kg answer is c"


Question: how many seconds will a train 120 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?

<gadget id="calculator">150 + 120</gadget>
<output>270</output>

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

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

<gadget id="calculator">270 / 10</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 17 sec
B. 21 sec
C. 25 sec
D. 27 sec
E. 29 sec

Explanation: "d = 120 + 150 = 270 s = 36 * 5 / 18 = 10 mps t = 270 / 10 = 27 sec"


Question: 3 / 4 of a number is 19 less than the original number . the number is ?

<gadget id="calculator">19 * 4</gadget>
<output>76</output>
<result>76</result>

Choices:
A. 84
B. 64
C. 76
D. 72
E. none

Explanation: answer let the original number be n . so from question n - 3 n / 4 = 19 ⇒ 4 n - 3 n = 76 ∴ n = 76 option : c


Question: the cost price of 40 articles is the same as the selling price of x articles . if the profit is 25 % , what is x ?

<gadget id="calculator">40 * 4</gadget>
<output>160</output>

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

<gadget id="calculator">160 / 5</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 26
B. 28
C. 30
D. 32
E. 34

divide(multiply(40, const_4), add(const_4, const_1))

Explanation: "let the cost price = y the cost price of 40 articles = 40 y the selling price of x articles = 1.25 y * x 1.25 y * x = 40 y x = 40 / 1.25 = 32 the answer is d ."


Question: a man can row 6 kmph in still water . when the river is running at 3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

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

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

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

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

<gadget id="calculator">27 / 12</gadget>
<output>9/4 = around 2.25</output>

<gadget id="calculator">(9/4) * 2</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>

Choices:
A. 5.75
B. 4.5
C. 5.76
D. 5.74
E. 5.71

multiply(divide(multiply(add(6, 3), subtract(6, 3)), add(add(6, 3), subtract(6, 3))), const_2)

Explanation: "m = 6 s = 3 ds = 9 us = 3 x / 9 + x / 3 = 1 x = 2.25 d = 2.25 * 2 = 4.5 answer : b"


Question: the interest on a certain deposit at 4.5 % p . a . is rs . 202.50 in one year . how much will the additional interest in one year be on the same deposit at 5 % p . a ?

<gadget id="calculator">4.5 / 100</gadget>
<output>0.045</output>

<gadget id="calculator">202.5 / 0.045</gadget>
<output>4_500</output>

<gadget id="calculator">4_500 * 5</gadget>
<output>22_500</output>

<gadget id="calculator">22_500 / 100</gadget>
<output>225</output>

<gadget id="calculator">225 - 202.5</gadget>
<output>22.5</output>
<result>22.5</result>

Choices:
A. rs . 20.25
B. rs . 22.50
C. rs . 25
D. rs . 42.75
E. none

subtract(divide(multiply(divide(202.50, divide(4.5, const_100)), 5), const_100), 202.50)

Explanation: "solution s . i = rs . 202.50 , r = 4.5 % , t = 1 year principal = rs ( 100 * 202.50 / 4.5 * 1 ) = rs . 4500 now p = rs . 4500 , r = 5 % , t = 1 year s . i = ( 4500 * 5 * 1 / 100 ) = rs . 225 different in interest = rs . ( 225 - 202.50 ) = rs . 22.50 answer b"


Question: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 5.0 = ?

<gadget id="calculator">1.9 * 0.6</gadget>
<output>1.14</output>

<gadget id="calculator">-1.14</gadget>
<output>-1.14</output>

<gadget id="calculator">2.6 * 1.2</gadget>
<output>3.12</output>

<gadget id="calculator">(-1.14) - 3.12</gadget>
<output>-4.26</output>

<gadget id="calculator">(-4.26) / 5</gadget>
<output>-0.852</output>
<result>-0.852</result>

Choices:
A. - 0.852
B. 1.0
C. 1.07
D. 1.71
E. 2.71

divide(subtract(negate(multiply(1.9, 0.6)), multiply(2.6, 1.2)), 5.0)

Explanation: "dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 0.852 answer a"


Question: if the wheel is 12 cm then the number of revolutions to cover a distance of 1056 cm is ?

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

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

<gadget id="calculator">300 + 10</gadget>
<output>310</output>

<gadget id="calculator">310 + 4</gadget>
<output>314</output>

<gadget id="calculator">314 / 100</gadget>
<output>157/50 = around 3.14</output>

<gadget id="calculator">2 * (157/50)</gadget>
<output>157/25 = around 6.28</output>

<gadget id="calculator">(157/25) * 12</gadget>
<output>1_884/25 = around 75.36</output>

<gadget id="calculator">1_056 / (1_884/25)</gadget>
<output>2_200/157 = around 14.012739</output>
<result>2_200/157 = around 14.012739</result>

Choices:
A. 18
B. 26
C. 14
D. 12
E. 91

divide(1056, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 12))

Explanation: "2 * 22 / 7 * 12 * x = 1056 = > x = 14 answer : c"