Cheukting/mathqa huggingface dataset:
Question (physics): a train 125 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 65 kmph , b ) 70 kmph , c ) 75 kmph , d ) 80 kmph , e ) 85 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 125 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 2250 x = 70 kmph answer is b"
Answer: b
Question (general): what is the units digit of the expression 14 ^ 7 − 15 ^ 4 ?
Options: a ) 0 , b ) 8 , c ) 4 , d ) 6 , e ) 3
Rationale: i think answer on this one should be b too . since we know that 14 ^ 7 > 15 ^ 4 , as will said one should always check if the number is positive .
Answer: b
Question (gain): at what rate percent on simple interest will rs . 750 amount to rs . 1050 in 5 years ?
Options: a ) 8 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "300 = ( 750 * 5 * r ) / 100 r = 8 % . answer : a"
Answer: a
Question (physics): the amount of time that three people worked on a special project was in the ratio of 4 to 3 to 5 . if the project took 120 hours , how many more hours did the hardest working person work than the person who worked the least ?
Options: a ) 25 hours , b ) 30 hours , c ) 20 hours , d ) 26 hours , e ) 32 hours
Rationale: "let the persons be a , b , c . hours worked : a = 4 * 120 / 12 = 40 hours b = 3 * 120 / 12 = 30 hours c = 5 * 120 / 12 = 50 hours c is the hardest worker and b worked for the least number of hours . so the difference is 50 - 30 = 20 hours . answer : c"
Answer: c
Question (geometry): a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 11 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276 , b ) 1200 , c ) 2832 , d ) 1299 , e ) 1320
Rationale: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 11 = 1320 answer : option e"
Answer: e
Question (general): a call center has two teams . each member of team a was able to process 3 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 11 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 3 calls , so total calls for team a = 15 fraction for team b = 40 / ( 40 + 15 ) = 8 / 11 = answer = c"
Answer: c
Question (gain): jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much r does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) r = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Question (general): cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 71.4 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 5.625 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.25 , e ) $ 6.80
Rationale: "0.85 * { original price } = $ 71.4 - - > { original price } = $ 84 . { final price } = $ 71.4 * 1.25 = $ 89.25 . the difference = $ 89.25 - $ 84 = $ 5.25 answer : d ."
Answer: d
Question (general): if ( n + 2 ) ! / n ! = 110 , n = ?
Options: a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "( n + 2 ) ! / n ! = 110 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 110 from here , we might just test the answer choices . since ( 11 ) ( 10 ) = 110 , we can see that n = 9 b"
Answer: b
Question (general): ( 1 / 5 ) ^ e * ( 1 / 4 ) ^ 18 = 1 / ( 2 ( 10 ) ^ 35 ) . what is e ?
Options: a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36
Rationale: we need to arrive at a common base . - - > ( 5 ) ^ ( - e ) * 2 ^ ( - 36 ) = 2 ^ ( - 36 ) * 5 ^ ( - 35 ) 5 ^ ( - e ) = 5 ^ ( - 35 ) - e = - 35 e = 35 = d
Answer: d
Question (gain): i bought two books ; for rs . 360 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 197 , b ) 210 , c ) 189 , d ) 278 , e ) 268
Rationale: "x * ( 85 / 100 ) = ( 360 - x ) 119 / 100 x = 210 answer : b"
Answer: b
Question (general): if n is a natural number , then ( 6 n 2 + 6 n ) is always divisible by :
Options: a ) 6 only , b ) 12 only , c ) 6 and 12 both , d ) by 18 only , e ) 15 only
Rationale: "( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . answer c ) 6 and 12 both ."
Answer: c
Question (general): | 13 - 3 | - | 4 - 10 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 13 - 3 | - | 4 - 10 | = | 10 | - | - 6 | = 10 - 6 = 4 correct answer e"
Answer: e
Question (physics): a fill pipe can fill 1 / 6 of cistern in 90 minutes in how many minutes , it can fill 5 / 6 of the cistern ?
Options: a ) 450 min , b ) 360 min , c ) 240 min , d ) 306 min , e ) 500 min
Rationale: "1 / 6 of the cistern can fill in 90 min 5 / 6 of the cistern can fill in = 90 * 6 * 5 / 6 = 450 min answer is a"
Answer: a
Question (gain): increasing the original price of an article by 6 percent and then increasing the new price by 6 percent is equivalent to increasing the original price by
Options: a ) 12.1 % , b ) 12.36 % , c ) 12.94 % , d ) 13.65 % , e ) 14.56 %
Rationale: 1.06 * 1.06 * x = 1.1236 * x the answer is b .
Answer: b
Question (general): the monthly salaries of 6 employees in a company are $ 1000 , $ 2500 , $ 3100 , $ 3650 , $ 1500 , $ 2000 . what is the mean of the salaries of 6 employees .
Options: a ) $ 2291.7 , b ) $ 1546.8 , c ) $ 2546.5 , d ) $ 1879.3 , e ) $ 3125.3
Rationale: mean of the salaries = ( $ 1000 + $ 2500 + $ 3100 + $ 3650 + $ 1500 + $ 2000 ) / 6 = 13750 / 6 = $ 2291.7 answer is a
Answer: a
Question (gain): ravi and sunil are partners in a business . ravi invests rs . 18,000 for 8 months and sunil invested rs . 10000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 36 : 25 , c ) 3 : 2 , d ) 4 : 5 , e ) 20 : 45
Rationale: "= ( 18000 * 8 ) : ( 10000 * 10 ) = 144000 : 100000 = 36 : 25 answer : b"
Answer: b
Question (general): if | x | = 5 x - 3 , then x = ?
Options: a ) 1 , b ) 1 / 2 , c ) 2 , d ) - 1 / 2 , e ) - 1
Rationale: "answer : a approach : substituted option a i . e x = 1 . inequality satisfied . c"
Answer: c
Question (geometry): the area of a square is 4489 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 43 : 134
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4489 a = 67 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 43 : 134 answer : e"
Answer: e
Question (general): a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 12 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 36
Rationale: "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 12 = > m = 36 answer e"
Answer: e
Question (geometry): a rectangular cube has sides measuring 3 inches long by 2 inches wide by 0.5 inches high . if the surface area of the rectangle is the same as a cube , what do the sides / walls of the cube measure ? round to the nearest whole number .
Options: a ) 4
b ) 5
c ) 6
d ) 7
e ) 2
Rationale: first calculate the surface area of the rectangle by multiplying the length and width of the rectangle together , then multiply by 2 to get both sides of the rectangle . this calculates to 12 inches . find the surface area of the sides of the rectangular cube . multiply the height by the length of the rectangle . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 3 inches . then multiply the width of the rectangle by the height . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 2 inches . add the totals together to get the rectangular cube surface area of 17 inches . since a square cube has 6 sides , divide the surface area by 6 . this calculates to 2.833 inches as the surface area of each side of the cube . the square root of 2.833 is 1.683 . rounding to the nearest whole number that makes each side of the cube measuring 2 inches . the correct answer is ( e ) .
Answer: e
Question (gain): company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 7.00 each , what was company c ’ s gross profit ?
Options: a ) $ 2,250 , b ) $ 2,500 , c ) $ 1,600 , d ) $ 1,250 , e ) $ 1,500
Rationale: "cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 7 = $ 3500 profit : 3500 - 1900 = $ 1600 option c is correct"
Answer: c
Question (general): a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 100 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
Options: a ) 79.55 $ , b ) 80.63 $ , c ) 81.63 $ , d ) 80.27 $ , e ) 83.15 $
Rationale: "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 100 x = 81.27 hence , the correct option is d"
Answer: d
Question (physics): a garrison of 2000 men has provisions for 54 days . at the end of 21 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1977 , b ) 1893 , c ) 1979 , d ) 1900 , e ) 1300
Rationale: "2000 - - - - 54 2000 - - - - 33 x - - - - - 20 x * 20 = 2000 * 33 x = 3300 2000 - - - - - - - 1300 answer : e"
Answer: e
Question (gain): a person buys an article at $ 200 . at what price should he sell the article so as to make a profit of 10 % ?
Options: a ) 240 , b ) 260 , c ) 220 , d ) 300 , e ) 360
Rationale: "c 220 cost price = $ 200 profit = 10 % of 200 = $ 20 selling price = cost price + profit = 200 + 20 = 220"
Answer: c
Question (other): 200 liters of a mixture contains milk and water in the ratio 4 : 1 . if 20 liters of this mixture be replaced by 20 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 6 : 1 , b ) 1 : 6 , c ) 2 : 3 , d ) 3 : 2 , e ) 4 : 1
Rationale: "quantity of milk in 200 liters if mix = 200 * 4 / 5 = 160 liters quantity of milk in 210 liters of new mix = 160 + 20 = 180 liters quantity of water in it = 210 - 180 = 30 liters ratio of milk and water in new mix = 180 : 30 = 6 : 1 answer is a"
Answer: a
Question (physics): if the speed of a man is 66 km per hour , then what is the distance traveled by him in 30 seconds ?
Options: a ) 550 m , b ) 500 m , c ) 375 m , d ) 420 m , e ) 440 m
Rationale: "the distance traveled in 30 sec = 66 * ( 5 / 18 ) * 30 = 550 m answer : a"
Answer: a
Question (general): when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 6.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12
Rationale: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 6.12 and remainder is 6 so . 12 x y = 6 hence y = 50 ans c"
Answer: c
Question (general): two identical trains aa and bb running in opposite direction at same speed tale 2 min to cross each other completely . the number of bogies of aa are increased from 12 to 16 . how much more time would they now require to cross each other ?
Options: a ) 40 sec , b ) 50 sec , c ) 60 sec , d ) 20 sec , e ) 25 sec
Rationale: total initial bogies is 12 + 12 = 2412 + 12 = 24 additional bogies = 16 â ˆ ’ 12 = 4 24 bogies is 12 + 12 = 24 additional bogies = 16 - 12 = 4 24 bogies take 2 min 2 * 60 / 24 * 4 = 20 sec answer d
Answer: d
Question (physics): express 5 mps in kmph ?
Options: a ) 22 , b ) 88 , c ) 90 , d ) 18 , e ) 24
Rationale: "5 * 18 / 5 = 18 kmph answer : d"
Answer: d
Question (general): a person starting with rs . 64 and making 6 bets , wins 3 times and loses 3 times , the wins and loses occurring in random order . the chance for a win is equal to the chance for a loss . if each wager is for 1 / 2 the money remaining at the time of the bet , then the final result is ?
Options: a ) rs . 23 , b ) rs . 37 , c ) rs . 45 , d ) rs . 67 , e ) rs . 77
Rationale: as the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5 , we will multiply initial amount by 1.5 thrice and by 0.5 thrice ( in any order ) . the overall resultant will remain same . so final amount with the person will be ( in all cases ) : = 64 ( 1.5 ) ( 1.5 ) ( 1.5 ) ( 0.5 ) ( 0.5 ) ( 0.5 ) = = 64 ( 1.5 ) ( 1.5 ) ( 1.5 ) ( 0.5 ) ( 0.5 ) ( 0.5 ) = rs 2727 hence the final result is : 64 − 27 = 3764 − 27 = 37 : a loss of rs . 37 b
Answer: b
Question (physics): a boat can travel with a speed of 25 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 90 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: "speed downstream = ( 25 + 5 ) km / hr = 30 km / hr . time taken to travel 90 km downstream = 90 / 30 hrs = 3 hrs . answer : c"
Answer: c
Question (gain): how many ounces of a 60 % salt solution must be added to 60 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 30 , c ) 50 , d ) 60 , e ) 70
Rationale: "let x = ounces of 60 % salt solution to be added . 2 * 60 + . 6 x = . 4 ( 60 + x ) x = 60 answer d"
Answer: d
Question (gain): in a college , 50 % of total 400 arts students are locals . 25 % of students from 100 science students are locals and 85 % of total 120 commerce students are locals . what is the total percentage of locals from arts , science and commerce .
Options: a ) 322 , b ) 340 , c ) 333 , d ) 327 , e ) 500
Rationale: locals from arts = 50 % of 400 = 200 locals from science = 25 % of 100 = 25 locals from commerce = 85 % of 120 = 102 total locals = 200 + 25 + 102 = 327 d
Answer: d
Question (physics): 12 : 6 seconds : : ? : 8 minutes
Options: a ) 10 , b ) 15 , c ) 16 , d ) 25 , e ) 30
Rationale: "12 * 8 = 6 * x x = 16 answer : c"
Answer: c
Question (general): a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability y that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: "simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer y : 1 – 4 / 25 = 21 / 25 . answer choice e ."
Answer: e
Question (general): if jake loses 15 pounds , he will weigh twice as much as his sister . together they now weigh 132 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 63 , b ) 93 , c ) 139 , d ) 147 , e ) 188
Rationale: "lets say j is the weight of jack and s is the wt of his sister . if he loses 15 pounds , he s twice as heavy as his sister . j - 15 = 2 * s also , together they weight 132 pounds j + s = 132 solvong the 2 equation , we get j = 93 pounds ! b"
Answer: b
Question (physics): a and b complete a work in 7 days . a alone can do it in 14 days . if both together can do the work in how many days ?
Options: a ) 4.6 days , b ) 4.78 days , c ) 5.65 days , d ) 3.77 days , e ) 5.75 days
Rationale: "1 / 7 + 1 / 14 = 3 / 14 14 / 3 = 4.6 days answer : a"
Answer: a
Question (physics): a car traveled the first quarter of a certain distance at 4 times the speed it traveled the remaining distance . what proportion of the total time traveled , was the time taken to travel the first quarter of the distance ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 13
Rationale: these problems can be solved through algebra or sly number picking . being a big fan of solving problems with numbers , let ' s pick a total distance divisible by 4 ( say 40 ) so we can break it up into quarters , and a speed that can easily be one fourth , say 10 . each quarter is thus 10 kilometers ( or miles or feet or angstroms for all it matters ) , and the runner ' s speed is 10 km / h for the first quarter and 5 / 2 km / h for the remaining quarters . he ' ll take 1 hour to do the first quarter and then 4 hours for the second quarter , 4 hours for the third and 4 hours for the fourth . on total he will take 13 hours to complete this race , of which 1 hour was spent on the first quarter . so 1 / 13 . answer e .
Answer: e
Question (gain): one fourth of one third of two fifth of a number is 17 . what will be 40 % of that number
Options: a ) 140 , b ) 204 , c ) 180 , d ) 200 , e ) 250
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 17 then x = 17 * 30 = 510 40 % of 510 = 204 answer : option b"
Answer: b
Question (general): what is the decimal equivalent of ( 1 / 5 ) ^ 2 ?
Options: a ) 0.0016 , b ) 0.04 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 5 ) ² = ( 1 / 5 ) ( 1 / 5 ) = 1 / 25 approach # 1 : use long division to divide 25 into 1 to get 1 / 25 = 0.04 b"
Answer: b
Question (other): at an international conference , “ red ” world countries and “ blue ” world countries are the only participants . the ratio of “ red ” world participants to “ blue ” world participants is 10 : 5 . if one - third of “ red ” world participants are left - handed and two - thirds of “ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ?
Options: a ) 4 / 10 , b ) 4 / 9 , c ) 6 / 5 , d ) 9 / 2 , e ) 6 / 4
Rationale: red : blue = 10 : 5 let red = 10 x and blue = 5 x 1 / 3 of red are left handed = > 1 / 3 * 10 x = 10 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 5 x = 10 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 10 x / 3 + 10 x / 3 ) / ( 10 x + 5 x ) = 20 / 45 = 4 / 9 answer : b
Answer: b
Question (general): the average salary / head of allthe workers in a workshop is rs . 750 , if the average salary / head of 5 technician is rs . 900 and the average salary / head of the rest is rs . 700 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y - 5 workers . 5 x 900 + 700 ( y - 5 ) = 750 y ⇒ 4500 + 700 y - 3500 = 750 y ⇒ 50 y = 1000 ∴ y = 20 so total number of workers = 20 b
Answer: b
Question (general): the average age of 10 men increases by 6 years when two women are included in place of two men of ages 18 and 22 years . find the average age of the women ?
Options: a ) 37 , b ) 26 , c ) 30 , d ) 50 , e ) 11
Rationale: "explanation : 18 + 22 + 10 * 6 = 100 / 2 = 50 answer : d"
Answer: d
Question (gain): a started a business with an investment of rs . 70000 and after 3 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 43000 , then the share of b is ?
Options: a ) 33888 , b ) 36000 , c ) 27778 , d ) 27772 , e ) 81122
Rationale: ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 9 ) = 7 : 36 total profit = rs . 43000 share of b = 36 / 43 ( 43000 ) = rs . 36000 answer : b
Answer: b
Question (physics): working together , printer a and printer b would finish the task in 10 minutes . printer a alone would finish the task in 30 minutes . how many pages does the task contain if printer b prints 5 pages a minute more than printer a ?
Options: a ) 125 , b ) 150 , c ) 175 , d ) 200 , e ) 225
Rationale: "10 * a + 10 * b = x pages in 10 mins printer a will print = 10 / 30 * x pages = 1 / 3 * x pages thus in 10 mins printer printer b will print x - 1 / 3 * x = 2 / 3 * x pages also it is given that printer b prints 5 more pages per min that printer a . in 10 mins printer b will print 50 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 50 = > x = 150 pages answer : b"
Answer: b
Question (other): the ratio of boys to girl in a school is 5 : 4 . if there are 1500 boys in the school , how many girls are there ?
Options: a ) 300 , b ) 1200 , c ) 1500 , d ) 1800 , e ) 2000
Rationale: think of the ratio as 5 parts : 4 parts . divide 1500 by 5 to find 1 ` ` part ' ' of the ratio . 1500 / 5 = 300 multiply this by 4 to get 4 ` ` parts ' ' of the ratio . 300 * 4 = 1200 there are 1200 girls in the school . the answer is b
Answer: b
Question (physics): a tank can be filled by two pipes a and b in 60 minutes and 40 minutes respectively . how many minutes will it take to fill the tank from empty state if b is used for the first half time and then a and b fill it together for the other half
Options: a ) 15 mins , b ) 20 mins , c ) 25 mins , d ) 30 mins , e ) none of these
Rationale: "explanation : let the total time be x mins . part filled in first half means in x / 2 = 1 / 40 part filled in second half means in x / 2 = 1 / 60 + 1 / 40 = 1 / 24 total = x / 2 ∗ 1 / 40 + x / 2 ∗ 1 / 24 = 1 = > x / 2 ( 1 / 40 + 1 / 24 ) = 1 = > x / 2 ∗ 1 / 15 = 1 = > x = 30 mins option d"
Answer: d
Question (physics): the diameter of a garden roller is 1.4 m and it is 2 m long . how much area will it cover in 4 revolutions ? ( use ï € = 22 â  „ 7 )
Options: a ) 35.2 m 2 , b ) 44 m 2 , c ) 48 m 2 , d ) 36 m 2 , e ) none of these
Rationale: "required area covered in 5 revolutions = 4 ã — 2 ï € rh = 4 ã — 2 ã — 22 â  „ 7 ã — 0.7 ã — 2 = 35.2 m 2 answer a"
Answer: a
Question (general): in a group of ducks and cows , the total number of legs are 48 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 28 , b ) 12 , c ) 24 , d ) 16 , e ) 19
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 48 = > 2 x = 48 = > x = 24 c"
Answer: c
Question (general): two - third of a positive number and 64 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 2 / 3 , e ) 146 / 25
Rationale: "let the number be x . then , 2 / 3 x = 64 / 216 * 1 / x x 2 = 64 / 216 * 3 / 2 = 64 / 144 = 4 / 9 x = 2 / 3 answer : d"
Answer: d
Question (general): when positive integer m is divided by positive integer n , the remainder is 12 . if m / n = 24.2 , what is the value of n ?
Options: a ) 120 , b ) 60 , c ) 30 , d ) 24 , e ) 12
Rationale: n = decimal part of 24.2 * remainder i . e . ( 12 ) hence 0.2 * n = 12 n = 60 . b
Answer: b
Question (general): if x and y are positive integers and 12 x = 21 y what is the least possible value of xy ?
Options: a ) 9 , b ) 28 , c ) 63 , d ) 84 , e ) 252
Rationale: "12 x = 21 y = > x / y = 7 / 4 = > 4 x = 7 y 4 ( 3 ) = 7 ( 3 ) = > x * y = 9 a"
Answer: a