Cheukting/mathqa huggingface dataset:
Question (geometry): what is the max number of rectangular boxes , each measuring 4 inches by 6 inches by 10 inches , that can be packed into a rectangular packing box measuring 16 inches by 18 inches by 30 inches , if all boxes are aligned in the same direction ?
Options: a ) 36
b ) 14
c ) 12
d ) 15
e ) 11
Rationale: the 4 inch side should be aligned to the 16 inch side ( 4 layer ) 6 inch side should be aligned to the 18 inch side . ( 3 layer ) and 10 inch side should be aligned to the 30 inch side . ( 3 layer ) maximum number of rectangles = 4 * 3 * 3 = 36 answer is a
Answer: a
Question (gain): after decreasing 80 % in the price of an article costs rs . 320 . find the actual cost of an article ?
Options: a ) 2777 , b ) 2987 , c ) 1200 , d ) 9977 , e ) 1600
Rationale: "cp * ( 20 / 100 ) = 320 cp = 16 * 100 = > cp = 1600 answer : e"
Answer: e
Question (physics): how many seconds will a 500 m long train take to cros a man walking with a speed of 3 kmph in the direction of the moving train if the speed of the train is 63 kmph
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 50
Rationale: time = distance ( here length of the train ) / relative speed ( 63 - 3 ) thus time = 500 / 60 * 5 / 18 = 500 * 18 / 60 * 5 = 30 seconds answer : b
Answer: b
Question (general): a batsman had a certain average of runs for 16 innings . in the 17 th innings , he made a score of 87 runs thereby increasing his average by 3 . what is his average after 17 innings ?
Options: a ) 39 , b ) 88 , c ) 266 , d ) 278 , e ) 221
Rationale: explanation : assume his initial average = xx his total runs after 16 innings = 16 xx after scoring 87 runs his average got increased by 3 to xx + 3 so his total runs after 17 innings = 17 × ( xx + 3 ) but it was given that the difference in the total scores after 16 innings and 17 innings = 87 therefore 17 × ( x + 3 ) − 16 x = 87 ⇒ x = 3617 × ( x + 3 ) − 16 x = 87 ⇒ x = 36 his new average = 36 + 3 = 39 answer : a
Answer: a
Question (probability): if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is - .
Options: a ) 2 / 10 , b ) 4 / 13 , c ) 3 / 5 , d ) 9 / 7 , e ) 1 / 4
Rationale: "explanation : p ( s ᴜ k ) = p ( s ) + p ( k ) - p ( s ∩ k ) , where s denotes spade and k denotes king . p ( s ᴜ k ) = 13 / 52 + 4 / 52 - 1 / 52 = 4 / 13 answer : b"
Answer: b
Question (probability): the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 3 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 1 / 24
Rationale: "probability of first member an english teacher = 3 / 10 probability of second member an english teacher = 2 / 10 probability of both being english teacher = 3 / 9 x 2 / 8 = 3 / 5 ( d )"
Answer: d
Question (gain): a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 1 / 5 % his yearly income diminishes by rs . 61.50 . his capital is
Options: a ) 22.378 , b ) 37.78 , c ) 76.88 , d ) 27.888 , e ) 12.771
Rationale: explanation : capital = rs . x , then 4 / 5 x = 61.5 x = 76.88 answer : c ) rs . 76.88
Answer: c
Question (gain): thirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 19 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?
Options: a ) 60 , b ) 70 , c ) 100 , d ) 120 , e ) 140
Rationale: "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 19 = 49 members have not passed the test , thus 0.7 * total = 49 - - > total = 70 . answer : b ."
Answer: b
Question (general): the decimal 0.1 is how many times greater than the decimal ( 0.01 ) ^ 3 ?
Options: a ) 10 , b ) 10 ^ 2 , c ) 10 ^ 5 , d ) 10 ^ 8 , e ) 10 ^ 10
Rationale: 0.1 = 10 ^ - 1 ( 0.01 ) ^ 3 = ( 10 ^ - 2 ) ^ 3 = 10 ^ - 6 10 ^ 5 * 10 ^ - 6 = 10 ^ - 1 the answer is c .
Answer: c
Question (physics): the current in a river is 5 mph . a boat can travel 20 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 88 miles , c ) 93,75 miles , d ) 100 miles , e ) 112 miles
Rationale: "upstream speed = 20 - 5 = 15 mph downstream speed = 20 + 5 = 25 mph d / 15 + d / 25 = 10 hours solving for d we get d = 93,75 answer : c"
Answer: c
Question (general): let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 16 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "the question is finding y such that ( 16 - y ) ! is a multiple of 16 . that means we need to have 2 ^ 4 in ( 16 - y ) ! 6 ! is the smallest factorial number with 2 ^ 4 as a factor . 16 - y = 6 y = 10 the answer is b ."
Answer: b
Question (gain): two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 249 marks in the second test and failed by 66 marks in that test . find the pass mark in the first test ?
Options: a ) 768 , b ) 243 , c ) 246 , d ) 280 , e ) 224
Rationale: "let the maximum mark in each test be m . the candidate failed by 66 marks in the second test . pass mark in the second test = 249 + 66 = 315 45 / 100 m = 315 pass mark in the first test = 40 / 100 m = 40 / 45 * 315 = 280 . answer : d"
Answer: d
Question (general): the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 14 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 14 = 406 hence , new average = 406 ⁄ 10 = 40.6 answer c"
Answer: c
Question (general): in 1990 the budgets for projects q and v were $ 500,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1997
Rationale: "let the no of years it takes is x . 500 + 30 x = 780 - 10 x - - > 40 x = 280 and x = 7 . thus , it happens in 1997 . e ."
Answer: e
Question (general): how many numbers between 100 and 798 are divisible by 2 , 3 , and 7 together ?
Options: a ) 112 , b ) 77 , c ) 267 , d ) 17 , e ) 99
Rationale: explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 798 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 798 : 798 / 42 = 19 hence , 42 * 19 = 798 is the last number divisible by 42 within 798 hence , total numbers divisible by 2 , 3 , 7 together are ( 19 â € “ 2 ) = 17 answer : d
Answer: d
Question (physics): a car traveled 340 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 504 , b ) 416 , c ) 321 , d ) 220 , e ) 170
Rationale: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 340 miles will be covered in 340 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 340 / h = > 336 / c = 340 / ( c + 6 ) = > 336 c + 336 * 6 = 340 c = > c = 336 * 6 / 4 = 504 answer a ."
Answer: a
Question (physics): 1850 men have provisions for 15 days . if 150 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.0 , c ) 13.9 , d ) 13.5 , e ) 12.1
Rationale: "1850 * 15 = 2000 * x x = 13.9 answer : c"
Answer: c
Question (geometry): the product of the squares of two positive integers is 100 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : c - 2 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 100 [ square root both sides ] xy = 10 10 = 1 x 10 , 10 x 1 , 2 x 5 , 5 x 2 cancel the repeats this leaves us with exactly 2 options . hence , c"
Answer: c
Question (gain): a number increased by 30 % gives 780 . the number is
Options: a ) 250 , b ) 400 , c ) 450 , d ) 600 , e ) 520
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 30 % = 130 % 130 % - - - - - - - > 780 ( 130 × 6 = 780 ) 100 % - - - - - - - > 600 ( 100 × 6 = 600 ) d )"
Answer: d
Question (general): if a > x > y > z on the number line , y is halfway between x and z , and x is halfway between w and z , then ( y - x ) / ( y - a ) =
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 3 / 4 , e ) 1
Rationale: let y - z = t - - - > since y is halfway between x and z and x > y we have x - y = t . moreover x - z = ( x - y ) + ( y - z ) = 2 t . similarly since x is halfway between w and z , we have a - x = 2 t . so y - x = - t , y - a = - 3 t . - - - > ( y - x ) / ( y - a ) = 1 / 3 . the answer is ( b ) .
Answer: b
Question (general): 3 friends james , david and charlie divide $ 1230 amongs them in such a way that if $ 5 , $ 10 and $ 15 are removed from the sums that james , david and charlie received respectively , then the share of the sums that they got will be in the ratio of 9 : 10 : 11 . how much did charlie receive ?
Options: a ) $ 600 , b ) $ 575 , c ) $ 550 , d ) $ 580 , e ) $ 615
Rationale: a + b + c = 1230 given ratio 9 : 10 : 11 let us say the shares of a , b , c deducting 5 , 1015 be a , b , c a + b + c = 1230 - 30 = 1200 = 30 k c share = ( 1200 x 30 ) / 60 = 600 c = charlie share = 600 + 15 = 615 option e
Answer: e
Question (general): if 2 + 3 = 31 ; 3 + 5 = 134 ; 5 + 7 = 368 then 7 + 11 = ?
Options: a ) 1250 , b ) 1360 , c ) 1270 , d ) 1380 , e ) 1290
Rationale: "2 ^ 2 + 3 ^ 3 = 4 + 27 = 31 3 ^ 2 + 5 ^ 3 = 9 + 125 = 134 5 ^ 2 + 7 ^ 3 = 25 + 343 = 368 and 7 ^ 2 + 11 ^ 3 = 49 + 1331 = 1380 answer : d"
Answer: d
Question (geometry): a rectangular grass field is 70 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1350 , b ) s . 1300 , c ) s . 1328 , d ) s . 1397 , e ) s . 1927
Rationale: "area = ( l + b + 2 d ) 2 d = ( 70 + 55 + 2.5 * 2 ) 2 * 2.5 = > 650 650 * 2 = rs . 1300 answer : b"
Answer: b
Question (geometry): calculate the area of a triangle , if the sides of are 39 cm , 36 cm and 15 cm , what is its area ?
Options: a ) 570 cm 2 , b ) 370 cm 2 , c ) 170 cm 2 , d ) 271 cm 2 , e ) 270 cm 2
Rationale: "the triangle with sides 39 cm , 36 cm and 15 is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : e"
Answer: e
Question (physics): a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 20 km in 20 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 6 , e ) 16
Rationale: "explanation : he covered 5 km in 1 hour , so he might cover 20 km in 4 hours . but he took 20 hours . he would have saved 20 â € “ 4 = 16 hours . answer : e"
Answer: e
Question (physics): one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 144 min , b ) 250 min , c ) 196 min , d ) 100 min , e ) 112 min
Rationale: "let the slower pipe alone fill the tank in x minutes then , faster pipe will fill it in x / 3 minutes 1 / x + 3 / x = 1 / 36 4 / x = 1 / 36 x = 144 min answer is a"
Answer: a
Question (physics): a man can do a job in 15 days . his father takes 20 days and his son finishes it in 15 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.3 , b ) 6.9 , c ) 5.5 , d ) 6.1 , e ) 6.2
Rationale: "1 day work of the three persons = ( 1 / 15 + 1 / 20 + 1 / 15 ) = 11 / 60 so , all three together will complete the work in 300 / 47 = 5.5 days . answer : c"
Answer: c
Question (gain): how long does a train 250 meters long running at the rate of 72 km / hr take to cross a bridge 150 meters in length ?
Options: a ) 10 sec , b ) 20 sec , c ) 25 sec , d ) 30 sec , e ) 35 sec
Rationale: "distance = length of train + length of bridge = 250 + 150 = 400 speed = 72 km / hr = 72 * 5 / 18 = 20 m / s required time = 400 / 20 = 20 seconds answer is b"
Answer: b
Question (general): the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 10 cents less than the price of commodity y ?
Options: a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) 2012
Rationale: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 10 cents less than commodity y . $ 2.00 / 25 cents = 8 years the answer is 2001 + 8 years = 2009 . the answer is b ."
Answer: b
Question (general): if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 , then find the total number of items the wholesaler distributes ?
Options: a ) 567 , b ) 167 , c ) 267 , d ) 467 , e ) 667
Rationale: here , a : b : c : d = 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 1 ) l . c . m of 12 : 13 : 15 : 2 is 780 2 ) find the number of books each friend received - - - - - - - - - ( to find no . of books each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 12 ) x 780 = 65 b = ( 1 / 13 ) x 780 = 60 c = ( 1 / 15 ) x 780 = 52 d = ( 1 / 2 ) x 780 = 390 3 ) total number of toys = ( 65 x + 60 x + 52 x + 390 x ) = 567 x minimum number of pens ( x ) = 1 therefore , total number of items = 567 items . correct option : a
Answer: a
Question (gain): john makes $ 50 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17.9 % , d ) 18.12 % , e ) 20 %
Rationale: "increase = ( 10 / 50 ) * 100 = ( 1 / 5 ) * 100 = 20 % . e"
Answer: e
Question (gain): in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 90 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 83 . , c ) 81 , d ) 91 , e ) 108
Rationale: "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 90 % of 250 = 225 are boys who play soccer . girls who play soccer = 25 . total girls who do not play soccer = 108 - 25 = 83 . correct option : b"
Answer: b
Question (gain): john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 14 , what was the price before the first discount ?
Options: a ) $ 45.10 , b ) $ 34.31 , c ) $ 24.88 , d ) $ 67.54 , e ) $ 65.23
Rationale: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 14 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 14 solve for x x = $ 24.88 correct answer c"
Answer: c
Question (geometry): the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1690 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 190 , d ) 321 , e ) 260
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1650 x = 60 required perimeter = 2 ( 60 + 70 ) = 260 e"
Answer: e
Question (general): the average weight of 4 person ' s increases by 1.5 kg when a new person comes in place of one of them weighing 95 kg . what might be the weight of the new person ?
Options: a ) 101 kg , b ) 103.4 kg , c ) 105 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increased = ( 4 x 1.5 ) kg = 6 kg . weight of new person = ( 95 + 6 ) kg = 101 kg . answer : option a"
Answer: a
Question (physics): each of the three people individually can complete a certain job in 3 , 5 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?
Options: a ) 4 / 15 , b ) 7 / 30 , c ) 11 / 30 , d ) 7 / 18 , e ) 5 / 18
Rationale: "the two slowest people work at rates of 1 / 5 and 1 / 6 of the job per hour . the sum of these rates is 1 / 5 + 1 / 6 = 11 / 30 of the job per hour . the answer is c ."
Answer: c
Question (general): the average of 5 consecutive odd numbers a , b , c , d and e is 33 . what percent of a is d ?
Options: a ) 86.8 , b ) 88.6 , c ) 89.2 , d ) 90.1 , e ) 92.2
Rationale: explanation : in such a case the middle number ( c ) is the average ∴ c = 33 and a = 31 and d = 35 required percentage = 31 / 35 x 100 = 88.6 answer : option b
Answer: b
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 30 cm ?
Options: a ) 827 cm 2 , b ) 570 cm 2 , c ) 285 cm 2 , d ) 178 cm 2 , e ) 176 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 30 ) = 570 cm 2 answer : b"
Answer: b
Question (gain): daniel went to a shop and bought things worth rs . 25 , out of which 60 paise went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) a ) 14.4 , b ) b ) 20 , c ) c ) 21.3 , d ) d ) 21.5 , e ) e ) 22
Rationale: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 60 paise = rs . 60 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 25 − 60 / 100 − x ) 6 / 100 = 60 / 100 ⇒ 6 ( 25 − 0.6 − x ) = 60 ⇒ ( 25 − 0.6 − x ) = 10 ⇒ x = 25 − 0.6 − 10 = 14.4 a"
Answer: a
Question (geometry): the volumes of two cubes are in the ratio 27 : 125 , what shall be the ratio of their surface areas ?
Options: a ) 6 : 25
b ) 3 : 5
c ) 9 : 25
d ) 16 : 25
e ) 19 : 25
Rationale: a 13 : a 23 = 27 : 125 a 1 : a 2 = 3 : 5 6 a 12 : 6 a 22 a 12 : a 22 = 9 : 25 answer : c
Answer: c
Question (general): when positive integer n is divided by positive integer j , the remainder is 15 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 187.5
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 134.08 here 134 is the quotient . given that remainder = 15 so , 134.08 = 134 + 15 / j so , j = 187.5 ans e"
Answer: e
Question (other): bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - .
Options: a ) 7 / 15 , b ) 2 / 8 , c ) 7 / 11 , d ) 13 / 5 , e ) 87
Rationale: explanation : drawing two balls of same color from seven green balls can be done in â  · c â ‚ ‚ ways . similarly from eight white balls two can be drawn in â  ¸ c â ‚ ‚ ways . p = â  · c â ‚ ‚ / â ¹ â  µ c â ‚ ‚ + â  ¸ c â ‚ ‚ / â ¹ â  µ c â ‚ ‚ = 7 / 15 a
Answer: a
Question (physics): two trains of equal length , running with the speeds of 60 and 40 kmph , take 75 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 15 sec , b ) 16 sec , c ) 14 sec , d ) 67 sec , e ) 13 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 75 d = 75 * 100 / 18 = 1250 / 3 rs = 60 + 50 = 100 * 5 / 18 t = 1250 / 3 * 18 / 500 = 15 sec answer : a"
Answer: a
Question (other): a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 11,900 sedans in anytown , how many motorcycles are there ?
Options: a ) 1260 , b ) 2100 , c ) 3400 , d ) 4200 , e ) 5200
Rationale: "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 11900 = > 7 x = 11900 = > x = 1700 total number of motorcycles = 2 x = 2 * 1700 = 3400 answer c"
Answer: c
Question (general): how many figures are required to number the pages the pages of a book containing 223 pages ?
Options: a ) 372 , b ) 661 , c ) 561 , d ) 467 , e ) 761
Rationale: "1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 223 = 124 * 3 = 372 - - - - - - - - - - - 561 answer : c"
Answer: c
Question (gain): if 40 % of a certain number is 160 , then what is 90 % of that number ?
Options: a ) 270 , b ) 380 , c ) 260 , d ) 360 , e ) 290
Rationale: "explanation : 40 % = 40 * 4 = 160 90 % = 90 * 4 = 360 answer : option d"
Answer: d
Question (general): if x / y = 8 / 7 , then ( 7 x + 6 y ) / ( 7 x â € “ 6 y ) = ?
Options: a ) 11 , b ) 8 , c ) 9 , d ) 7 , e ) 6
Rationale: "answer dividing numerator as well as denominator by y , we get given exp . = ( 7 x + 6 y ) / ( 7 x â € “ 6 y ) = ( 7 x / y + 6 ) / ( 7 x / y â € “ 6 ) since x / y = 8 / 7 this implies that = [ ( 7 * 8 ) / 7 + 6 ] / [ ( 7 * 8 ) / 7 - 6 ) ] = ( 8 + 6 ) / ( 8 - 6 ) = 7 option : d"
Answer: d
Question (general): subtracting 30 from a number , the remainder is one fourth of the number . find the number ?
Options: a ) 29 , b ) 88 , c ) 40 , d ) 28 , e ) 27
Rationale: explanation : 3 / 4 x = 30 = > x = 40 answer : c
Answer: c
Question (general): the sum of three consecutive multiples of 3 is 108 . what is the largest number ?
Options: a ) 36 , b ) 39 , c ) 33 , d ) 30 , e ) 42
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 108 9 x = 99 x = 11 largest number = 3 x + 6 = 39 answer : b"
Answer: b
Question (physics): the sum of four consecutive even integers is 1284 . the greatest of them is :
Options: a ) 324 , b ) 342 , c ) 364 , d ) 382 , e ) none
Rationale: "sol . let the four integers be x , x + 2 , x + 4 and x + 6 then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) = 1284 ⇔ 4 x = 1272 ⇔ x = 318 ∴ greatest integer = x + 6 = 324 . answer a"
Answer: a
Question (geometry): the area of a square field is 24200 sq m . how long will a lady take to cross the field diagonally at the rate of 6.6 km / hr ?
Options: a ) 3 minutes , b ) 0.04 hours , c ) 2 minutes , d ) 2.4 minutes , e ) 2 minutes 40 seconds
Rationale: "explanatory answer step 1 : compute the length of the diagonal of the square let ' a ' meters be the length of a side of the square field . therefore , its area = a 2 square meters . - - - ( 1 ) the length of the diagonal ' d ' of a square whose side is ' a ' meters = √ 2 a - - - ( 2 ) from ( 1 ) and ( 2 ) , we can deduce that the square of the diagonal = d 2 = 2 a 2 = 2 ( area of the square ) or d = √ 2 * area meters . d = √ 2 ∗ 24200 = 48400 = 220 m . step 2 : compute the time taken to cross the field the time taken to cross a distance of 220 meters while traveling at 6.6 kmph = 220 m / 6.6 kmph convert unit of speed from kmph to m / min 1 km = 1000 meters and 1 hour = 60 minutes . so , 6.6 kmph = 6.6 ∗ 1000 / 60 m / min = 110 m / min ∴ time taken = 220 / 110 = 2 minutes choice c"
Answer: c
Question (general): anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 6 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 25 , b ) 26 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 12 + 6 + 8 = 26 . answer is b ."
Answer: b