Cheukting/mathqa huggingface dataset:
Question (general): if x and y are positive integers and 9 + x + y + xy = 23 , what is the value of x + y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "try each answer choices . for a : 9 + 3 + xy = 23 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 9 + 5 + xy = 23 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 9 + 6 + xy = 23 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 9 + 8 + xy = 23 ; xy = 6 ( no combination of xy = 6 and x + y = 8 ) for e : 9 + 9 + xy = 23 ; xy = 5 ( impossible , 5 prime number . 1 + 5 does n ' t equal 9 ) therefore , answer c ."
Answer: c
Question (other): a container holding 15 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 4 : 7 , e ) 7 : 16
Rationale: container 1 has 15 ounces in the ratio 1 : 2 or , x + 2 x = 15 gives x ( alcohol ) = 5 and remaining water = 10 container 2 has 8 ounces in the ratio 1 : 3 or , x + 3 x = 8 gives x ( alcohol ) = 2 and remaining water = 6 mixing both we have alcohol = 5 + 2 and water = 10 + 6 ratio thus alcohol / water = 7 / 16 answer e
Answer: e
Question (physics): how many plants will be there in a circular bed whose outer edge measure 31 cms , allowing 4 cm 2 for each plant ?
Options: a ) 19
b ) 750
c ) 24
d ) 120
e ) none of these
Rationale: circumference of circular bed = 31 cm area of circular bed = ( 31 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 31 ) 2 â  „ 4 ï € ã · 4 = 19.11 = 19 ( approx ) answer a
Answer: a
Question (general): 3 cannons are firing at a target . if their individual probabilities to hit the target are 0.5 , 0.2 , and 0.3 respectively , what is the probability that none of the cannons will hit the target after one round of fire ? prob . that all the cannons will hit the target = . 06 prob . that none of the cannons will hit = 1 - . 06 = . 94
Options: a ) 0.06 , b ) 0.12 , c ) 0.21 , d ) 0.29 , e ) 0.28
Rationale: the probability that eachdoesn ' thit is : 0.5 , 0.8 , and 0.7 . when we have multiple independent events , we multiply the probabilities : . 5 * . 8 * . 7 = 0.28 . option : e
Answer: e
Question (general): if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 5000 in a long term bond that pays 4 percent interest , compounded annually , what will be the approximate total amount of investment 36 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 18 years investment will become $ 5,000 * 2 = $ 10,000 and in another 18 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a ."
Answer: a
Question (general): 2 / 5 of 3 / 7 of 23 / 11 of ? = 64 × 3
Options: a ) 511 , b ) 419 , c ) 616 , d ) 636 , e ) 686
Rationale: "explanation : 2 / 5 & time ; 3 / 7 & time ; 20 / 11 & time ; x = 192 x = 192 & time ; 11 & time ; 7 & time ; 5 / 2 & time ; 3 & time ; 20 = 616 answer : option c"
Answer: c
Question (gain): the annual interest rate earned by an investment increased by 11 percent from last year to this year . if the annual interest rate earned by the investment this year was 22 percent , what was the annual interest rate last year ?
Options: a ) 17 % , b ) 19 % , c ) 18 % , d ) 20 % , e ) 22 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.11 i ( last year ) = 1.11 i ( last year ) 22 = 1.11 x i ( last year ) i ( last year ) = 22 / 1.1 = 220 / 11 = 20 % answer : d"
Answer: d
Question (general): if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: there are 3 single digit multiple of 3 , that is , 3 , 69 . there are 8 prime nos less than 20 - 23 , 57 , 1113 , 1719 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability = 1 / 24 . answer c .
Answer: c
Question (general): if p ^ 2 – 13 p + 40 = h , and p is a positive integer between 1 and 10 , inclusive , what is the probability that h < 0 ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 10
Rationale: p 2 – 13 p + 40 = h so ( p – 8 ) ( p – 5 ) = h for q to be negative , the expressions ( p – 8 ) and ( p – 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p – 8 ) and ( p – 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer ) . that means that there are only two integer values for p , 6 and 7 , that would yield a negative q . with a total of 10 possible p values , only 2 yield a negative q , so the probability is 2 / 10 or 1 / 5 . the correct answer is b .
Answer: b
Question (geometry): abcd is a square where ab = â ˆ š 4004 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000
Rationale: "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4004 / 2 = 2002 . correct answer b"
Answer: b
Question (general): two - third of a positive number and 16 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 12 / 5 , c ) 1 / 3 , d ) 144 / 25 , e ) 146 / 25
Rationale: let the number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 = 1 / 9 x = 1 / 3 answer : c
Answer: c
Question (general): if x < y < z and y - x > 9 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 13 , e ) 10
Rationale: we have : 1 ) x < y < z 2 ) y - x > 9 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 9 , the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 13 ( y - 2 = 11 , y = 13 ) 2 < 13 < z , since z is odd , the least possible value for z is 15 z - x = 15 - 2 = 13 answer d
Answer: d
Question (gain): in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are marketing majors ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 11 , e ) 17
Rationale: "pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are marketing majors is r = 7 . the answer is c ."
Answer: c
Question (general): if x = 8 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.007 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.007 answer : b"
Answer: b
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 5 seconds . find the length of the train .
Options: a ) 83.33 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 5 = 83.33 meter . answer : a"
Answer: a
Question (gain): on a purchase of $ 118 , a store offered a payment plan consisting of a $ 18 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ?
Options: a ) 16.7 % , b ) 16.2 % , c ) 16.5 % , d ) 15.5 % , e ) 15.3 %
Rationale: "12 * 10 + 18 = 138 ( 18 / 118 ) * 100 = 15.3 answer : e"
Answer: e
Question (physics): if 70 honey bees make 70 grams of honey in 70 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 70
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 70 : : 70 : x honey 70 : 1 = > 1 x 70 x x = 70 x 1 x 70 = > x = 70 . answer : e"
Answer: e
Question (general): 3 times the first of 3 consecutive odd integers is 3 more than twice the third . the third integer is ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 26
Rationale: let the three integers be x , x + 2 and x + 4 . then , 3 x = 2 ( x + 4 ) + 3 x = 11 . third integer = x + 4 = 15 . option a
Answer: a
Question (physics): two trains , each 100 m long , moving in opposite directions , cross other in 10 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 76 km / hr , b ) 66 km / hr , c ) 48 km / hr , d ) 67 km / hr , e ) 22 km / hr
Rationale: let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 10 = 3 x = > x = 20 / 3 . so , speed of the faster train = 40 / 3 = 40 / 3 * 18 / 5 = 48 km / hr . answer : c
Answer: c
Question (general): if a certain number is divided by 9 , the quotient , dividend , and divisor , added together , will amount to 69 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 54
Rationale: let x = the number sought . then x / 9 + x + 9 = 69 . and x = 54 . e
Answer: e
Question (general): a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did b get in a profit of rs . 2400 ?
Options: a ) s . 532 , b ) s . 600 , c ) s . 822 , d ) s . 812 , e ) s . 810
Rationale: "let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 b ' s share in the profit of rs . 2400 = 15 ( 2400 / 60 ) = rs . 600 . answer : b"
Answer: b
Question (gain): if 10 litres of an oil of rs . 50 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 51.03 , c ) rs . 54.17 , d ) rs . 55.33 , e ) none of the above
Rationale: "50 * 10 = 500 66 * 5 = 330 830 / 15 = 55.33 answer : d"
Answer: d
Question (general): if the price of a book is first decreased by 25 % and then increased by 20 % , then the decrease in the price will be ?
Options: a ) 20 % , b ) 10 % , c ) 25 % , d ) 18 % , e ) 30 %
Rationale: "let the original price be $ 100 new final price = 120 % of ( 75 % of $ 100 ) = 120 / 100 * 75 / 100 * 100 = $ 90 decrease is 10 % answer is b"
Answer: b
Question (general): the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg
Rationale: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 35 + 20 ) kg = 55 kg the answer is e ."
Answer: e
Question (physics): from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 2 hours at 8 kilometers per hour , while ferry q takes a route that is three times longer . if ferry p is slower than ferry q by 4 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: the distance traveled by ferry p is 16 km . then the distance traveled by ferry q is 48 km . ferry q travels at a speed of 12 kph . the time of the journey for ferry q is 48 / 12 = 4 hours , which is 2 hours more than ferry p . the answer is b .
Answer: b
Question (physics): a car takes 6 hours to cover a distance of 324 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 65 kmph , d ) 36 kmph , e ) none
Rationale: "time = 6 distence = 324 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 324 / 9 = 36 kmph d )"
Answer: d
Question (general): in a renowned city , the average birth rate is 4 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 86,400 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 2 persons are added ( 4 - 2 ) . every second 1 person are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option a"
Answer: a
Question (physics): steve traveled the first 5 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 53.33 mph , b ) 88 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: average speed = total distance / total time = ( 40 * 5 + 80 * 3 ) / ( 5 + 3 ) = 440 / 5 = 88 answer : b
Answer: b
Question (geometry): if circles x and y have the same area and circle x has a circumference of 20 π , half of the radius of circle y is :
Options: a ) 16 , b ) 5 , c ) 4 , d ) 2 , e ) 1
Rationale: "x b é radius of circle x ý b é radius of circle y given : pi * x ^ 2 = pi * ý ^ 2 also , 2 * pi * x = 20 * pi x = 10 thus ý = 10 y / 2 = 5 ans : b"
Answer: b
Question (general): what is theleast number should be added to 1056 , so the sum of the number is completely divisible by 23 ?
Options: a ) 20 , b ) 23 , c ) 25 , d ) 27 , e ) 28
Rationale: ( 1056 / 23 ) gives remainder 21 21 + 2 = 23 , so we need to add 2 b
Answer: b
Question (gain): ravi and sunil are partners in a business . ravi invests rs . 20,000 for 8 months and sunil invested rs . 16000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4
Rationale: "= ( 15000 * 8 ) : ( 8000 * 10 ) = 160000 : 160000 = 1 : 1 answer : a"
Answer: a
Question (physics): tanks c and b are each in the shape of a right circular cylinder . the interior of tank c has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank c is what percent of the capacity of tank b ?
Options: a ) 75 %
b ) 80 %
c ) 100 %
d ) 120 %
e ) 125 %
Rationale: b . for c , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi c / b = 160 pi / 200 pi = 0.8
Answer: b
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , the how old is b ?
Options: a ) 7 , b ) 9 , c ) 8 , d ) 11 , e ) 10
Rationale: "explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 ⇒ 5 x = 20 ⇒ x = 4 . hence , b ' s age = 2 x = 8 years . answer : c"
Answer: c
Question (gain): in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 78 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 53 , d ) 91 , e ) 108
Rationale: "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 78 % of 250 = 195 are boys who play soccer . girls who play soccer = 55 . total girls who do not play soccer = 108 - 55 = 53 . correct option : c"
Answer: c
Question (general): the price of 3 pants and 6 t - shirts is rs . 1500 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?
Options: a ) 700 , b ) 300 , c ) 250 , d ) 550 , e ) 800
Rationale: let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 1500 . . . . ( i ) and x + 12 y = 1500 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 500 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 1500 ( - ) x + 2 y = 500 - - - - - - - - - - - - - - - - 10 y = 1000 - - - - - - - - - - - - - - - - cost of 8 t - shirts = 8 * 100 = 800 answer : e
Answer: e
Question (general): rs . 770 were divided among a , b , c in such a way that a had rs . 40 more than b and c had rs 30 more than a . how much was b â € ™ s share ?
Options: a ) rs . 260 , b ) rs . 270 , c ) rs . 280 , d ) rs . 290 , e ) rs . 300
Rationale: let b gets rs x . then we can say a gets rs ( x + 40 ) and c gets rs ( x + 70 ) . x + 40 + x + x + 70 = 770 3 x = 660 x = 220 . b â € ™ s share = rs ( 220 + 70 ) = rs . 290 d
Answer: d
Question (physics): what is the greatest of 3 consecutive integers whose sum is 39 ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "39 / 3 = 13 the three numbers are 12 , 13 , and 14 . the answer is a ."
Answer: a
Question (physics): john and jacob set out together on bicycle traveling at 15 and 9 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 15 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 3 , b ) 3 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 1 1 / 4
Rationale: john ' s speed - 15 miles / hr jacob ' s speed - 9 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 15 x 2 / 3 = 10 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 9 x 5 / 3 = 15 miles . now , when john starts riding back , the distance between them is 7.5 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 15 - 9 = 6 miles / hr . thus , to cover 7.5 miles at 6 miles / hr , john will take 7.5 / 6 = 1.25 hours answer e
Answer: e
Question (general): 23 × 19 × ? ÷ 19 ÷ 17 = 115
Options: a ) 65 , b ) 75 , c ) 85 , d ) 95 , e ) 45
Rationale: "explanation : 23 × 19 × ? ÷ 19 ÷ 17 = 115 = > ( 23 × 19 × ? ) / ( 19 × 17 ) = 115 = > ? = ( 115 × 19 × 17 ) / ( 23 × 19 ) = 85 answer : option c"
Answer: c
Question (general): a city with a population of 97500 is to be divided into 6 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 15,000 , b ) 15,500 , c ) 16,000 , d ) 16,500 , e ) 17,000
Rationale: the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 97,500 = p + 5 ( 1.1 ) p 6.5 p = 97,5000 p = 15,000 the answer is a .
Answer: a
Question (physics): pipe a can fill a tank in 10 hr , pipe b in 20 hr and pipe c in 40 hr . if all the pipes are open in how many hours will tank be filled ?
Options: a ) 1 hr , b ) 30 min , c ) 15 min , d ) 17 min , e ) 10 min
Rationale: part filled by ( a + b + c ) in 1 hour = 1 / 10 + 1 / 20 + 1 / 40 = 7 / 40 all the 3 pipes together will fill the tank in 17 min approximately answer is d
Answer: d
Question (other): a 40 kg metal bar made of alloy of tin and silver lost 4 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 4 kg when 40 kg alloy is immersed . this is a loss of ( 4 / 40 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e
Answer: e
Question (other): in a sports club with 28 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "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 + 2 = 28 38 - 2 x + x = 28 38 - x = 28 x = 10 so 8 members play both badminton and tennis . d"
Answer: d
Question (general): village x has a population of 74000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 16 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 74000 - 1200 p = 42000 + 800 p 2000 p = 32000 p = 16 answer is b ."
Answer: b
Question (physics): the radius of a semi circle is 6.5 cm then its perimeter is ?
Options: a ) 32.7 , b ) 32.4 , c ) 33.4 , d ) 32.8 , e ) 32.1
Rationale: "36 / 7 r = 6.5 = 33.4 answer : c"
Answer: c
Question (general): a number x is 3 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 66.6 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 3 . then y = 1 is less than x = 3 by ( 3 - 1 ) / 3 * 100 = 2 / 3 * 100 = 66.6 % . answer : b ."
Answer: b
Question (physics): two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 36 kmph . in how much time will the trains cross each other ?
Options: a ) 12 sec , b ) 13 sec , c ) 15 sec , d ) 16 sec , e ) 17 sec
Rationale: "d relative speed = ( 54 + 36 ) * 5 / 18 = 5 * 5 = 25 mps . the time required = d / s = ( 100 + 100 + 200 ) / 25 = 400 / 25 = 16 sec ."
Answer: d
Question (physics): if a car had traveled 20 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 60 km , at what speed did it travel ?
Options: a ) 35 kmh , b ) 40 kmh , c ) 50 kmh , d ) 60 kmh , e ) 65 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 60 / x - 60 / ( x + 20 ) = 1 / 2 substitute the value of x from the options . - - > x = 40 - - > 60 / 40 - 60 / 60 = 3 / 2 - 1 = 1 / 2 answer : b"
Answer: b
Question (general): a student has to obtain 33 % of the total marks to pass . he got 59 marks and failed by 40 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 500 , d ) 610 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 59 + 40 33 x / 100 = 99 x = 300 answer is b"
Answer: b
Question (geometry): the ratio of the volumes of two cubes is 1728 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 144 : 121 , b ) 141 : 127 , c ) 144 : 191 , d ) 181 : 161 , e ) 81 : 182
Rationale: "explanation : ratio of the sides = ³ √ 1728 : ³ √ 1331 = 12 : 11 ratio of surface areas = 12 ^ 2 : 11 ^ 2 = 144 : 121 answer : option a"
Answer: a