Cheukting/mathqa huggingface dataset:
Question (gain): lucy bought a 1 - year , 10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually . what was the total amount of interest paid on this certificate at maturity ?
Options: a ) 10464 , b ) 864 , c ) 816 , d ) 800 , e ) 480
Rationale: solution : it says , 8 percent per annum per compounded semi annually . therefore r = 8 / 2 = 4 % . so , p = 10000 r = 4 n = 2 net amount a = 10816 , i = 800 . answer : d
Answer: d
Question (general): if x ^ 2 + ( 1 / x ^ 2 ) = 6 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 34 , e ) 15
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 6 ^ 2 - 2 = 34 . thus , the answer is d ."
Answer: d
Question (gain): a bag marked at $ 125 is sold for $ 120 . the rate of discount is ?
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 4 %
Rationale: rate of discount = 5 / 125 * 100 = 4 % answer is e
Answer: e
Question (geometry): the radius of a cylindrical vessel is 8 cm and height is 3 cm . find the whole surface of the cylinder ?
Options: a ) 308 sq cm , b ) 220 sq cm , c ) 440 sq cm , d ) 553.1 sq cm , e ) 138 sq cm
Rationale: "r = 8 h = 3 2 π r ( h + r ) = 2 * 22 / 7 * 8 ( 11 ) = 553.1 answer : d"
Answer: d
Question (other): the marks obtained by vijay and amith are in the ratio 6 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 1 : 5 , b ) 4 : 5 , c ) 9 : 5 , d ) 9 : 8 , e ) 9 : 7
Rationale: "6 : 5 3 : 2 - - - - - - - 18 : 15 : 10 18 : 10 9 : 5 answer : c"
Answer: c
Question (general): for what value of x , is | x – 3 | + | x + 1 | + | x | = 10 ?
Options: a ) 0 , b ) 3 , c ) - 3 , d ) 4 , e ) - 2
Rationale: "there are 3 transition points : - 1 , 0 , 3 when x > 3 , | x − 3 | + | x + 1 | + | x | = 10 | x − 3 + x + 1 + x = 10 x = 4 satisfies when 0 < x < 3 | x − 3 | + | x + 1 | + | x | = 10 − ( x − 3 ) + ( x + 1 ) + x = 10 x = 6 ( not possible since 0 < x < 3 ) when - 1 < x < 0 | x − 3 | + | x + 1 | + | x | = 10 − ( x − 3 ) + − ( x + 1 ) + x = 10 x = - 8 ( not possible since - 1 < x < 0 ) when x < - 1 | x − 3 | + | x + 1 | + | x | = 10 - ( x - 3 ) - ( x + 1 ) - x = 10 x = - 8 / 3 satisfies answer : d"
Answer: d
Question (general): when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 3 ) ^ 2 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 5 x + 3 , for some integer x ( n + 3 ) ^ 2 = ( 5 x + 6 ) ^ 2 = 5 y + 36 , for some integer y when we divide this by 5 , the remainder is 1 . the answer is b ."
Answer: b
Question (other): right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 66 years . what is molly ' s age right now ?
Options: a ) 15 years , b ) 35 years , c ) 25 years , d ) 45 years , e ) 55 years
Rationale: "now , sandy is 66 - 6 = 60 molly ' s age is ( 3 / 4 ) * 60 = 45 the answer is d ."
Answer: d
Question (physics): a and b can do a work in 5 days and 10 days respectively . a starts the work and b joins him after 4 days . in how many days can they complete the remaining work ?
Options: a ) 6 days , b ) 2 / 3 days , c ) 8 days , d ) 3 days , e ) 9 days
Rationale: "work done by a in 4 days = 4 / 5 remaining work = 1 / 5 work done by both a and b in one day = 1 / 5 + 1 / 10 = 3 / 10 remaining work = 1 / 5 * 10 / 3 = 2 / 3 days . answer : b"
Answer: b
Question (general): ( 935421 x 625 ) = ?
Options: a ) 542622125 , b ) 584632125 , c ) 544638125 , d ) 584638125 , e ) none of these
Rationale: "explanation : 935421 × 625 = 935421 × 54 = 935421 × ( 10 / 2 ) 4 = ( 935421 × 10000 ) / 16 = 584638125 . answer : option d"
Answer: d
Question (general): a certain fraction is equivalent to 3 / 5 . if the numerator of the fraction is increased by 4 and the denominator is doubled , the new fraction is equivalent to 1 / 3 . what is the sum of the numerator and denominator of the original fraction ?
Options: a ) 49 , b ) 35 , c ) 28 , d ) 56 , e ) 21
Rationale: "x / y = 3 / 5 - > 1 ( x + 4 ) / 2 y = 1 / 3 - > 2 divide 1 by 2 : = > 2 x / ( x + 4 ) = 9 / 5 = > 10 x = 9 x + 36 = > x = 36 = > y = 5 / 3 * 12 = 20 so x + y = 56 the answer is d ."
Answer: d
Question (gain): a survey was sent to 65 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 4 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "case 1 : ( 7 / 65 ) = x / 100 x = 10 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 10 ) % = 4 % answer is b"
Answer: b
Question (gain): bert and rebecca were looking at the price of a condominium . the price of the condominium was 100 % more than bert had in savings , and separately , the same price was also 60 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
Options: a ) 1 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 5 , e ) 1 : 1
Rationale: "suppose bert had 100 so price becomes 200 , this 200 = 1.6 times r ' s saving . . so r ' s saving becomes 125 so required ratio is 100 : 125 = 4 : 5 answer : d"
Answer: d
Question (physics): a man swims downstream 30 km and upstream 20 km taking 5 hours each time , what is the speed of the man in still water ?
Options: a ) 7 , b ) 8 , c ) 2 , d ) 5 , e ) 4
Rationale: "30 - - - 5 ds = 6 ? - - - - 1 20 - - - - 5 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : d"
Answer: d
Question (gain): andrew purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 1055 , c ) 1060 , d ) 1075 , e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 b"
Answer: b
Question (general): how many integers v are prime numbers in the range 200 < v < 220 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: my friend , every single odd number greater than can be written either as 4 v + 1 or as 4 v + 3 . if you divide any odd number by 4 , you will get a remainder of either 1 or 3 . that ' s not a rule unique to prime numbers at all . the 6 v + 1 or 6 v - 1 rule is basically every odd number that is not divisible by three , so it narrows the search a little . here ' s how i thought about the problem . first , eliminate all the even numbers and the odd multiples of 5 in that range . that leaves us with : { 201 , 203 , 207 , 209 , 211 , 213 , 217 , 219 } eliminate the four multiples of 3 . notice that 21 is a multiple of 3 , so 210 is also a multiple of 3 . if we add or subtract 3 or 9 , we get more multiples of three . when we eliminate those , we are left with . { 203 , 209 , 211 , 217 } now , notice that a cool thing about this range is that 210 is also a multiple 7 ( again , because 21 is a multiple of 7 ) . this means that 210 - 7 = 203 210 + 7 = 217 those two numbers are also multiples of 7 , so eliminate them from the list . now , we are left with { 209 , 211 } . we ' ve already checked all the prime numbers less than 10 , so we know that neither of these numbers is divisible by anything less than 10 . we have to check 11 now . we know that 22 is a multiple of 11 , so 220 is also a multiple of 11 . this means that 220 - 11 = 209 is also a multiple of 11 . we can eliminate this from the list also . that leaves us with just 211 . there ' s no zero option in the question , so this must be a prime number . answer = ( a )
Answer: a
Question (general): if the average of 20 digits is 500 and the average of 14 of them is 390 , calculate the average of the remaining 6 numbers ?
Options: a ) 756.7 , b ) 751.7 , c ) 753.7 , d ) 752.7 , e ) 722.7
Rationale: "explanation : total of the 20 digits - 20 * 500 = 10000 total of the 14 digits - 14 * 390 = 5460 total of the remaining 6 digits - 10000 - 5460 = 4540 average of the remaining 6 numbers = 4540 / 6 = 756.7 answer : a"
Answer: a
Question (physics): two bullet train s 140 m and 180 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 11.52 sec . , c ) 11.8 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 180 ) m = 320 m . required time = 320 x 9 / 250 = 11.52 sec . answer b"
Answer: b
Question (gain): a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 25 per kg , then his gain percent is
Options: a ) 12 % , b ) 33 % , c ) 14 % , d ) 15 % , e ) 16 %
Rationale: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 25 ) = rs . 200 . profit = 200 - 150 = 50 so , profit % = ( 50 / 150 ) * 100 = 33 % option b"
Answer: b
Question (geometry): the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 768 sq meters , then what is the width ( in meters ) of the rectangular plot ?
Options: a ) 24 m , b ) 16 m , c ) 35 m , d ) 54 m , e ) 43 m
Rationale: "area = l * w = 3 w ^ 2 = 768 w ^ 2 = 256 w = 16 the answer is b ."
Answer: b
Question (general): a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 500 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "given that p is smallest integer greater than 200 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 b"
Answer: b
Question (general): if p / q = 4 / 5 , then the value of 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 4 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer given exp . = 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 25 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 25 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 25 / 7 + 6 / 14 = 25 / 7 + 3 / 7 = 28 / 7 = 4 correct option : a"
Answer: a
Question (gain): a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price r of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price r = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"
Answer: c
Question (general): bottle r contains 350 capsules and costs $ 6.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.25 , b ) $ 0.12 , c ) $ 0.0052 , d ) $ 0.003 , e ) $ 0.002
Rationale: "cost per capsule in r is 6.25 / 350 = 0.0178 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.0052 the answer is c"
Answer: c
Question (general): the milk level in a rectangular box measuring 58 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 5437.5 , e ) 5635.5
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 58 * 25 * 1 / 2 = 725 feet ^ 3 of milk must be removed , which equals to 725 * 7.5 = 5437.5 gallons . answer : d ."
Answer: d
Question (general): on a certain date , pat invested $ 7,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 28,000 , in how many years total will the total value of the investment plus interest increase to $ 56,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "28,000 = 7,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 56,000 = 7,000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Question (general): on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 160,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 80 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years total 24 years . answer e"
Answer: e
Question (geometry): a rectangular block 15 cm by 30 cm by 75 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 6
b ) 40
c ) 15
d ) 10
e ) 22
Rationale: volume of the block = 15 * 30 * 75 = 33750 cm ^ 3 side of the largest cube = h . c . f of 15 , 30,75 = 15 cm volume of the cube = 15 * 15 * 15 = 3375 cm ^ 3 number of cubes = 33750 / 3375 = 10 answer is d
Answer: d
Question (general): after replacing an old member by a new member , it was found that the average age of 5 members of a club is the same as it was 3 years ago . what is the difference between the ages of the replaced and the new member ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: explanation : i ) let the ages of the five members at present be a , b , c , d & e years . and the age of the new member be f years . ii ) so the new average of five members ' age = ( a + b + c + d + f ) / 5 - - - - - - - ( 1 ) iii ) their corresponding ages 3 years ago = ( a - 3 ) , ( b - 3 ) , ( c - 3 ) , ( d - 3 ) & ( e - 3 ) years so their average age 3 years ago = ( a + b + c + d + e - 15 ) / 5 = x - - - - - ( 2 ) = = > a + b + c + d + e = 5 x + 15 = = > a + b + c + d = 5 x + 15 - e - - - - - - ( 3 ) iv ) substituting this value of a + b + c + d = 5 x + 15 - e in ( 1 ) above , the new average is : ( 5 x + 15 - e + f ) / 5 equating this to the average age of x years , 3 yrs , ago as in ( 2 ) above , ( 5 x + 15 - e + f ) / 5 = x = = > ( 5 x + 15 - e + f ) = 5 x solving e - f = 15 years . thus the difference of ages between replaced and new member = 15 years . answer : d
Answer: d
Question (general): zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 26.1 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 26.1 kg zinc , mixture , melted = [ 20 / 9 x 26.1 ] kg = 58 kg . answer a"
Answer: a
Question (other): the ratio of boys to girls is 6 : 4.60 % of the boys and 40 % of girls take lunch in the canteen . what % of class takes lunch ?
Options: a ) 51 % , b ) 52 % , c ) 53 % , d ) 54 % , e ) 55 %
Rationale: let total no of students 100 , boy 60 and girl 40 , so lunch taken by boy and girl respectively 60 * 60 / 100 = 36 and 40 * 40 / 100 = 16 so total 52 students takes lunch out of 100 students . . so required % is 52 % answer : b
Answer: b
Question (general): a person x started at 3 hours earlier at 40 km / h from a place p , then another person y followed him at 60 km / h . started his journey at 3 o ' clock , afternoon . what is the diference in time when x was 30 km ahead of y and when y was 30 km ahead of x ?
Options: a ) 8 h , b ) 3 h , c ) 6 h , d ) 3 h , e ) 1 h
Rationale: explanation : time ( when x was 30 km ahead of y ) = ( 120 - 30 ) / 20 = 4.5 h time ( when y was 30 km ahead of x ) = ( 120 + 30 ) / 20 = 7.5 h thus , required difference in time = 3 h answer : b
Answer: b
Question (physics): a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with squre tiles . find the least number of squre tiles required to cover the floor ?
Options: a ) 178 , b ) 128 , c ) 127 , d ) 176 , e ) 171
Rationale: "area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d"
Answer: d
Question (physics): if i walk at 6 km / h , i miss the bus by 12 minutes . if i walk at 5 km / h , i reach 14 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
Options: a ) 13 km , b ) 12 km , c ) 11 km , d ) 6.5 km , e ) 5.5 km
Rationale: "d = product of speed difference of time / difference of speed [ here , â € “ ve sign indicates before the schedule time ] d = 6 ã — 5 / 60 [ 12 â ˆ ’ ( â ˆ ’ 14 ) / 6 - 5 ] â ‡ ’ d = 13 km answer a"
Answer: a
Question (gain): if 35 % of a number is 24 less than 50 % of that number , then the number is ?
Options: a ) 180 , b ) 450 , c ) 160 , d ) 170 , e ) 185
Rationale: explanation : let the number be n . then , 50 % of n - 35 % of n = 24 50 / 100 n - 35 / 100 n = 24 n = ( 24 x 100 ) / 15 = 160 . answer c
Answer: c
Question (gain): tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4500 . they earned a profit of rs . 5400 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 3000 , b ) 2200 , c ) 2309 , d ) 2400 , e ) 3200
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 5400 = 3000 a"
Answer: a
Question (gain): if the selling price of 60 articles is equal to the cost price of 30 articles , then the loss or gain percent is :
Options: a ) 55 % , b ) 35 % , c ) 66 % , d ) 45 % , e ) 50 %
Rationale: "let c . p . of each article be re . 1 . then , c . p . of 60 articles = rs . 60 ; s . p . of 60 articles = rs . 30 . loss % = 30 / 60 * 100 = 50 % answer : e"
Answer: e
Question (general): there are 5 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 150 , d ) 180 , e ) 200
Rationale: number of ways of selecting 2 fiction books = 5 c 2 number of ways of selecting 2 non fiction books = 6 c 2 5 c 2 * 6 c 2 = 10 * 15 = 150 answer : c
Answer: c
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 = 1,155 , and if 1 < p < q < r < s , how many students in the class are accounting majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17
Rationale: "prime factorization of the product pqrs = 1155 = 3 * 5 * 7 * 11 since 1 < p < q < r < s number of students who are accounting majors , p = 3 answer a"
Answer: a
Question (geometry): the area of a triangle is with base 4 m and height 6 m ?
Options: a ) 11 m 2 , b ) 10 m 2 , c ) 18 m 2 , d ) 19 m 2 , e ) 12 m 2
Rationale: "1 / 2 * 4 * 6 = 12 m 2 answer : e"
Answer: e
Question (physics): if 40 sheep eat 40 bags of grass in 40 days . in how many days one sheep will eat one bag of grass ?
Options: a ) 1 , b ) 20 , c ) 40 , d ) 80 , e ) 70
Rationale: explanation : let the required number of days be x . less sheep , more days ( indirect proportion ) less bags , less days ( direct proportion ) sheep 1 : 40 : : 40 : x bags 40 : 1 1 x 40 x x = 40 x 1 x 40 x = 40 . answer : c
Answer: c
Question (gain): increasing the original price of an article by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by
Options: a ) 40 % , b ) 41 % , c ) 42 % , d ) 43 % , e ) 44 %
Rationale: "1.2 * 1.2 * x = 1.44 * x the answer is e ."
Answer: e
Question (general): the age of somu is one - third his father ' s . 6 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 10
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 6 = 3 x - 6 / 5 = x = 12 answer : option d"
Answer: d
Question (geometry): john builds a square with a side of 12 cm from some wire . if from the same wire , he builds a rectangle with a width of 6 cm , what will be the length of the rectangle ?
Options: a ) 18 cm
b ) 19 cm
c ) 20 cm
d ) 21 cm
e ) none
Rationale: solution : if the side of the square is 12 cm , then its perimetre will be 48 cm . we build the rectangle from the same wire , so it will have the same perimetre . its width is 6 cm , so its length will be ( 48 - 12 ) ÷ 2 = 36 ÷ 2 = 18 cm answer a
Answer: a
Question (physics): a train 560 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 28 , e ) 32
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 560 * 2 / 35 = 32 sec answer : option e"
Answer: e
Question (gain): the banker â € ™ s gain on a sum due 3 years hence at 12 % per annum is rs . 180 . the banker â € ™ s discount is
Options: a ) rs . 960 , b ) rs . 840 , c ) rs . 1020 , d ) rs . 680 , e ) none
Rationale: solution t . d = ( b . g x 100 / r x t ) = rs . ( 180 x 100 / 12 x 3 ) = rs . 500 . b . d = rs ( 500 + 180 ) = rs . 680 . answer d
Answer: d
Question (general): 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 10 .
Options: a ) 150 , b ) 152 , c ) 154 , d ) 163 , e ) 144
Rationale: "d = d * q + r d = 17 * 9 + 10 d = 153 + 10 d = 163 answer d"
Answer: d
Question (geometry): a lady builds 8 cm length , 15 cm width , and 5 cm height box using 10 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 60 , c ) 70 , d ) 89 , e ) 78
Rationale: "number of cubes required = volume of box / volume of cube = 8 * 15 * 5 / 10 = 60 cubes answer : b"
Answer: b
Question (gain): a furniture dealer purchased a desk for $ 100 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "anyway , in this question , there is no discount but the mark up is given as 40 % of the selling price . so it is not 40 % of $ 100 but instead , 40 % of selling price which is obtained by adding mark up to $ 100 . so if selling price is s , 100 + 40 % of s = s or 100 = 0.6 s therefore s = 100 / 0.6 = s = profit = 100 / 0.6 - 100 which is calculated on cost price in % terms . so 40 / 100 * 100 = 40 % is profit . a"
Answer: a