Cheukting/mathqa huggingface dataset:
Question (general): cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 6 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 1 , e ) 1 : 3
Rationale: "( 10 / 100 ) a + ( 2 / 100 ) b = ( 6 / 100 ) ( a + b ) 4 a = 4 b = > a / b = 1 / 1 answer is d ."
Answer: d
Question (general): zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 7 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 7 questions did zachary answer correctly ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "i got two equations : 3 x - 2 y = 25 x + y = 7 3 x - 2 ( 7 - x ) = 25 3 x - 14 + 2 x = 25 5 x = 39 x = 7.8 or between 7 and 8 . ( ans b )"
Answer: b
Question (general): find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case .
Options: a ) 366 , b ) 236 , c ) 367 , d ) 365 , e ) 386
Rationale: "explanation : the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 35 , 11 ) + 1 = 386 . answer : e"
Answer: e
Question (physics): the speed of a car is 90 km in the first hour and 75 km in the second hour . what is the average speed of the car ?
Options: a ) 89 kmph , b ) 82.5 kmph , c ) 75 kmph , d ) 65 kmph , e ) 77 kmph
Rationale: "s = ( 90 + 75 ) / 2 = 82.5 kmph b"
Answer: b
Question (geometry): a larger cube has 64 cubic inch as a volume and in the cube there are 64 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 64 smaller cubes and the surface area of the larger cube , in square inch ?
Options: a ) 54 , b ) 64 , c ) 81 , d ) 288 , e ) 120
Rationale: "volume of larger cube = 64 = 4 ^ 3 side of larger cube = 4 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 4 ^ 2 = 96 surface area of 27 smaller cubes = 64 * 6 * 1 = 384 difference = 384 - 96 = 288 answer : d"
Answer: d
Question (physics): a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 8 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 34 hr , e ) 36 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 8 ) = 1 / 34 leak will empty the tank in 34 hrs . answer : d"
Answer: d
Question (physics): two buses each 3125 m long are running in opposite directions on parallel roads . their speeds are 40 km / hr and 35 km / hr respectively . find the time taken by the slower bus to pass the driver of the faster one ?
Options: a ) 50 sec , b ) 66 sec , c ) 48 sec , d ) 55 sec , e ) 45 sec
Rationale: relative speed = 40 + 35 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 3125 + 3125 = 6250 m . required time = 6250 * 6 / 125 = 50 sec . answer : a
Answer: a
Question (physics): if the perimeter of a rectangular garden is 500 m , its length when its breadth is 100 m is ?
Options: a ) 299 m , b ) 777 m , c ) 200 m , d ) 167 m , e ) 150 m
Rationale: "2 ( l + 100 ) = 500 = > l = 150 m answer : e"
Answer: e
Question (physics): a man goes from a to b at a speed of 15 kmph and comes back to a at a speed of 12 kmph . find his average speed for the entire journey ?
Options: a ) 13.7 kmph , b ) 13.3 kmph , c ) 13.8 kmph , d ) 13.9 kmph , e ) 12.3 kmph
Rationale: distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 15 ) + ( d / 12 ] = ( 2 d ) / [ 9 d / 60 ) = > 13.3 kmph . answer : b
Answer: b
Question (geometry): a cube is divided into 729 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that the cube is coloured with green colour on one set of adjacent faces , red on the other set of adjacent faces , blue on the third set . so , how many cubelets are there which are painted with exactly one colour ?
Options: a ) 293 , b ) 294 , c ) 295 , d ) 296 , e ) 298
Rationale: "total cubes created are 729 so a plane of big cube has 9 * 9 cubes out of that ( n - 2 ) * ( n - 2 ) = 7 * 7 = 49 are painted only one side and a cube has six sides = 6 * 49 = 294 answer : b"
Answer: b
Question (general): in a mixed college 160 students are there in one class . out of this 160 students 3 / 4 students are girls . how many boys are there ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 120 , e ) 140
Rationale: "total number of students : 160 total girls : 160 * 3 / 4 = 120 total boys : 160 - 120 = 40 answer is a"
Answer: a
Question (geometry): the perimeter of a triangle is 60 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
Options: a ) a ) 72 , b ) b ) 828 , c ) c ) 729 , d ) d ) 75 , e ) e ) 35
Rationale: "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 60 / 2 = 35 cm 2 answer : option d"
Answer: d
Question (general): the product z of two prime numbers is between 10 and 30 . if one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24 , then what is z ?
Options: a ) 21 , b ) 15 , c ) 14 , d ) 10 , e ) 6
Rationale: "the smallest possible product is 21 which is 3 * 7 . all other products are too big . the answer is a ."
Answer: a
Question (general): how many integers from 0 to 44 , inclusive , have a remainder of 1 when divided by 3 ?
Options: a ) 13 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 43 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 43 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 42 or , n - 1 = 12 or , n = 13 a"
Answer: a
Question (general): he total marks obtained by a student in physics , chemistry and mathematics is 150 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : c"
Answer: c
Question (physics): a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 7 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 24 hr , e ) 30 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 7 ) = 1 / 30 leak will empty the tank in 30 hrs . answer : e"
Answer: e
Question (general): a ranch has both horses and ponies . exactly 5 / 7 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 3 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 33 , b ) 37 , c ) 41 , d ) 45 , e ) 49
Rationale: "5 / 7 * p are ponies with horseshoes , so p is a multiple of 7 . 2 / 3 * 5 / 7 * p = 10 / 21 * p are icelandic ponies with horseshoes , so p is a multiple of 21 . the minimum value of p is 21 . then h = p + 3 = 24 . the minimum number of horses and ponies is 45 . the answer is d ."
Answer: d
Question (probability): there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl or 2 boys are selected ?
Options: a ) 88 , b ) 90 , c ) 92 , d ) 96 , e ) 98
Rationale: "n ( s ) = sample space = 23 c 3 = 1771 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 13 or 1 girl from 10 = 13 c 2 + 10 c 1 = 88 ans - a"
Answer: a
Question (gain): a student gets 70 % in one subject , 80 % in the other . to get an overall of 75 % how much should get in third subject .
Options: a ) 75 % , b ) 25 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "a student gets 70 % in one subject , 80 % in the other . average of 2 subjects is 75 % , if they have equal weightage . to get an overall of 75 % , he should get 75 % in third subject to maintain same % age . . if they have equal weightage . answer : a"
Answer: a
Question (general): carina has 85 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 85 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 75 / 15 . = 5 a"
Answer: a
Question (general): how much water must be added to 56 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 12 litres , c ) 14 litres , d ) 18 litres , e ) none of these
Rationale: "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 56 litres of milk = ( 1 ⁄ 4 × 56 ) litres = 14 litres . answer c"
Answer: c
Question (gain): if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2000 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2500 , c ) 2507 , d ) 3200 , e ) 11500
Rationale: "p - 2000 = ( p * 5 * 4 ) / 100 p = 2500 answer : b"
Answer: b
Question (probability): if two integers x , y ( x > y ) are selected from - 10 to 10 ( inclusive ) , how many possible cases are there ?
Options: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 240
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 21 c 2 = 21 * 20 / 2 = 210 . therefore , the answer is d"
Answer: d
Question (gain): jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: "if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 926 . answer : e ."
Answer: e
Question (general): the sum of the numbers is 110 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 30 , b ) 54 , c ) 72 , d ) 84 , e ) 27
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 110 11 x / 3 = 110 x = 30 answer : a"
Answer: a
Question (general): total dinning bill of 3 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 21.84 , b ) 50.96 , c ) 53.84 , d ) 24.84 , e ) 50.26
Rationale: "dinner bill of 3 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 3 = $ 50.96 answer : b"
Answer: b
Question (geometry): the ratio of the radius of two circles is 5 : 3 , and then the ratio of their areas is ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 25 : 9 , d ) 1 : 3 , e ) 1 : 2
Rationale: "r 1 : r 2 = 5 : 3 π r 12 : π r 22 r 12 : r 22 = 25 : 9 answer : c"
Answer: c
Question (general): the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 512,000 locusts ?
Options: a ) 18 , b ) 15 , c ) 13 , d ) 14 , e ) 12
Rationale: "- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 + 12 hours : 256,000 + 14 hours : 512,000 answer : d"
Answer: d
Question (general): if the price of gasoline increases by 20 % and a driver intends to spend only 14 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 1 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.2 * p ) y = 1.14 ( p * x ) y = ( 1.14 / 1.2 ) x = 0.95 x which is a reduction of 5 % . the answer is d .
Answer: d
Question (geometry): a cube is divided into 343 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 125 , b ) 150 , c ) 175 , d ) 200 , e ) 225
Rationale: "each side of the cube has 7 x 7 = 49 cubelets . only the interior cubelets are painted one colour . on each side , 5 x 5 = 25 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 25 = 150 the answer is b ."
Answer: b
Question (general): the average of 7 consecutive numbers is 20 . the largest of these numbers is :
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "explanation : let the numbers be x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5 and x + 6 , then ( x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) ) / 7 = 20 . or 7 x + 21 = 140 or 7 x = 119 or x = 17 . latest number = x + 6 = 23 . answer : c"
Answer: c
Question (general): a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is 5 , what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 2 , d ) 1 and - 5 , e ) can not be determined .
Rationale: "a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 4 - - > x ^ 2 + 4 x = 5 i . e x ^ 2 + 4 x - 5 = 0 is the quadratic equation which needs to be solved . ( x - 1 ) ( x + 5 ) = 0 hence x = 1 . c = - 5 imo d"
Answer: d
Question (physics): 12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 1 cm height . what is the diameter of each sphere ?
Options: a ) 2 cm , b ) 4 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm
Rationale: "volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 12 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 16 = 1 cm ^ 3 r = 1 cm d = 2 cm the answer is a ."
Answer: a
Question (general): 9 neighbors are to split the cost of topsoil . the cost of the 5 truck loads of dirt was $ 690.47 . what is the least amount of money ( in whole number of dollars ) that they must add to bill if they wants to split this money evenly among his 9 neighbors ?
Options: a ) 690.48 , b ) 690.49 , c ) 690.5 , d ) 690.51 , e ) 690.52
Rationale: if the bill was $ 690.47 dollars , how much money should be removed with 1 cent as the smallest unit ? this is equivalent to finding the first number that is divisible by 9 that occurs after 690.47 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 6 + 9 + 0 + 4 + 7 = 26 . if you add 1 , the number is divisible by 9 ( 26 + 1 ) . 27 is divisible by 9 . hence , we need to add 1 cent from this number for it to be divisible by 9 . correct option : a
Answer: a
Question (general): evaluate : 11 + sqrt ( - 4 + 6 × 4 ÷ 3 )
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "according to order of operations , inner brackets first where 6 × 4 ÷ 3 is first calculated since it has a multiplication and a division . 6 × 4 ÷ 3 = 24 ÷ 3 = 8 hence 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer e ) 13"
Answer: e
Question (physics): 16 people can write 52 book in 12 days working 8 hour a day . then in how many day 206 can be written by 64 people ?
Options: a ) 309 / 26 , b ) 309 / 28 , c ) 309 / 22 , d ) 319 / 26 , e ) 339 / 26
Rationale: "work per day epr hour per person = 52 / ( 12 * 8 * 16 ) / / eq - 1 people = 64 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 206 / ( p * 8 * 64 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 309 / 26 answer : a"
Answer: a
Question (general): total dinning bill for 7 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 33.16
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 7 = 34.66 answer : c"
Answer: c
Question (geometry): what is the area of square field whose side of length 20 m ?
Options: a ) 200 sq m , b ) 186 sq m , c ) 586 sq m , d ) 287 sq m , e ) 400 sq m
Rationale: "20 * 20 = 400 sq m answer : e"
Answer: e
Question (physics): a cyclist bikes x distance at 8 miles per hour and returns over the same path at 812 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 8.1 , b ) 8.3 , c ) 8.6 , d ) 9.6 , e ) 9.0
Rationale: "distance = d 1 = x miles speed = s 1 = 8 miles per hour time = t 1 = distance / speed = x / 8 2 . going from b to a distance = d 2 = x miles speed = s 2 = 12 miles per hour time = t 2 = distance / speed = x / 12 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 12 + x / 8 = x ( 1 / 12 + 1 / 8 ) = = 5 x / 24 speed = 2 x / ( 5 x / 24 ) = 48 / 5 = 9.6 answer : d"
Answer: d
Question (physics): in a survey of 345 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 7 / 12 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 40 / 69
Rationale: "- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 291 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 345 we have to find not part time and not uninsured . in other words not part time and insured = x / 345 = ( 291 - 104 + 13 ) / 345 = 40 / 69 answer is e ."
Answer: e
Question (physics): two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team w . if team a ' s average speed was 5 mph greater than team w ' s , what was team w ' s average mph ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team w ' s speed was s . then team w ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team w . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team w is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."
Answer: d
Question (general): if a ( a - 5 ) = 6 and b ( b - 5 ) = 6 where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 2 , d ) 9 , e ) 5
Rationale: "i . e . if a = - 1 then b = 6 or if a = 6 then b = - 1 but in each case a + b = - 1 + 6 = 5 answer : option e"
Answer: e
Question (general): how many positive integers less than 100 have a remainder of 6 when divided by 13 ?
Options: a ) 2 , b ) 7 , c ) 6 , d ) 9 , e ) 10
Rationale: "we have to include 6 also . as 13 * 0 + 6 = 6 if somebody says to divide 6 by 13 , we will be telling we have 0 quotient and remainder as 6 . answer is c"
Answer: c
Question (general): given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 1 = f ( 3 x – 6 )
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "explanations we have the function f ( x ) = 3 x – 5 , and we want to some sophisticated algebra with it . let ’ s look at the two sides of the prompt equation separately . the left side says : 2 * [ f ( x ) ] – 1 — - this is saying : take f ( x ) , which is equal to its equation , and multiply that by 2 and then subtract 1 . 2 * [ f ( x ) ] – 1 = 2 * ( 3 x – 5 ) – 1 = 6 x – 10 – 1 = 6 x – 11 the right side says f ( 3 x – 6 ) — this means , take the algebraic expression ( 3 x – 6 ) and plug it into the function , as discussed above in the section “ how a mathematician things about a function . ” this algebraic expression , ( 3 x – 6 ) , must take the place of x on both sides of the function equation . f ( 3 x – 6 ) = 3 * [ 3 x – 6 ] – 5 = 9 x – 18 – 5 = 9 x – 23 now , set those two equal and solve for x : 9 x – 23 = 6 x – 11 9 x = 6 x – 11 + 23 9 x = 6 x + 12 9 x – 6 x = 12 3 x = 12 x = 4 answer = b"
Answer: b
Question (general): in n is a positive integer less than 200 , and 18 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( a ) . 18 n / 60 must be an integer . = > 3 n / 10 must be an integer . hence n must be a multiple of 2 * 5 . = > n has 2 different prime integers ."
Answer: a
Question (other): the ratio of numbers is 3 : 4 and their h . c . f is 8 . their l . c . m is :
Options: a ) 12 , b ) 96 , c ) 24 , d ) 48 , e ) 98
Rationale: let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 8 . so , the numbers are 24 and 32 . l . c . m of 24 and 32 = 96 . answer : b
Answer: b
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 59000 ?
Options: a ) 81000 , b ) 81007 , c ) 74671.875 , d ) 81066 , e ) 81022
Rationale: "59000 * 9 / 8 * 9 / 8 = 74671.875 answer : c"
Answer: c