Cheukting/mathqa huggingface dataset:
Question (geometry): two circular signs are to be painted . if the diameter of the larger sign is 7 times that of the smaller sign , how many times more paint is needed to paint the larger sign ? ( we can assume that a given amount of paint covers the same area on both signs . )
Options: a ) 7 , b ) 14 , c ) 42 , d ) 49 , e ) 98
Rationale: let r be the radius of the smaller sign . then the diameter of the smaller sign is 2 r , the diameter of the larger sign is 14 r , and the radius of the larger sign is 7 r . the area a of the smaller sign is a = pir ^ 2 . the area of the larger sign is pi ( 7 r ) ^ 2 = 49 pir ^ 2 = 49 a . since the area is 49 times larger , we need 49 times more paint for the larger sign . the answer is d .
Answer: d
Question (general): when a merchant imported a certain item , he paid a 9 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 76.50 , what was the total value of the item ?
Options: a ) $ 1,250 , b ) $ 1,450 , c ) $ 1,650 , d ) $ 1,850 , e ) $ 2,050
Rationale: "let x be the value in excess of $ 1,000 . 0.09 x = 76.5 x = $ 850 the total value was $ 850 + $ 1,000 = $ 1,850 . the answer is d ."
Answer: d
Question (physics): a man swims downstream 40 km and upstream 30 km taking 5 hours each time , what is the speed of the man in still water ?
Options: a ) 12 , b ) 8 , c ) 36 , d ) 5 , e ) 7
Rationale: "40 - - - 5 ds = 8 ? - - - - 1 30 - - - - 5 us = 6 ? - - - - 1 m = ? m = ( 8 + 6 ) / 2 = 7 answer : e"
Answer: e
Question (physics): a train 125 m long passes a man , running at 8 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 36 , b ) 53 , c ) 88 , d ) 66 , e ) 22
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 8 ) km / hr . x - 8 = 45 = = > x = 53 km / hr . answer : b"
Answer: b
Question (gain): 85 % of a number is added to 24 , the result is the same number . find the number ?
Options: a ) 13 √ 5 , b ) 13 √ 2 , c ) 13 √ 9 , d ) 12 √ 9 , e ) 13 √ 1
Rationale: "4 a = 48 4 a = 20 a = 12 a = 5 a 2 = 144 a 2 = 25 combined area = a 2 = 169 = > a = 13 d = 13 √ 2 answer : b"
Answer: b
Question (other): the ratio of 2 numbers is 1 : 2 and their h . c . f . and l . c . m are 10 and 20 . find the numbers .
Options: a ) 20 , 10 , b ) 10 , 20 , c ) 20 , 30 , d ) 30 , 20 , e ) 10 , 10
Rationale: "let the numbers be x and 2 x their h . c . f . = 10 l . c . m = 20 ie ) 2 x ^ 2 = 200 x ^ 2 = 100 , x = 10 t the numbers are x and 2 x , ie ) 10 , 20 respectively . answer is b"
Answer: b
Question (general): if x is 20 percent greater than 88 , then x =
Options: a ) 68 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108
Rationale: "x is 20 % greater than 88 means x is 1.2 times 88 ( in other words 88 + 20 / 100 * 88 = 1.2 * 88 ) therefore , x = 1.2 * 88 = 105.6 answer : d"
Answer: d
Question (general): set a consists of all the prime numbers between 15 and 36 . what is the range of set a ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 17 , e ) 23
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 31 lowest number = 17 range = highest - lowest = 31 - 17 = 14 option c"
Answer: c
Question (physics): in one hour , a boat goes 21 km along the stream and 9 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 10 , d ) 9 , e ) 15
Rationale: "solution speed in still water = 1 / 2 ( 21 + 9 ) kmph . = 15 kmph . answer e"
Answer: e
Question (general): in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 70 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 644 . , e ) 736 .
Rationale: "answer is e : 736 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 70 % of total is 515 , so 100 % is approx . 736 ."
Answer: e
Question (physics): machines x and y produce bottles at their respective constant rates . machine x produces k bottles in 6 hours and machine y produces k bottles in 12 hours . how many hours does it take machines x and y , working simultaneously , to produce 24 k bottles ?
Options: a ) 48 , b ) 42 , c ) 45 , d ) 98 , e ) 96
Rationale: "x rate = k / 6 y rate = k / 12 k / 6 + k / 12 = 24 k / t solving t = 96 answer e"
Answer: e
Question (general): on the number line , if x is halfway between - 4 and 4 , and if y is halfway between - 2 and 6 , what number is halfway between x and y ?
Options: a ) - 1 , b ) - 1 / 2 , c ) 0 , d ) 1 / 2 , e ) 1
Rationale: "x = 0 and y = 2 . the answer is e ."
Answer: e
Question (general): 5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3294 , how much was it in the beginning ?
Options: a ) 2988 , b ) 2776 , c ) 4079 , d ) 2871 , e ) 881
Rationale: x * ( 95 / 100 ) * ( 85 / 100 ) = 3294 x = 4079 answer : c
Answer: c
Question (physics): tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 6 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 a is what percent of the capacity of tank b ?
Options: a ) 48 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: "for a , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 6 = 96 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 96 pi / 200 pi = 0.48 a"
Answer: a
Question (general): the number of singles that a baseball player hit increased 12 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 2 percent . if the total number of singles and doubles that she hit increased 2 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 1 : 2 , b ) 2 : 5 , c ) 1 : 3 , d ) 2 : 3 , e ) 3 : 5
Rationale: "soln : - 1.12 s + 0.98 d = 1.02 [ s + d ] 0.10 s = 0.04 d s / d = 2 / 5 answer : b"
Answer: b
Question (general): on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 350 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 287 , c ) 197 , d ) 287 , e ) 700
Rationale: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 350 ) = 2 + 2 ( extra ) = > 2 x - 700 = x = > x = 700 . answer : e"
Answer: e
Question (general): every digit of a number written in binary is either 0 or 1 . to translate a number from binary , multiply the nth digit ( reading from right to left ) by 2 ^ ( n - 1 ) what is the largest prime number ( written in binary ) that is a factor of both 10010000 and 100100000 ?
Options: a ) 10 , b ) 11 , c ) 1001 , d ) 1011 , e ) 10001
Rationale: binary divison can provide a quick answer if you are comfortable with it . as option e is the biggest binary number we try with it first : 100010000 / 1001 = 10000 1000100000 / 1001 = 100000 so answer is option is c
Answer: c
Question (physics): a cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 27 , b ) 20 , c ) 40 , d ) 73 , e ) 72
Rationale: "1 / 8 - 1 / x = 1 / 10 x = 40 answer : c"
Answer: c
Question (physics): find the distance covered by a man walking for 24 min at a speed of 10 km / hr ?
Options: a ) 1 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "distance = 10 * 24 / 60 = 4 km answer is c"
Answer: c
Question (geometry): the diagonals of a rhombus are 30 cm and 20 cm . find its area ?
Options: a ) 176 , b ) 190 , c ) 150 , d ) 278 , e ) 300
Rationale: "1 / 2 * 30 * 20 = 300 answer : e"
Answer: e
Question (gain): at what price must an article costing rs . 50 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 69.44 , b ) 62.0 , c ) 62.6 , d ) 62.1 , e ) 62.2
Rationale: "cp = 50 sp = 50 * ( 125 / 100 ) = 62.50 mp * ( 90 / 100 ) = 62.50 mp = 69.44 answer : a"
Answer: a
Question (general): every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` cat ' ' ?
Options: a ) 45 , b ) 54 , c ) 63 , d ) 72 , e ) 81
Rationale: "` ` cat ' ' = ( 3 + 1 + 20 ) * 3 = 72 . the answer is d ."
Answer: d
Question (gain): a man two flats for $ 512456 each . on one he gains 20 % while on the other he loses 20 % . how much does he gain or lose in the whole transaction ?
Options: a ) 10 % , b ) 5 % , c ) 12 % , d ) 6 % , e ) 4 %
Rationale: in such a case there is always a loss loss % = ( 20 / 10 ) ^ 2 = 4 % answer is e
Answer: e
Question (physics): a train travels 225 km in 3.5 hours and 370 km in 5 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 60 kmph , c ) 70 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 225 + 370 = 595 km thus , total speed = 8.5 hrs or , average speed = 595 / 8.5 or , 70 kmph . answer : c"
Answer: c
Question (gain): the cash difference between the selling prices of an article at a profit of 4 % and 8 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 52 , b ) 52 : 54 , c ) 53 : 54 , d ) 54 : 55 , e ) none of these
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 104 % of x ) / ( 108 % of x ) = 104 / 108 = 52 / 54 = 52 : 54 . answer : b"
Answer: b
Question (general): if | 4 x + 6 | = 36 , then find the sum of the values of x ?
Options: a ) - 3 , b ) 4 , c ) 3 , d ) - 5 , e ) 6
Rationale: "| 4 x + 6 | = 36 4 x + 6 = 36 or 4 x + 6 = - 36 4 x = 30 or 4 x = - 42 x = 7.5 or x = - 10.5 sum = 7.5 - 10.5 = - 3 answer is a"
Answer: a
Question (physics): the speed of a boat in still water in 42 km / hr and the rate of current is 8 km / hr . the distance travelled downstream in 44 minutes is :
Options: a ) 86.6 km , b ) 46.6 km , c ) 36.6 km , d ) 35.6 km , e ) 26.6 km
Rationale: "speed downstream = ( 42 + 8 ) = 50 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 50 = 36.6 km answer : c"
Answer: c
Question (gain): an article is sold at a certain price . by selling it at 2 / 3 of that price one loses 10 % . find the gain percent at original price .
Options: a ) 15 % , b ) 35 % , c ) 25 % , d ) 50 % , e ) 30 %
Rationale: "let the original s . p be rs . x . then new s . p = rs . 2 / 3 x , loss = 10 % so c . p = rs . [ 100 / 90 * 2 / 3 x ] = 20 x / 27 . now c . p = rs . 20 x / 27 , s . p = rs . x , gain = rs . [ x - 20 x / 27 ] = rs . 7 x / 27 . gain % = [ 7 x / 27 * 27 / 20 x * 100 ] % = 35 % answer : b"
Answer: b
Question (general): 120 + 520 ÷ 5.00 = ?
Options: a ) 100 , b ) 150 , c ) 120 , d ) 520 , e ) none
Rationale: answer given expression = 120 + 520 ÷ 5.00 = 120 + 104 = 224 correct option : e
Answer: e
Question (physics): if 50 apprentices can finish a job in 4 hours , and 30 journeymen can finish the same job in 6 hours , how much of the job should be completed by 10 apprentices and 15 journeymen in one hour ?
Options: a ) 1 / 9 , b ) 29 / 180 , c ) 26 / 143 , d ) 2 / 15 , e ) 39 / 121
Rationale: 50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 6 * 2 = 12 hours ; in 1 hour 15 journeymen can finish 1 / 12 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 12 = 2 / 15 of the job . answer : d .
Answer: d
Question (gain): a shopkeeper sells 600 metres of cloth for rs . 36000 at a loss of rs . 10 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 59 , b ) s . 58 , c ) s . 09 , d ) s . 70 , e ) s . 13
Rationale: "sp per metre = 36000 / 600 = rs . 60 loss per metre = rs . 10 cp per metre = 60 + 10 = rs . 70 answer : d"
Answer: d
Question (physics): how long will take a leak at the bottom of a tank to empty it if it will take 8 hours to fill it without the leak , but due to the leak it will take 9 hours to be filled ?
Options: a ) 50 hours , b ) 33 hours , c ) 72 hours , d ) 82 hours , e ) 92 hours
Rationale: part filled without leak in 1 hour = 1 / 8 part filled with leak in 1 hour = 1 / 9 work done by leak in 1 hour = 1 / 8 â ˆ ’ 1 / 9 = 72 hours answer : c
Answer: c
Question (gain): on a sum of money , the simple interest for 2 years is rs . 325 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 15 % , b ) 14.25 % , c ) 9.23 % , d ) 10.5 % , e ) 11.5 %
Rationale: "explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 325 = 15 ( r ã — si ) / ( 2 ã — 100 ) = 15 ( r ã — 325 ) / ( 2 ã — 100 ) = 15 r = 9.23 % answer : option c"
Answer: c
Question (gain): a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 400 , find the original price per kg ?
Options: a ) s . 7 , b ) s . 9 , c ) s . 10 , d ) s . 11 , e ) s . 19
Rationale: 100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 400 - - - 80 ? - - - 2 = > rs . 10 answer : c
Answer: c
Question (general): the product of a and b is equal to 1 more than twice the sum of a and b . if b = 7 , what is the value of b - a ?
Options: a ) 2 , b ) 5 , c ) 4 , d ) 24 , e ) 35
Rationale: "ab = 1 + 2 ( a + b ) 7 a = 1 + 2 a + 14 5 a = 15 a = 3 b - a = 7 - 3 = 4 c is the answer"
Answer: c
Question (physics): he greatest possible length which can be used to measure exactly the lengths 7 m , 3 m 85 cm , 12 m 95 cm is :
Options: a ) 15 cm , b ) 25 cm , c ) 35 cm , d ) 42 cm , e ) 45 cm
Rationale: required length = h . c . f . of 700 cm , 385 cm and 1295 cm = 35 cm . answer : option c
Answer: c
Question (general): 12 is 6 % of a , and 6 is 12 % of b . c equals b / a . what is the value of c ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 12
Rationale: 6 a / 100 = 12 a = 200 12 b / 100 = 6 b = 50 c = b / a = 50 / 200 = 1 / 4 the answer is c .
Answer: c
Question (general): ( 17 ) 4.5 x ( 17 ) ? = 178
Options: a ) 3.5 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these
Rationale: "solution let ( 17 ) 4.5 * ( 17 ) x = 178 . then , ( 17 ) 4.5 + x = ( 17 ) 8 . ∴ 4.5 + x = 8 ⇔ x = ( 8 - 4.5 ) ⇔ x = 3.5 answer a"
Answer: a
Question (general): working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 15 , 10 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 5 / 2 , b ) 8 / 3 , c ) 9 / 4 , d ) 10 / 3 , e ) 12 / 5
Rationale: "the time it takes printer x is 15 hours . the combined rate of y and z is 1 / 10 + 1 / 20 = 3 / 20 the time it takes y and z is 20 / 3 the ratio of times is 15 / ( 20 / 3 ) = 3 * 15 / 20 = 9 / 4 the answer is c ."
Answer: c
Question (physics): excluding stoppages , the speed of a train is 35 kmph and including stoppages it is 22 kmph . of how many minutes does the train stop per hour ?
Options: a ) 82 , b ) 17 , c ) 22 , d ) 82 , e ) 18
Rationale: "explanation : t = 13 / 35 * 60 = 22 answer : option c"
Answer: c
Question (probability): jane and thomas are among the 7 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "the total number of ways to choose 3 people from 7 is 7 c 3 = 35 . the number of committees without jane or thomas is 5 c 3 = 10 . there are 35 - 10 = 25 possible committees which include jane and / or thomas . the answer is b ."
Answer: b
Question (general): the rate of interest on a sum of money is 8 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occured on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 1,200 , b ) 2,000 , c ) 2,100 , d ) 2,250 , e ) 2,540
Rationale: explanation : i 1 = ( p x 3 x 8 ) / 100 = 6 p / 25 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 6 p / 25 + 4 p / 25 + p / 20 = 540 9 p / 20 = 540 p = 1200 answer : option a
Answer: a
Question (general): a team of 8 persons joins in a shooting competition . the best marksman scored 85 points . if he had scored 92 points , the average score for the team would have been 84 . the number of points , the team scored was
Options: a ) 665 , b ) 127 , c ) 272 , d ) 287 , e ) 227
Rationale: "let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a"
Answer: a
Question (gain): if tim had lunch at $ 50.50 and he gave 15 % tip , how much did he spend ?
Options: a ) $ 58 , b ) $ 60.60 , c ) $ 70.60 , d ) $ 40.60 , e ) $ 50.60
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 15 % of 50.50 = ( 15 / 100 ) * 50.50 = $ 7.575 total spent 50.50 + 7.575 = $ 58 correct answer a"
Answer: a
Question (other): if the numbers 1 to 98 are written on 98 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 98 , d ) 1 , e ) 2
Rationale: "there are 25 primes , 72 composite numbers from 1 to 98 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 98 . answer : c"
Answer: c
Question (general): if ( x + 3 ) ^ 2 / ( 3 x + 65 ) = 2 , then the difference between the two possible values of x is :
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "( x + 3 ) ^ 2 / ( 3 x + 65 ) = 2 ( x + 3 ) ^ 2 = 2 ( 3 x + 65 ) x ^ 2 + 6 x + 9 = 6 x + 130 x ^ 2 - 121 = 0 ( x - 11 ) ( x + 11 ) = 0 x = 11 or x = - 11 the answer is d ."
Answer: d
Question (general): if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 70 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 17
Rationale: "four wheeler = 17 * 4 = 68 ( max ) 2 wheel = 1 so no of 4 wheeler = 17 answer : e"
Answer: e
Question (gain): on a purchase of $ 112 , a store offered a payment plan consisting of a $ 12 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 ) 10.7 % , b ) 11.7 % , c ) 12.7 % , d ) 13.7 % , e ) 14.7 %
Rationale: "12 * 10 + 12 = 132 ( 12 / 112 ) * 100 = 10.7 answer : a"
Answer: a
Question (physics): john bought 9.25 m of cloth for $ 425.50 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 58 , d ) 56 , e ) 54
Rationale: cloth bought by john = 9.25 m cost of 9.25 m = $ 425.50 cost per metre = 425.50 ÷ 9.25 the cost of the cloth per metre = $ 46 answers : a
Answer: a
Question (general): a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord e , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . e = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d"
Answer: d
Question (physics): a can go round a circular path 8 times in 40 minutes . if the diameter of the circle is increased to 10 times the original diameter , then the time required by a to go round the new path once , travelling at the same speed as before is
Options: a ) 20 min , b ) 35 min , c ) 50 min , d ) 70 min , e ) none
Rationale: solution let original diameter be d metres . then , its circumference = ( π d ) metres . time taken to cover ( 8 π d ) m = 40 min . new diameter = ( 10 d ) m . then , its circumference = ( π x 10 d ) m . time taken to go round it once ‹ = › [ 40 / 8 π d x 10 π d ] m ‹ = › 50 min . answer c
Answer: c
Question (gain): find compound interest on rs . 8000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) rs 400 , b ) rs 300 , c ) rs 3109 , d ) rs 250 , e ) rs 400
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = rs ' . [ 8000 x ( 1 + ¬ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = rs . [ 8000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = rs . 11109 . . : . c . i . = rs . ( 11109 - 8000 ) = rs . 3109 . answer c rs 3109"
Answer: c
Question (general): x is the product of each integer from 1 to 75 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 9 , e ) 10
Rationale: "the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 75 = 50 ! no . of trailing zeros in 75 ! = 75 / 5 + 75 / 5 ^ 2 = 15 + 3 = 18 100 ^ k = 10 ^ 2 k → k = 18 / 2 = 9 d"
Answer: d
Question (general): a will was written such that an estate would be divided among 3 guys with the remainder donated to charity . one stipulation in the will is that no one from the guys can receive an amount within 30 % of another ' s amount . if one of the guys received $ 20000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 3 guys ?
Options: a ) $ 4096 , b ) $ 5904 , c ) $ 7892 , d ) $ 10052 , e ) $ 20736
Rationale: 1 st - 20000 . 2 nd - 0.7 * 20000 = 14000 3 rd - 0.7 * 14000 = 9800 range = 20000 - 9800 = 10200 . answer : d .
Answer: d
Question (gain): find 40 % of 440
Options: a ) 96 , b ) 94 , c ) 86 , d ) 176 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 40 % of 440 40 / 100 × 440 = 176 answer : d"
Answer: d