Cheukting/mathqa huggingface dataset:
Question (physics): a 35 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 10 , b ) 20 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 35 = 10 answer : a"
Answer: a
Question (physics): car a is 30 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 1.5 , b ) 4.5 , c ) 4.75 , d ) 3.75 , e ) 3.5
Rationale: "relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 30 miles and drive 8 miles ahead so to drive 38 miles it ' ll need 38 / 8 = 3.5 hours . answer : c"
Answer: c
Question (physics): if a car went the first third of the distance at 80 kmh , the second third at 18 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 34 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 720 ( this number is convenient because it is divisible by 80 , 18 and 48 ) so : 720 = 80 * t 1 = 9 hrs 720 = 18 * t 2 = 40 hrs 720 = 48 * t 3 = 15 hrs t = t 1 + t 2 + t 3 = 64 hrs d = rt ( 720 * 3 ) = r * 64 r = 33.75 answer : a"
Answer: a
Question (general): in a group of ducks and cows , the total number of legs are 22 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 13 , d ) 15 , e ) 16
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 22 = > 2 x = 22 = > x = 11 a"
Answer: a
Question (gain): how long does a train 110 meters long running at the rate of 36 km / hr take to cross a bridge 132 meters in length ?
Options: a ) 24.2 sec , b ) 30.6 sec , c ) 32.6 sec , d ) 28.1 sec , e ) 20.4 sec
Rationale: "distance = length of train + length of bridge = 110 + 132 = 242 speed = 36 km / hr = 36 * 5 / 18 = 10 m / s required time = 242 / 10 = 24.2 seconds answer is a"
Answer: a
Question (gain): a certain airline ' s fleet consisted of 100 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "let x be the number of years . 4 x > 100 - 3 x 7 x > 100 x > 14 + 2 / 7 the answer is b ."
Answer: b
Question (gain): the price of an article is cut by 10 % . to restore it to the former value , the new price must be increased by
Options: a ) 10 % , b ) 9 1 / 11 % , c ) 11 1 / 9 % , d ) 11 % , e ) none
Rationale: "explanation : let original price = rs . 100 then , new price = rs . 90 increase on rs . 90 = rs . 100 increase % = ( 10 / 90 × 100 ) % = 11 1 / 9 % correct option : c"
Answer: c
Question (general): on dividing 23 by a number , the quotient is 5 and the remainder is 3 . find the divisor .
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 7
Rationale: d = ( d - r ) / q = ( 23 - 3 ) / 5 = 20 / 5 = 4 c
Answer: c
Question (general): ( 2 ^ 2 + 4 ^ 2 + 6 ^ 2 + . . . . . + 14 ^ 2 ) = ?
Options: a ) 88 , b ) 560 , c ) 99 , d ) 550 , e ) 540
Rationale: = ( 1 x 2 ) ^ 2 + ( 2 x 2 ) ^ 2 , + ( 2 x 3 ) ^ 3 + . . . . . . ( 2 x 7 ) ^ 2 = 2 ^ 2 x ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . . . . . + 7 ^ 2 ) formula is = 1 / 6 n ( n + 1 ) ( 2 n + 1 ) = ( 4 x 1 / 6 x 7 x 8 x 15 ) = ( 4 x 140 ) = 560 answer is b
Answer: b
Question (general): a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 2 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 33 , b ) 46 , c ) 49 , d ) 54 , e ) 86
Rationale: "n = 4 k + 1 = 5 j + 2 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 5 j + 2 . 1 , 5 , 9 , 13 , 17 = 5 ( 3 ) + 2 the next such number is 17 + 4 * 5 = 37 . 17 + 37 = 54 the answer is d ."
Answer: d
Question (general): find large number from below question the difference of two numbers is 100 . on dividing the larger number by the smaller , we get 9 as quotient and the 4 as remainder
Options: a ) 120 , b ) 100 , c ) 112 , d ) 150 , e ) 105
Rationale: "let the smaller number be x . then larger number = ( x + 100 ) . x + 100 = 9 x + 4 8 x = 96 x = 12 large number = 12 + 100 = 112 c"
Answer: c
Question (general): if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.30 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 5.20 , e ) $ 2.80
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.3 ) = $ 4.2 ( as the charge is 0.3 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 4.2 = 5.2 answer is d ."
Answer: d
Question (other): there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 18 , then find the smaller number ?
Options: a ) 30 , b ) 66 , c ) 77 , d ) 88 , e ) 44
Rationale: "let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 18 3 x = 18 = > x = 6 = > smaller number = 5 x = 30 . answer : a"
Answer: a
Question (physics): find the area of trapezium whose parallel sides are 18 cm and 12 cm long , and the distance between them is 14 cm ?
Options: a ) 288 cm 2 , b ) 277 cm 2 , c ) 224 cm 2 , d ) 226 cm 2 , e ) 227 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 18 + 12 ) * ( 14 ) = 224 cm 2 answer : c"
Answer: c
Question (general): the function f ( x ) = x + 4 is given . solve the equation : [ 3 . f ( x - 2 ) ] / f ( 0 ) + 4 = f ( 2 x + 1 )
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) none of these
Rationale: solution : we calculate f ( 0 ) , f ( x - 2 ) , f ( 2 x + 1 ) , namely f ( 0 ) = 0 + 4 = 4 ; f ( x - 2 ) = x - 2 + 4 = x + 2 ; f ( 2 x + 1 ) = 2 x + 1 + 4 = 2 x + 5 the equation gets this look [ 3 ( x + 2 ) ] / 4 + 4 = 2 x + 5 < = > 3 ( x + 2 ) + 16 = 4 ( 2 x + 5 ) < = > 3 x + 6 + 16 = 8 x + 20 < = > 22 - 20 = 8 x - 3 x < = > 2 = 5 x < = > x = 0.4 answer c
Answer: c
Question (gain): a 340 - liter solution of kola is made from 80 % water , 6 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 14 % .
Rationale: denominator : 340 + 10 + 3.2 + 6.8 = 360 numerator : 340 ( 1 - . 80 - . 06 ) + 3.2 340 ( 0.14 ) + 3.2 47.6 + 3.2 50.8 ratio : 50.8 / 360 = 0.14 answer : e
Answer: e
Question (general): find the largest 6 digit number which is exactly divisible by 88 ?
Options: a ) 998765 , b ) 998907 , c ) 999944 , d ) 999954 , e ) 999990
Rationale: largest 6 digit number is 999999 after doing 999999 ÷ 88 we get remainder 55 hence largest 6 digit number exactly divisible by 88 = 999999 - 55 = 999944 c
Answer: c
Question (general): ( 0.12 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.12 ) ( power 2 ) + 0.012 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.68 , b ) 0.086 , c ) 0.86 , d ) 0.068 , e ) none of them
Rationale: "given expression = ( 0.12 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.12 ) ( power 2 ) + ( 0.12 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.12 - 0.1 ) = 0.02 answer is e ."
Answer: e
Question (general): if the sum of two numbers is 18 and the sum of their squares is 220 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 52 , d ) 88 , e ) 90
Rationale: "sol . let the numbers be x and y . then , ( x + y ) = 18 and x 2 + y 2 = 220 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 18 ) 2 - 220 = 324 - 220 = 104 xy = 52 . answer c"
Answer: c
Question (general): how many positive integers less than 10,000 are there in which the sum of the digits equals 5 ?
Options: a ) 31 , b ) 51 , c ) 56 , d ) 62 , e ) 93
Rationale: basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a separator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit separators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . answer : c
Answer: c
Question (gain): from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 20 percent . the enrollment on january 1 , 1993 , was 50 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: 1.20 x = 50 - - > 6 / 5 * x = 50 - - > x = 50 * 5 / 6 = 250 / 6 = ~ 42 . answer : e .
Answer: e
Question (general): if the remainder is 7 when positive integer n is divided by 10 , what is the remainder when n is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 2
Rationale: "assume x is quotient here , n = 10 x + 7 - - - - - - - - - - ( 1 ) and n = 5 x + ? we can also write equation ( 1 ) as : n = ( 10 x + 5 ) + 2 . ie 5 ( 2 x + 1 ) + 1 ie the first term is perfectly divisible by 5 . so , the remainder left is 2 so , answer ( e ) is right choice ."
Answer: e
Question (gain): on a sum of money , the simple interest for 2 years is rs . 330 , 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 ) 6.06 % , 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 - 330 = 10 ( r ã — si ) / ( 2 ã — 100 ) = 10 ( r ã — 330 ) / ( 2 ã — 100 ) = 10 r = 6.06 % answer : option c"
Answer: c
Question (general): the average age of 30 students in a class is 10 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 59 , b ) 55 , c ) 61 , d ) 41 , e ) 36
Rationale: "total age of 50 students = 30 * 10 = 300 total age of 51 persons = 31 * 11 = 341 age of teacher = 341 - 300 = 41 years answer is d"
Answer: d
Question (general): what must be added to each term of the ratio 7 : 11 , so as to make it equal to 3 : 4 ?
Options: a ) 8 , b ) 7.5 , c ) 6.5 , d ) 5 , e ) 6
Rationale: "solution : let x be added to each term . according to question , ( 7 + x ) / ( 11 + x ) = 3 / 4 ; or , 33 + 3 x = 28 + 4 x ; or , x = 5 . answer : option d"
Answer: d
Question (general): jaime earned enough money by selling seashells at 22 cents each to buy several used paperback books at 55 cents each . if he spent all of the money he earned selling seashells to buy the books , what is the least number of seashells he could have sold ?
Options: a ) 5 , b ) 11 , c ) 17 , d ) 25 , e ) 30
Rationale: "let ' s test answer a : 5 seashells . . . with 5 seashells , jamie would have 5 ( 22 ) = 110 cents . this would allow him to buy 2 books for 110 cents total , so this is the correct answer . a"
Answer: a
Question (geometry): the water level in a rectangular swimming pool measuring 60 feet by 20 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 4500 , d ) 1200 , e ) 5625
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 20 * 1 / 2 = 600 feet ^ 3 of water must be removed , which equals to 600 * 7.5 = 4500 gallons . answer : c ."
Answer: c
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 57 ?
Options: a ) 3944 , b ) 920 , c ) 7290 , d ) 3876 , e ) 3729
Rationale: "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 57 = rs . 3876 . answer : option d"
Answer: d
Question (general): 3 friends alice , bond and charlie divide $ 1105 amongs them in such a way that if $ 10 , $ 20 and $ 15 are removed from the sums that alice , bond and charlie received respectively , then the share of the sums that they got will be in the ratio of 11 : 18 : 24 . how much did charlie receive ?
Options: a ) $ 495 , b ) $ 510 , c ) $ 480 , d ) $ 375 , e ) $ 360
Rationale: explanatory answer let the sums of money received by a , b and c be x , y and z respectively . then x - 10 : y - 20 : z - 15 is 11 a : 18 a : 24 a when $ 10 , $ 20 and $ 15 are removed , we are removing a total of $ 45 from $ 1105 . therefore , 11 a + 18 a + 24 a = 1105 - 45 = 1060 i . e . , 53 a = 1060 or a = 20 . we know that z - 15 = 24 a = 24 * 20 = 480 therefore , z = 480 + 15 = $ 495 correct choice is ( a )
Answer: a
Question (general): mother , her daughter and her grand child weighs 150 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 46 , b ) 47 , c ) 42 , d ) 49 , e ) 50
Rationale: "mother + daughter + child = 150 kg daughter + child = 60 kg mother = 150 - 60 = 90 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 90 = 18 kg so now daughter = 120 - ( mother + child ) = 150 - ( 90 + 18 ) = 42 kg answer : c"
Answer: c
Question (general): in a weight - lifting competition , the total weight of joe ' s two lifts was 900 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options: a ) 225 , b ) 275 , c ) 325 , d ) 350 , e ) 400
Rationale: "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 900 pounds . we sum the two variables to obtain : f + s = 900 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 900 3 f = 1,200 f = 400 answer is e ."
Answer: e
Question (other): the h . c . f . of two numbers is 25 and the other two factors of their l . c . m . are 14 and 16 . the larger of the two numbers is
Options: a ) 276 , b ) 299 , c ) 312 , d ) 400 , e ) none
Rationale: "solution clearly , the numbers are ( 25 x 14 ) and ( 25 x 16 ) . larger number = ( 25 x 16 ) = 400 . answer d"
Answer: d
Question (physics): in what time will a train 180 meters long cross an electric pole , if its speed is 154 km / hr
Options: a ) 5 seconds , b ) 4.3 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 154 * ( 5 / 18 ) = 42 m / sec time = distance / speed = 180 / 42 = 4.3 seconds option b"
Answer: b
Question (general): a miniature roulette wheel is divided into 9 equal sectors , each bearing a distinct integer from 1 to 9 , inclusive . each time the wheel is spun , a ball randomly determines the winning sector by settling in that sector . if the wheel is spun four times , approximately what is the probability that the product of the four winning sectors ’ integers will be even ?
Options: a ) 50 % , b ) 67 % , c ) 80 % , d ) 90 % , e ) 95 %
Rationale: "the only way to have an odd product is if all 4 integers are odd . p ( odd product ) = 5 / 9 * 5 / 9 * 5 / 9 * 5 / 9 = 625 / 6561 p ( even product ) = 1 - 625 / 6561 = 5936 / 6561 which is about 90 % the answer is d ."
Answer: d
Question (gain): an article is bought for rs . 575 and sold for rs . 675 , find the gain percent ?
Options: a ) 17.39 % , b ) 33 1 / 6 % , c ) 33 1 / 3 % , d ) 38 1 / 3 % , e ) 33 2 / 3 %
Rationale: "575 - - - - 100 100 - - - - ? = > 17.39 % answer : a"
Answer: a
Question (gain): a cycle is bought for rs . 900 and sold for rs . 1150 , find the gain percent ?
Options: a ) 15 , b ) 20 , c ) 27.77 , d ) 40 , e ) 12
Rationale: "900 - - - - 250 100 - - - - ? = > 27.77 % answer : c"
Answer: c
Question (physics): an employer pays rs . 20 for each day a worker works and for felts rs . 3 for each day is ideal at the end of sixty days a worker gets rs . 280 . for how many days did the worker remain ideal ?
Options: a ) 10 , b ) 40 , c ) 30 , d ) 20 , e ) 50
Rationale: suppose a worker remained ideal for x days then he worked for 60 - x days 20 * ( 60 - x ) - 3 x = 280 1200 - 23 x = 280 23 x = 920 x = 40 answer is b .
Answer: b
Question (physics): a train usually travels at a speed of 72 kmph crossing a pole in 7 sec , what would be the length of the train ?
Options: a ) 140 m , b ) 142 m , c ) 146 m , d ) 152 m , e ) 158 m
Rationale: explanation : d = 72 * 5 / 18 * 7 = 140 m answer : option a
Answer: a
Question (general): a man received a cheque . the amount in rs . has been transposed for paise and vice versa . after spending rs . 5 and 42 paise , he discovered he now had exactly 6 times the value of the correct cheque amount . what amount he should have received ?
Options: a ) rs 5.30 , b ) rs 6.44 , c ) rs 60.44 , d ) rs 16.44 , e ) none of these
Rationale: explanation : option 4 : - on reversal will be 44 rs 16 ps , after spending 5 rs 42 ps , remaining will be around 40 rs which is not 6 times 16 rs 44 ps . option 3 : - on reversal will lead a smaller value . hence we can eliminate that as well . option 1 : - on reversal is 30 rs 5 paise , after spending 5 rs 42 ps , remaining will be 24 rs 63 paise , 24 rs 63 ps is not 6 times 5 rs 30 paise . option 2 on reversal is 44 rs 06 paise , after spending 5 rs 42 ps , remaining will be 38 rs 64 ps , which is 6 times 6 rs 44 paise . hence rs 6.44 is the answer . we need not even consider option 4 and option 3 as reversed number itself is not 6 times the original number . option 1 when reversed is odd , and when even ( 5 rs 42 ps ) is subtracted from odd , we get a odd number , and an odd number can not be 6 times another number answer : b
Answer: b
Question (general): if 30 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 33.3 % , e ) 20 %
Rationale: "30 % of ( x - y ) = 20 % of ( x + y ) 30 / 100 ( x - y ) = 20 / 100 ( x + y ) x = 5 y required percentage = y / x * 100 = y / 5 y * 100 = 20 % answer is e"
Answer: e
Question (general): the digit in units place of the product 81 x 82 x . . . . . x 89 is
Options: a ) 0 , b ) 2 , c ) 6 , d ) 8 , e ) 9
Rationale: sol . required digit = unit digit in ( 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 ) = 0 . answer a
Answer: a
Question (gain): alfred buys an old scooter for $ 4700 and spends $ 800 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ?
Options: a ) 5.45 % , b ) 6.23 % , c ) 7 % , d ) 8.12 % , e ) 10 %
Rationale: "c . p . = 4700 + 800 = $ 5500 s . p . = $ 5800 gain = 5800 - 5500 = $ 300 gain % = 300 / 5500 * 100 = 5.45 % answer is a"
Answer: a
Question (physics): a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 380 m long platform ?
Options: a ) 50 , b ) 27 , c ) 29 , d ) 47 , e ) 28
Rationale: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 380 ) / 36 * 5 / 18 = 50 min . answer : a"
Answer: a
Question (general): find the value of 3 + 2 • ( 8 – 3 )
Options: a ) ( a ) 25 , b ) ( b ) 13 , c ) ( c ) 17 , d ) ( d ) 24 , e ) ( e ) 15
Rationale: "3 + 2 • ( 8 – 3 ) = 3 + 2 ( 5 ) = 3 + 2 × 5 = 3 + 10 = 13 answer : ( d )"
Answer: d
Question (geometry): if the height of a cone is increased by 160 % then its volume is increased by ?
Options: a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 160
Rationale: "160 % answer : e"
Answer: e
Question (general): if x is an integer and 2.134 × 10 ^ x is less than 210,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "21340 * 10 ^ - 4 * 10 ^ x < 210,000 , x = 4 because the next zero on the right side will make 21,340 > 210,000 answer d ,"
Answer: d
Question (general): in a renowned city , the average birth rate is 4 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 43,100 , b ) 43,200 , c ) 43,300 , d ) 43,400 , e ) 43,450
Rationale: "this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 4 - 3 = 1 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 1 = 43,200 . hence b ."
Answer: b
Question (other): a certain university will select 2 of 5 candidates eligible to fill a position in the mathematics department and 3 of 8 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 540 , d ) 565 , e ) 560
Rationale: "5 c 2 * 8 c 3 = 10 * 56 = 560 the answer is ( e )"
Answer: e
Question (general): the unit digit in the product ( 784 x 618 x 917 x 463 ) is
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) none of them
Rationale: "unit digit in the given product = unit digit in ( 4 x 8 x 7 x 3 ) = 2 answer is a"
Answer: a
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 6 : 2 : 4 : 3 . if c gets $ 500 more than d , what is d ' s share ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 3600 , e ) $ 4200
Rationale: "let the shares of a , b , c and d be 6 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 a ' s share = 6 x = 6 * $ 500 = $ 3000 the answer is c ."
Answer: c
Question (general): in an examination , 300 students appeared . out of these students ; 25 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 63 , b ) 37 , c ) 54 , d ) 99 , e ) 01
Rationale: "the number of students with first division = 25 % of 300 = 25 / 100 × 300 = 8400 / 100 = 75 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 75 + 162 ) = 63 answer : a"
Answer: a
Question (physics): walking at 4 / 7 of its usual speed , a train is 9 minutes late . find its usual time to cover the journey .
Options: a ) 8 min . , b ) 10 min . , c ) 12 min . , d ) 15 min . , e ) 17 min .
Rationale: explanation : solution : new speed = 4 / 7 of the usual speed . let usual time be x . . ' . new time taken = 7 / 4 of usual time = 7 x / 4 so , ( 7 x / 4 ) - x = 9 min . = > 3 x = 36 = > x = 12 min . answer : c
Answer: c
Question (general): a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 25 as remainder . find the no . is ?
Options: a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220025
Rationale: "( 555 + 445 ) * 2 * 110 + 25 = 220000 + 25 = 220025 e"
Answer: e