Cheukting/mathqa huggingface dataset:
Question (general): for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.567 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 1 , c ) 27 , d ) 0 , e ) can not be determined
Rationale: k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . d
Answer: d
Question (general): in the faculty of reverse - engineering , 100 second year students study numeric methods , 100 second year students study automatic control of airborne vehicles and 25 second year students study them both . how many students are there in the faculty if the second year students are approximately 50 % of the total ?
Options: a ) 340 , b ) 335 , c ) 370 , d ) 360 , e ) 350
Rationale: "total number of students studying both are 100 + 100 - 25 = 175 ( subtracting the 25 since they were included in the both the other numbers already ) . so 50 % of total is 175 , so 100 % is 350 answer is e"
Answer: e
Question (other): the probability that a computer company will get a computer hardware contract is 3 / 4 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 5 / 6 , what is the probability that it will get both the contracts ?
Options: a ) 7 / 30 , b ) 11 / 40 , c ) 17 / 50 , d ) 19 / 60 , e ) 33 / 80
Rationale: let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 3 / 4 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 5 / 6 = ( 3 / 4 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 19 / 60 . hence , the required probability is 19 / 60 . the answer is d .
Answer: d
Question (physics): a man sitting in a train which is travelling at 60 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 72 kmph . , d ) 80 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 60 ) kmph = 52 kmph . answer a"
Answer: a
Question (general): a straight line in the xy - plane has slope 2 . on this line the x - coordinate of the point is 300 and y - coordinate is 900 then what is the y intercept of the plane ?
Options: a ) 200 , b ) 250 , c ) 100 , d ) 300 , e ) 220
Rationale: "eq of line = y = mx + c m = 2 x = 300 y = 300 * 2 + c , substitute y by 900 as given in question . 900 = 600 + c , c = 200 correct option is a"
Answer: a
Question (other): a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 11,200 sedans in anytown , how many motorcycles are there ?
Options: a ) 1260 , b ) 2100 , c ) 3600 , d ) 3200 , e ) 5200
Rationale: "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 11200 = > 7 x = 11200 = > x = 1600 total number of motorcycles = 2 x = 2 * 1600 = 3200 answer d"
Answer: d
Question (physics): to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two - fifth of its present ?
Options: a ) 62.5 , b ) 65 , c ) 61 , d ) 64 , e ) 60
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 25 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 25 x ) / ( 2 x / 5 ) = ( 25 x ) x 5 / 2 x = 125 / 2 = 62.5 answer is a ."
Answer: a
Question (physics): the walker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the walker continues to walk at her constant rate , how many minutes must the cyclist wait until the walker catches up ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: after passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 3 miles . in those 5 mins the hiker travels a distance of 1 / 3 miles . so the hiker still has to cover 4 / 3 miles to meet the waiting cyclist . the hiker will need 1 / 3 hours or 20 mins to cover the remaining 4 / 3 miles . so the answer is c .
Answer: c
Question (physics): a train traveled the first d miles of its journey it an average speed of 60 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 94 miles per hour , what is the value of y ?
Options: a ) 98 , b ) 84 , c ) 90 , d ) 120 , e ) 135
Rationale: "average speed = total distance traveled / total time taken 3 d / d / 60 + d / y + d / 160 = 94 solving for d and y , 15 y = 11 y + 480 5 y = 480 y = 98 answer a"
Answer: a
Question (general): what is the total number of positive integers that are less than 1000 and that have no positive factor in common with 1000 other than 1 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "since 1000 = 2 ^ 3 * 5 ^ 3 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 500 odd numbers from 1 to 1000 . we then need to eliminate the 100 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 995 . there are a total of 500 - 100 = 400 such numbers between 1 and 1000 . the answer is d ."
Answer: d
Question (other): the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 13000 , then find the annual income of a ?
Options: a ) rs . 420000 , b ) rs . 180000 , c ) rs . 436800 , d ) rs . 504000 , e ) none of these
Rationale: "b ' s monthly income = 13000 * 112 / 100 = rs . 14560 b ' s monthly income = 2 parts - - - - > rs . 14560 a ' s monthly income = 5 parts = 5 / 2 * 14560 = rs . 36400 a ' s annual income = rs . 36400 * 12 = rs . 436800 answer : c"
Answer: c
Question (general): 3 * 13 + 3 * 14 + 3 * 17 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 143 , e ) 151
Rationale: "3 * 13 + 3 * 14 + 3 * 17 + 11 = 39 + 42 + 51 + 11 = 143 the answer is d ."
Answer: d
Question (general): in mrs . susna ' s class , 1 / 4 of her students are getting an a , 1 / 2 are getting a b , 1 / 8 are getting a c , 1 / 12 are getting a d , and 1 / 24 are getting a f . what fraction of mrs . susna ' s class getting a passing grade of c or higher .
Options: a ) 5 / 6 , b ) 3 / 4 , c ) 7 / 8 , d ) 1 / 8 , e ) 1 / 2
Rationale: if mrs . susna ' s class has 24 students , the number of students receiving as , bs , or cs , are 6 , 12 , and 3 respectively . that means 21 / 24 of her students are receiving passing grades or 7 / 8 . ( answer : c )
Answer: c
Question (geometry): the area of the house of a hall is 20 m 2 that of a longer wall 10 m 2 and of the shorter wall 8 m 2 , find the edge of the new cube ?
Options: a ) 45 m 3
b ) 40 m 3
c ) 60 m 3
d ) 600 m 3
e ) 300 m 3
Rationale: lb = 20 ; lh = 10 ; fh = 8 ( lbh ) 2 = 20 * 10 * 8 = > lbh = 40 m 3 answer : b
Answer: b
Question (physics): there is a 45 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 45 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 10
Rationale: "only the prime numbers greater than 10 and less than 45 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , and 43 . the total is 10 . the answer is e ."
Answer: e
Question (gain): the present population of a town is 4032 . population increase rate is 20 % p . a . find the population of town before 2 years ?
Options: a ) 2500 , b ) 2800 , c ) 3500 , d ) 3600 , e ) 2050
Rationale: "p = 4032 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 4032 / ( 1 + 20 / 100 ) ^ 2 = 4032 / ( 6 / 5 ) ^ 2 = 2800 ( approximately ) answer is b"
Answer: b
Question (physics): a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 2 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 240 , c ) 289 , d ) 270 , e ) 927
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 2 = 240 answer : b"
Answer: b
Question (gain): the present population of a town is 10000 . population increase rate is 10 % p . a . find the population of town after 2 years ?
Options: a ) 10000 , b ) 11100 , c ) 15000 , d ) 12100 , e ) 14520
Rationale: "p = 10000 r = 10 % required population of town = p ( 1 + r / 100 ) ^ t = 10000 ( 1 + 10 / 100 ) ^ 2 = 10000 ( 11 / 10 ) ^ 2 = 12100 answer is d"
Answer: d
Question (general): john has taken 4 ( 4 ) tests that have an average of 82 . in order to bring his course grade up to a ‘ b ’ , he will need to have a final average of 86 . what will he need to average on his final two tests to achieve this grade ?
Options: a ) 87 , b ) 90 , c ) 92 , d ) 94 , e ) 97
Rationale: traditional method : total scored till now 82 * 4 = 328 total score to avg 86 in 6 tests = 86 * 6 = 516 total to be scored on 2 tests = 516 - 328 = 188 avg on 2 tests = 188 / 2 = 94 answer : d
Answer: d
Question (geometry): find the surface area of a 8 cm x 4 cm x 2 cm brick .
Options: a ) 136 cu cm , b ) 112 cu cm , c ) 164 cu cm , d ) 180 cu cm , e ) none
Rationale: "sol . surface area = [ 2 ( 8 x 4 + 4 x 2 + 8 x 2 ) ] = ( 2 x 56 ) = 112 cu cm answer b"
Answer: b
Question (physics): a car started running at a speed of 38 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 47 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: a 47 km the total distance covered by the car in the first 10 hours = 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 + 54 + 56 = sum of 10 terms in ap whose first term is 30 and last term is 56 = 10 / 2 [ 38 + 56 ] = 470 km .
Answer: a
Question (other): 3 containers a , b and c are having mixtures of milk and water in the ratio of 1 : 5 and 3 : 5 and 5 : 7 respectively . if the capacities of the containers are in the ratio of all the 3 containers are in the ratio 5 : 4 : 5 , find the ratio of milk to water , if the mixtures of all the 3 containers are mixed together .
Options: a ) 53 : 115 , b ) 55 : 115 , c ) 115 : 55 , d ) 5 : 115 , e ) 115 : 53
Rationale: assume that there are 500400 and 500 liters respectively in the 3 containers . then , we have , 83.33 , 150 and 208.33 liters of milk in each of the three containers . thus , the total milk is 441.66 liters . hence , the amount of water in the mixture is 1400 - 441.66 = 958.33 liters . hence , the ratio of milk to water is 441.66 : 958.33 = > 53 : 115 ( using division by . 3333 ) the calculation thought process should be ( 441 * 2 + 2 ) : ( 958 * 3 + 1 ) = 1325 : 2875 dividing by 25 = > 53 : 115 . answer a 53 : 115
Answer: a
Question (geometry): the length of a rectangle is reduced by 22 % . by what % would the width have to be increased to maintainthe original area ?
Options: a ) 15 % , b ) 20 % , c ) 28 % , d ) 35 % , e ) 40 %
Rationale: "sol . required change = ( 22 * 100 ) / ( 100 - 22 ) = 28 % c"
Answer: c
Question (general): if 5 x = 7 y and xy ≠ 0 , what is the ratio of 1 / 5 * x to 1 / 6 * y ?
Options: a ) 25 / 6 , b ) 42 / 25 , c ) 6 / 5 , d ) 5 / 6 , e ) 25 / 36
Rationale: "5 x = 7 y = > x / y = 7 / 5 1 / 5 * x to 1 / 6 * y = x / y * 6 / 5 = ( 7 / 5 ) * ( 6 / 5 ) = 42 / 25 ans : b"
Answer: b
Question (gain): if 10 litres of an oil of rs . 50 per litres be mixed with 5 litres of another oil of rs . 67 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 51.03 , c ) rs . 54.17 , d ) rs . 55.66 , e ) none of the above
Rationale: "50 * 10 = 500 67 * 5 = 335 835 / 15 = 55.66 answer : d"
Answer: d
Question (general): the sum of first 45 natural numbers is :
Options: a ) 1035 , b ) 1040 , c ) 1042 , d ) 1045 , e ) 1050
Rationale: "let sn = ( 1 + 2 + 3 + . . . + 45 ) . this is an a . p . in which a = 1 , d = 1 , n = 45 . sn = n [ 2 a + ( n - 1 ) d ] = 45 x [ 2 x 1 + ( 45 - 1 ) x 1 ] = 45 x 46 = ( 45 x 23 ) 2 2 2 = 45 x ( 20 + 3 ) = 45 x 20 + 45 x 3 = 900 + 135 = 1035 . shorcut method : sn = n ( n + 1 ) = 45 ( 45 + 1 ) = 1035 . 2 2 a"
Answer: a
Question (geometry): if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 226 m , what is its area ?
Options: a ) 2510 , b ) 2535 , c ) 3060 , d ) 2515 , e ) 2520
Rationale: "length = breadth + 23 . therefore , 4 × breadth + 2 × 23 = 226 m ⇒ breadth = 45 m length = 45 + 23 = 68 m area = 68 × 45 = 3060 m 2 answer is c ."
Answer: c
Question (probability): there is a 30 % chance sandy will visit china this year , while there is a 60 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ?
Options: a ) 42 % , b ) 48 % , c ) 54 % , d ) 60 % , e ) 66 %
Rationale: p ( china and not malaysia ) = 0.3 * 0.4 = 0.12 p ( malaysia and not china ) = 0.6 * 0.7 = 0.42 total probability = 0.12 + 0.42 = 0.54 = 54 % the answer is c .
Answer: c
Question (general): mike earns $ 14 per hour and phil earns $ 10.5 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 25 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %
Rationale: "let it be x % less , then = 14 ( 1 - x / 100 ) = 10.5 1 - x / 100 = 10.5 / 14 x = 350 / 14 x = 25 % answer : a"
Answer: a
Question (general): the total price of a basic computer and printer are $ 2500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 6 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000
Rationale: let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 6 of that new total price : p = 1 / 6 * $ 3,000 = $ 500 . plug this value in the first equation : c + 500 = $ 2,500 - - > c = $ 2000 answer : e .
Answer: e
Question (general): find the average of first 4 multiples of 9 ?
Options: a ) 10 , b ) 12.6 , c ) 22.5 , d ) 31.3 , e ) 40.8
Rationale: "average = ( 9 + 18 + 27 + 36 ) / 4 = 22.5 answer is c"
Answer: c
Question (general): company a ' s workforce consists of 10 percent managers and 90 percent software engineers . company b ' s workforce consists of 30 percent managers , 10 percent software engineers , and 60 percent support staff . the two companies merge , every employee stays with the resulting company , and no new employees are added . if the resulting company í s workforce consists of 25 percent managers , what percent of the workforce originated from company a ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 75 %
Rationale: let say company a has x employes and b has y employees . now they merge and total no of employees = x + y employees . per the question company a ' s workforce consists of 10 percent managers and 90 percent software engineers . company b ' s workforce consists of 30 percent managers , 10 percent software engineers , and 60 percent support staff . we translate it into equation as follows : . 1 x + . 3 y = . 25 ( x + y ) = > x + 3 y = 2.5 ( x + y ) = > . 5 y = 1.5 x = > y = 3 x . now we know total employee = x + y . we need to find % age of x in total ( x + y ) ie x / ( x + y ) x 100 % = > x / ( 3 x + x ) [ substitute y = 3 x ] = > x / 4 x x 100 % = > . 25 x 100 % = > 25 % . answer : c
Answer: c
Question (general): how many positive integers less than 100 are neither multiples of 5 or 6 .
Options: a ) a ) 30 , b ) b ) 31 , c ) c ) 32 , d ) d ) 33 , e ) e ) 67
Rationale: "to answer this q we require to know 1 ) multiples of 5 till 100 = 100 / 5 = 20 2 ) multiples of 6 till 100 = 100 / 6 = 16.66 = 16 add the two 20 + 16 = 36 ; subtract common terms that are multiple of both 5 and 6 . . lcm of 5 and 6 = 30 multiples of 30 till 100 = 100 / 30 = 3.3 = 3 so total multiples of 2 and 3 = 36 - 3 = 33 ans = 100 - 33 = 67 e"
Answer: e
Question (physics): a and b walk around a circular track . they start at 9 a . m . from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 12 : 00 p . m . ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 25 , e ) 20
Rationale: "sol . relative speed = ( 2 + 3 ) = 5 rounds per hour . so , they cross each other 5 times in an hour . hence , they cross each other 20 times before 12 : 00 p . m . answer e"
Answer: e
Question (general): if n is a positive integer and n ^ 3 is a multiple of 550 , what is the least possible value of n ?
Options: a ) 8 , b ) 27 , c ) 81 , d ) 110 , e ) 125
Rationale: "cube of a number entails having 3 copies of the original prime factors . since 550 is a factor of n ^ 3 the least possible value of n is 5 ( 11 ) 2 = 110 the answer is d ."
Answer: d
Question (physics): two goods trains each 375 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 40 , b ) 45 , c ) 48 , d ) 51 , e ) 36
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 375 + 375 = 750 m . required time = 750 * 6 / 125 = 36 sec . answer : option e"
Answer: e
Question (gain): if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 300 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 307.50 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 15,000 . now , put the value of x = 3000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 3000 + 5 % of 3000 = 3150 . 2 nd year , amount = 3150 + 5 % of 3150 = 3307.50 . we can see after 2 years interest = 3307.50 - 3000 = 307.50 . hence , it satisfies the question . hence e is the correct answer"
Answer: e
Question (gain): a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 25 % . staff are allowed a further 20 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.6 d , b ) 0.7 d , c ) 0.5 d , d ) 0.8 d , e ) 0.9 d
Rationale: "effective discount = a + b + ab / 100 = - 25 - 20 + ( - 25 ) ( - 20 ) / 100 = - 40 sale price = d * ( 1 - 40 / 100 ) sale price = . 6 * d answer ( a )"
Answer: a
Question (gain): what is the normal price of an article sold at $ 108 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 130 , b ) $ 140 , c ) $ 150 , d ) $ 160 , e ) $ 170
Rationale: "0.8 * 0.9 * cost price = $ 108 cost price = $ 150 the answer is c ."
Answer: c
Question (probability): kim has 8 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 16 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 15
Rationale: "total pairs = 16 c 2 = 120 ; same color pairs = 8 c 1 * 1 c 1 = 8 ; prob = 1 / 15 ans e"
Answer: e
Question (other): how many factors does 16 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 4 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 2 * 2 = 4 answer c ."
Answer: c
Question (general): there are 14 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 91 , b ) 98 , c ) 105 , d ) 112 , e ) 119
Rationale: "14 c 2 = 91 the answer is a ."
Answer: a
Question (other): a technology company made a $ 5 million profit on its first $ 15 million in sales and a $ 12 million profit on its next $ 30 million in sales . by what percent did the ratio of profit to sales increase from the first $ 15 million in sales to the next $ 30 million in sales ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: solution : this is a percent increase problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of profits to sales . the first ratio will be for the first 15 million in sales , and the second ratio will be for the next 30 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 15 million profit / sales = 5 / 15 = 1 / 3 next 30 million profit / sales = 12 / 30 = 2 / 5 we can simplify each ratio by multiplying each by the lcm of the two denominators , which is 15 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 15 million royalties / sales = ( 1 / 3 ) x 15 = 5 next 30 million royalties / sales = ( 2 / 5 ) x 15 = 6 we can plug 5 and 6 into our percent change formula : ( new – old ) / old x 100 [ ( 6 – 5 ) / 5 ] x 100 1 / 5 x 100 , so a 20 % increase . answer b .
Answer: b
Question (general): a number is doubled and 9 is added . if the resultant is trebled , it becomes 63 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 63 2 x = 12 = > x = 6 answer : b"
Answer: b
Question (other): a bag holds 4 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 4 / 14 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: "given : 4 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 4 red and 3 green marbles after one red has been picked , we need to pick 1 red from a total of 3 red and 3 green marbles . p ( both red ) = ( 4 / 7 ) * ( 3 / 6 ) = 4 / 14 option a"
Answer: a
Question (physics): a train speeds past a pole in 15 seconds and speeds past a platform 100 meters long in 25 seconds . its length in meters is :
Options: a ) 60 m , b ) 70 m , c ) 100 m , d ) 120 m , e ) 150 m
Rationale: "let the length of the train be x metres and its speed be y metres / sec . then x / y = 15 y = x / 15 x + 100 / 25 now , ( x + 100 ) / 25 = x / 15 x = 150 m answer : e"
Answer: e
Question (general): a cab driver 5 days income was $ 300 , $ 150 , $ 750 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 500 , b ) $ 650 , c ) $ 420 , d ) $ 375 , e ) $ 625
Rationale: "avg = sum of observations / number of observations avg income = ( 300 + 150 + 750 + 400 + 500 ) / 5 = 420 answer is c"
Answer: c
Question (general): if 12401 is divided by any no . then quotient is 76 and remainder is 13 . what is divisor ?
Options: a ) 154 , b ) 124 , c ) 153 , d ) 163 , e ) 183
Rationale: divisor = ( dividend - remainder ) / quotient = ( 12401 - 13 ) / 76 = 12388 / 76 = 163 divisor = 163 answer d
Answer: d