regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 800 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 3999 , b ) 10000 , c ) 2500 , d ) 2772 , e ) 2912
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 800 b capital = 60000 * 1 / 6 = 10000 . answer : b"
Answer: b
Problem: a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 32 now , the son age 5 years back was
Options: a ) 11 , b ) 17 , c ) 11 , d ) 19 , e ) 99
Rationale: let the son ' s present age be x years . then , ( 32 - x ) = x x = 16 . son ' s age 5 years back = ( 16 - 5 ) = 11 years answer : a
Answer: a
Problem: the current in a river is 8 mph . a boat can travel 20 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 84 miles , c ) 96 miles , d ) 100 miles , e ) 112 miles
Rationale: "upstream speed = 20 - 8 = 12 mph downstream speed = 20 + 8 = 28 mph d / 12 + d / 28 = 10 hours solving for d we get d = 84 answer : b"
Answer: b
Problem: to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 9 hours a day ?
Options: a ) 34 , b ) 36 , c ) 32 , d ) 40 , e ) 44
Rationale: "man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 9 = 180 therefore number of days = 5760 / 180 = 32 days ans = c"
Answer: c
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 56 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 32 , d ) 20 , e ) 25
Rationale: "12 * 56 = 672 672 % 21 = 32 answer : c"
Answer: c
Problem: the h . c . f of two numbers is 36 and their l . c . m is 1600 . if one of the numbers is 160 , find the other ?
Options: a ) 320 , b ) 350 , c ) 360 , d ) 330 , e ) 320
Rationale: "explanation : the other number is = 36 * 1600 / 160 = 360 answer : option c"
Answer: c
Problem: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 21 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 63 , d ) 17 , e ) 01
Rationale: "explanation : as there is meal for 70 adults and 21 have their meal , the meal left can be catered to 49 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 49 adults = 63 children hence , the meal can be catered to 63 children . answer : c"
Answer: c
Problem: how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 30 / 51 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "there is no certain way to solve 2 unknown with 1 equation . the best way is to look at the question and retrospect the most efficient way . in this question , a and b are only positive integers . so that is a big relief . now , we can start with putting a = 1,2 , . . and so on till the time we are confident about one of the options . so , we start with a = 1 , we get b as - ve . out a = 2 , we get b as 6 . yes ( now ( a , b ) = ( 2,6 ) . we can directly see that ( a , b ) = ( 6,2 ) will also satisfy . so we have 2 possible solutions ) a = 3 , we get b as 3 . yes ( now we have 3 possible solutions ) a = 4 , we get b as fraction . out a = 5 , we get b again as some fraction . out a = 6 already taken . we have a , b options left . c , d , e are out . a is 6 . to have 6 as the answer , we will need one more pair like 2,6 and one more solution where a = b . when a = b , we have only 1 solution = 1 . so , one more solution , where a = b is not possible . so , answer will be d ."
Answer: d
Problem: rahim bought 42 books for rs . 520 from one shop and 22 books for rs . 248 from another . what is the average price he paid per book ?
Options: a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 11 , e ) s . 10
Rationale: "average price per book = ( 520 + 248 ) / ( 42 + 22 ) = 768 / 64 = rs . 12 answer : c"
Answer: c
Problem: a train running at the speed of 52 km / hr crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 260 metres , d ) 150 metres , e ) 100 meters
Rationale: "speed = 52 x 5 / 18 m / sec = 130 / 9 m / sec . length of the train = ( speed x time ) . length of the train = 130 / 9 x 18 m = 260 m . answer : c"
Answer: c
Problem: tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 45000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 10000 , c ) 25000 , d ) 34000 , e ) 30000
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 45000 = 25000 c"
Answer: c
Problem: a train running at the speed of 300 km / hr crosses a pole in 33 seconds . what is the length of the train ?
Options: a ) 2750 , b ) 2850 , c ) 2950 , d ) 3050 , e ) 3150
Rationale: "speed = ( 300 x ( 5 / 18 ) m / sec = ( 250 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 250 / 3 ) x 33 ) m = 2750 m a"
Answer: a
Problem: a rectangle having length 105 cm and width 40 cm . if the length of the rectangle is increased by 20 5 percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 25 % , b ) 19.23 % , c ) 40 % , d ) 75 % , e ) none of these
Rationale: explanation : solution : ( 25 / ( 105 + 25 ) * 100 ) % = 19.23 % answer : b
Answer: b
Problem: if n divided by 7 has a remainder of 2 , what is the remainder when 6 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "as per question = > n = 7 p + 2 for some integer p hence 6 n = > 42 q + 12 = > remainder = > 12 for some integer q alternatively = > n = 2 > 6 n = > 12 = > 12 divided by 7 will leave a remainder 5 hence d"
Answer: d
Problem: if 40 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 540 , b ) 528 , c ) 530 , d ) 520 , e ) 510
Rationale: "we know 37.5 % people study biology , therefore the no of people not studying = 100 - 40 = 60 % > therefore the people not studying biology out of a total 880 people are = 60 % of 880 > ( 60 / 100 ) * 880 = 528 people b"
Answer: b
Problem: the smallest number which when diminished by 3 , is divisible by 12 , 16 , 18 , 21 and 28 is
Options: a ) 1008 , b ) 1011 , c ) 1022 , d ) 1032 , e ) 1043
Rationale: "required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 3 = 1008 + 3 = 1011 answer : b"
Answer: b
Problem: a rectangular lawn of dimensions 80 m * 50 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) a ) 3820 , b ) b ) 930 , c ) c ) 9309 , d ) d ) 3600 , e ) e ) 8302
Rationale: "explanation : area = ( l + b – d ) d ( 80 + 50 – 10 ) 10 = > 1200 m 2 1200 * 3 = rs . 3600 answer : option d"
Answer: d
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.2 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 7 : 3 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 1 : 1
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.2 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.2 ) < = > k = 0.6 / 0.6 = 1 / 1 . required ratio = 1 / 1 : 1 = 1 : 1 . answer : e"
Answer: e
Problem: 3 candidates in an election and received 1000 , 2000 and 4000 votes respectively . what % of the total votes did the winning candidate got in that election ?
Options: a ) 45 % , b ) 50 % , c ) 57.14 % , d ) 60 % , e ) 65.12 %
Rationale: "total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 so , required percentage = 4000 / 7000 * 100 = 57.14 % c"
Answer: c
Problem: two numbers are less than third number by 20 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 5 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 12 %
Rationale: "let the third number is x . then first number = ( 100 - 20 ) % of x = 80 % of x = 80 x / 100 second number is ( 63 x / 100 ) difference = 80 x / 100 - 63 x / 100 = 17 x / 100 so required percentage is , difference is what percent of first number ( 17 x / 100 * 100 / 80 x * 100 ) % = 5 % answer : a"
Answer: a
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 45 % ?
Options: a ) 600 , b ) 887 , c ) 256 , d ) 654 , e ) 725
Rationale: "cost price = rs . 500 profit = 45 % of 500 = rs . 225 selling price = cost price + profit = 500 + 225 = 725 answer : e"
Answer: e
Problem: the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 20 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ?
Options: a ) $ 100 , b ) $ 120 , c ) $ 140 , d ) $ 160 , e ) $ 180
Rationale: "3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 20 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 20 ) = $ 120 . the answer is b ."
Answer: b
Problem: salesperson a ' s compensation for any week is $ 240 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 7000 , b ) $ 9000 , c ) $ 11,000 , d ) $ 13,000 , e ) $ 15,000
Rationale: "240 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 180 x = $ 9,000 the answer is b ."
Answer: b
Problem: a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 1300 . how many workers were part of the latter production run ?
Options: a ) a ) 6 , b ) b ) 10 , c ) c ) 9 , d ) d ) 15 , e ) e ) 23.5
Rationale: "the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 1300 . . thus for the current period = 1300 - 500 = 800 ( 5 n + 45 ) k = 800 k = 800 / 5 n + 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 equate 1 and 2 500 / 5 n + 20 = 800 / 5 n + 45 500 ( 5 n + 45 ) = 800 ( 5 n + 20 ) 25 n + 225 = 40 n + 160 - 15 n = - 65 n = 4 thus n + 5 = 9 hence c"
Answer: c
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 15 inches by 20 inches and jordan ' s rectangle is 6 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "area of first rectangle is 15 * 20 = 300 hence area of second would be 6 x = 300 x x = 50 answer is d"
Answer: d
Problem: martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 18.00 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 18 0.4 x = 2 = > x = 5 discounted tickets = 10 - x = 5 ans : c"
Answer: c
Problem: the purchase price of an article is $ 48 . in order to include 15 % of cost for overhead and to provide $ 12 of net profit , the markup should be
Options: a ) 15 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "cost price of article = 48 $ % of overhead cost = 15 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 15 = 40 % answer d"
Answer: d
Problem: in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 8 days , working 13.33 hours a day , the number of men required is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 13.33 : 8 : : 12 : x = > 8 x 13.33 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 13.33 ) = > x = 9 answer : e"
Answer: e
Problem: papaya , a popular soft drink , contains only 4 ingredients . soda water comprise 4 / 7 of papaya and natural lemon juice makes 1 / 3 of papaya . the amounts of sugar and papaya puree in papaya are equal . due to a malfunction , the mixing machine mixes double the regular amount of lemon juice and 3 times the regular amount of papaya puree . if no other changes were made to the relative quantities of the ingredients , what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine ?
Options: a ) 7 / 30 , b ) 7 / 21 , c ) 2 / 5 , d ) 12 / 29 , e ) 4 / 7
Rationale: soda water = 12 / 21 natural lemon juice = 7 / 21 the quantities of sugar and papaya puree are equal . total units are 21 of which 12 + 7 = 19 are used up by above two . remaining is 2 which is equally divided between sugar and papaya puree : sugar = 1 / 21 papaya puree = 1 / 21 thus ratio of soda : lemon : sugar : puree = 12 : 7 : 1 : 1 now , lemon is doubled , puree is three times and remaining are the same . resultant ratio is = 12 : 14 : 1 : 3 ratio of soda water in the resultant mixture = 12 / ( 12 + 14 + 1 + 3 ) = 12 / 30 = 2 / 5 answer : c
Answer: c
Problem: how long does a train 130 m long running at the speed of 80 km / hr takes to cross a bridge 140 m length ?
Options: a ) 13.9 sec , b ) 12.3 sec , c ) 17.9 sec , d ) 61.9 sec , e ) 47.98 sec
Rationale: "speed = 80 * 5 / 18 = 22 m / sec total distance covered = 130 + 140 = 270 m . required time = 270 / 22 = 12.3 sec . answer : b"
Answer: b
Problem: ramesh , xyz and rajeev put a partnership . profit is 36000 , if ramesh and xyz ratio is 5 : 4 and xyz and rajeev 8 : 9 . find rajeev ' s share .
Options: a ) 14000 , b ) 15000 , c ) 16000 , d ) 12000 , e ) 17000
Rationale: ramesh : xyz = 5 : 4 xyz : rajeev = 8 : 9 then ramesh : xyz / rajeev : xyz = 5 : 4 / 9 : 8 ramesh / rajeev = 10 / 9 therefore ramesh : xyz : rajeev = 10 : 8 : 9 then rajeev share = ( 9 / 27 ) * 36000 = 12000 answer : d
Answer: d
Problem: a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 10 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 30 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .
Options: a ) 20 % , b ) 43 % , c ) 99.33 % , d ) 75.109 % , e ) 47 %
Rationale: anyways , one can infer that he ' steals ' 10 % from suppliers and then charges 30 % extra to customers so basically 1.1 * 1.3 = 1.43 given that 1 is start point , we get 43 % more hence answer is b
Answer: b
Problem: in measuring the sides of a rectangle , one side is taken 14 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 2.4 % , c ) 8.3 % , d ) 5 % , e ) 2.6 %
Rationale: "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 114 * 95 = 10,830 , which is 8.3 % greater than the actual area . answer : c ."
Answer: c
Problem: in an office , totally there are 5200 employees and 45 % of the total employees are males . 50 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 1040 , b ) 1170 , c ) 1150 , d ) 4160 , e ) none of these
Rationale: "number of male employees = 5200 * 45 / 100 = 2340 required number of male employees who are less than 50 years old = 4160 * ( 100 - 50 ) % = 2340 * 50 / 100 = 1170 . answer : b"
Answer: b
Problem: a lady builds 12 cm length , 16 cm width , and 6 cm height box using 3 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 345 , b ) 384 , c ) 378 , d ) 398 , e ) 300
Rationale: "number of cubes required = volume of box / volume of cube = 12 * 16 * 6 / 3 = 384 cubes answer : b"
Answer: b
Problem: oil cans x and y are right circular cylinders and the height and radius of y are each 10 times those of x . if the oil in can x filled to capacity sells for $ 1 , how much does the oil in y sell for if y is only half filled ?
Options: a ) $ 400 , b ) $ 450 , c ) $ 500 , d ) $ 550 , e ) $ 600
Rationale: "formula for vol of a cyl is pi * r ^ 2 * h so vy = 1000 * vy y when half filled will cost 500 times x so ans is c"
Answer: c
Problem: the perimeter of a semi circle is 121 cm then the radius is ?
Options: a ) 17 , b ) 28 , c ) 24 , d ) 26 , e ) 12
Rationale: "36 / 7 r = 121 = > r = 24 answer : c"
Answer: c
Problem: if you write down all the numbers from 1 to 100 , then how many multiples of 3 ?
Options: a ) a ) 32 , b ) b ) 38 , c ) c ) 30 , d ) d ) 31 , e ) e ) 33
Rationale: division rule for 3 - sum of all digits is multiple of 3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 ans - e
Answer: e
Problem: if x + ( 1 / x ) = 5 , what is the value q of x ^ 2 + ( 1 / x ) ^ 2 ?
Options: a ) q = 21 , b ) q = 22 , c ) q = 23 , d ) 24 , e ) 27
Rationale: squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c
Answer: c
Problem: if 2 ^ 4 , 3 ^ 3 , and 13 ^ 3 are factors of the product of 1452 and w , where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 198 , b ) 288 , c ) 363 , d ) 396 , e ) 468
Rationale: i will go with e ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 13 ^ 1 = 468
Answer: e
Problem: a man is walking at a speed of 10 km per hour . after every kilometre , he takes rest for 7 minutes . how much time will be take to cover a distance of 7 kilometres ?
Options: a ) 80 min . , b ) 70 min . , c ) 84 min . , d ) 55 min . , e ) none of these
Rationale: "rest time = number of rest ã — time for each rest = 6 ã — 7 = 42 minutes total time to cover 7 km = ( 7 â  „ 10 ã — 60 ) minutes + 42 minutes = 84 minutes answer c"
Answer: c
Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 20 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 20 , b ) 1 / 20 , c ) 8 / 20 , d ) 3 / 20 , e ) 7 / 20
Rationale: "let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 } n ( x ) = 8 , n ( s ) = 20 hence , the required probability is 8 / 20 . answer : c"
Answer: c
Problem: in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many w eggs does the plant process per day ?
Options: a ) 100 , b ) 300 , c ) 400 , d ) 3,000 , e ) 4,000
Rationale: "straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there w = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c ."
Answer: c
Problem: if two painters can complete two rooms in two hours , how many rooms painted if 10 painters work for 6 hours ?
Options: a ) 35 , b ) 25 , c ) 20 , d ) 30 , e ) 15
Rationale: "explanation : two painters can complete two rooms in two hours . so 30 rooms can be painted in 6 hrs by 10 painters answer : d ) 10 painters"
Answer: d
Problem: what is the probability of getting exactly 2 heads in a single throw of five fair coins ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 16 , e ) 11 / 32
Rationale: "one possible case is hhttt . p ( hhttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 2 = 10 possible cases . p ( 2 heads ) = 10 * 1 / 32 = 5 / 16 the answer is d ."
Answer: d
Problem: the compound ratio of 2 : 3 , 3 : 4 and 4 : 5 ?
Options: a ) 1 : 2 , b ) 2 : 5 , c ) 3 : 4 , d ) 3 : 5 , e ) 3 : 9
Rationale: 2 / 3 * 3 / 4 * 4 / 5 = 2 / 5 2 : 5 answer : b
Answer: b
Problem: a certain university will select 2 of 6 candidates eligible to fill a position in the mathematics department and 3 of 5 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 ) 150 , d ) 165 , e ) 315
Rationale: "6 c 2 * 5 c 3 = 15 * 10 = 150 the answer is ( c )"
Answer: c
Problem: the probability that event b occurs is 0.4 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event a will occur ?
Options: a ) 0.05 , b ) 0.45 , c ) 0.15 , d ) 0.5 , e ) 0.55
Rationale: "p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.6 = 0.4 + p ( a ) - 0.25 p ( a ) = 0.45 ans : b"
Answer: b
Problem: when anunfaircoin is tossed twice , the probability of getting one tails and one heads is 1 / 2 . what is the probability of getting two heads and two tails if the coin is tossed 4 times ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 9
Rationale: let the probability of heads be x and the probability of tails be 1 - x . so , we are given that p ( one tails and one heads ) = 2 * x * ( 1 - x ) = 1 / 2 . p ( two heads and two tails ) = 4 ! / ( 2 ! 2 ! ) * x ^ 2 * ( 1 - x ) ^ 2 = 6 * ( x * ( 1 - x ) ) ^ 2 . we are multiplying by 4 ! / ( 2 ! 2 ! ) because hhtt scenario can occur in several ways : hhtt , htht , thht , . . . ( permutation of 4 letters hhtt where 2 t ' s and 2 h ' s are the same ) . since from 2 * x * ( 1 - x ) = 1 / 2 it follows that x * ( 1 - x ) = 1 / 4 , then 4 * ( x * ( 1 - x ) ) ^ 2 = 4 * ( 1 / 6 ) ^ 2 = 1 / 9 . answer : e .
Answer: e
Problem: amar takes as much time in running 15 meters as a car takes in covering 40 meters . what will be the distance covered by amar during the time the car covers 1.9 km ?
Options: a ) 700 m , b ) 720 m , c ) 712 m , d ) 600 m , e ) 640 m
Rationale: distance covered by amar = 15 / 40 ( 1.9 km ) = 3 / 8 ( 1900 ) = 712 m answer : c
Answer: c
Problem: at the end of the first quarter , the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 55 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 40 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 55 = 25 + b + 25 b / 100 b = 24 answer ( a )"
Answer: a
Problem: a marketing firm determined that , of 200 households surveyed , 80 used neither brand e nor brand b soap , 60 used only brand e soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45
Rationale: solution for soap e and soap b ( d ) 40
Answer: d
Problem: two employees x and y are paid a total of rs . 570 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 259 , b ) s . 289 , c ) s . 299 , d ) s . 300 , e ) s . 389
Rationale: let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 570 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 570 ⇒ y [ 12 / 10 + 1 ] = 570 ⇒ 22 y / 10 = 570 ⇒ 22 y = 5700 ⇒ y = 5700 / 22 = rs . 259 a )
Answer: a
Problem: a train 390 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 52 sec
Rationale: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 390 × 2 / 15 ) sec = 52 sec answer : e"
Answer: e
Problem: if 90 % of a = 30 % of b and b = x % of a , then the value of x is ?
Options: a ) 800 , b ) 300 , c ) 700 , d ) 400 , e ) none of these
Rationale: "0.9 a = 0.3 b so b = 3 a means 300 % of a answer : b"
Answer: b
Problem: data sufficiency question : if solution ( x ) with alcohol ( 14 % ) and solution ( y ) with alcohol ( 20 % ) mixed together to form 24 liters of mixture .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 3
Rationale: explanation : let a liters of first solution , and ' b ' liters of second solution has been taken . so using weighted average formula = n 1 × a 1 + n 2 × a 2 n 1 + n 2 n 1 × a 1 + n 2 × a 2 n 1 + n 2 = n 1 × 14 + n 2 × 20 n 1 + n 2 = 15 n 1 × 14 + n 2 × 20 n 1 + n 2 = 15 ⇒ n 1 = 5 n 2 ⇒ n 1 n 2 = 51 ⇒ n 1 = 5 n 2 ⇒ n 1 n 2 = 51 as total volume was given as 24 liters , first solution = 16 × 24 = 416 × 24 = 4 so statement 1 is sufficient . answer : a
Answer: a
Problem: the average of 6 number is 3.95 . the average of two of them is 3.8 , while the average of the other two is 3.85 . what is the average of the remaining two number ?
Options: a ) 4.5 , b ) 4.2 , c ) 4.7 , d ) 4.8 , e ) none of these
Rationale: solution : sum of the remaining two numbers = ( 3.95 × 6 ) - [ ( 3.8 × 2 ) + ( 3.85 × 2 ) ] = 23.70 - ( 7.6 + 7.7 ) = 23.70 - 15.3 = 8.4 . ∴ required average = 8.4 / 2 = 4.2 answer b
Answer: b
Problem: a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points q that an individual player might have scored ?
Options: a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23
Rationale: general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points q for 12 th player is 100 - 77 = 23 . answer : e .
Answer: e
Problem: jill has 7 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 14
Rationale: let the number of each size of jar = w then 1 / 4 w + 1 / 2 w + w = 7 1 3 / 4 w = 7 w = 4 the total number of jars = 3 w = 12 answer : d
Answer: d
Problem: the sum of ages of 5 children born 2 years different each is 50 yrs . what is the age of the elder child ?
Options: a ) 8 , b ) 14 , c ) 16 , d ) 17 , e ) 18
Rationale: let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 5 x = 30 x = 6 x + 8 = 6 + 8 = 14 answer : b
Answer: b
Problem: vijay sells a cupboard at 14 % below cost price . had he got rs . 2086 more , he would have made a profit of 14 % . what is the cost price of the cupboard ?
Options: a ) 7458 , b ) 7456 , c ) 7450 , d ) 7454 , e ) 7453
Rationale: "explanation : cost price = 2086 / ( 0.14 + 0.14 ) = 2086 / 0.28 = rs . 7450 answer : c"
Answer: c
Problem: we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 390 . how many math books did we buy ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "m + h = 80 h = 80 - m 4 m + 5 h = 390 4 m + 5 * ( 80 - m ) = 390 m = 10 the answer is a ."
Answer: a
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 132 mins , e ) 130 mins
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 36 = > 4 / x = 1 / 36 x = 36 â ˆ — 4 = 144 mins answer is a"
Answer: a
Problem: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 6 dm by 5 dm . the number of stones required is :
Options: a ) 180 , b ) 1800 , c ) 18 , d ) 18000 , e ) 1.8
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 60 * 50 ) therefore , number of stones = ( 3600 * 1500 / 60 * 50 ) = 1800 answer : b"
Answer: b
Problem: walking with 4 / 5 of my usual speed , i arrive at the bus stop 10 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48
Rationale: "let t = usual time = distance / usual speed t + 10 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 40 the answer is c ."
Answer: c
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 480 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 32 / 15 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 5 / 3
Rationale: "distance traveled by eddy = 480 km time taken by eddy = 3 hours average speed of eddy = 480 / 3 = 160 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 160 / 75 = 32 / 15 answer a"
Answer: a
Problem: a pharmaceutical company received $ 2 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "( 9 / 108 ) / ( 2 / 20 ) = 30 / 54 = 55,5 % it means that 9 / 108 represents only 83,3 % . therefore a decrease of 15 % . answer b"
Answer: b
Problem: ram , who is half as efficient as krish , will take 24 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 8 days , d ) 6 days , e ) 18 days
Rationale: "answer ram takes 24 days to complete the task , if he works alone . krish is twice as efficient as ram is . so , working alone , krish will take half the time to complete the task . i . e . , 12 days . ram will complete 1 / 24 th of the task in a day . krish will complete 1 / 12 th of the task in a day . when they work together , they will complete 1 / 24 + 1 / 12 = 1 / 8 th of the task in a day . therefore , when they work together they will complete the task in 8 days . choice c"
Answer: c
Problem: i bought two books ; for rs . 540 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 197 , b ) 280 , c ) 189 , d ) 278 , e ) 315
Rationale: "x * ( 85 / 100 ) = ( 540 - x ) 119 / 100 x = 315 answer : e"
Answer: e
Problem: a sum of money deposited at c . i . amounts to rs . 1980 in 3 years and to rs . 2492 in 4 years . find the rate percent ?
Options: a ) 30 % , b ) 10 % , c ) 25 % , d ) 19 % , e ) 50 %
Rationale: "1980 - - - 512 100 - - - ? = > 25 % answer : c"
Answer: c
Problem: what is the greatest possible length which can be used to measure exactly the lengths 10 m , 14 m 50 cm and 20 m 40 cm cm ?
Options: a ) 20 cm , b ) 10 cm , c ) 25 cm , d ) 50 cm , e ) 28 cm
Rationale: "required length = hcf of 1000 cm , 1450 cm , 2040 cm = 10 cm answer is b"
Answer: b
Problem: an alloy weighing 18 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
Options: a ) 6 , b ) 90 , c ) 12 , d ) 24 , e ) 48
Rationale: "in 24 ounces , gold is 18 * ( 70 / 100 ) = 12.6 ounces . now we add x ounces of pure gold to make it 90 % gold . so 12.6 + x = ( 24 + x ) * 90 / 100 = > x = 90 . answer is b ."
Answer: b
Problem: john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 55 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 55 = > v = 50 ( option c ) ."
Answer: c
Problem: a train 400 m long can cross an electric pole in 40 sec and then find the speed of the train ?
Options: a ) 36 kmph , b ) 40 kmph , c ) 42 kmph , d ) 45 kmph , e ) 38 kmph
Rationale: "length = speed * time speed = l / t s = 400 / 40 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : a"
Answer: a
Problem: a train 220 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is :
Options: a ) 41 , b ) 40.6 , c ) 40.8 , d ) 42 , e ) 42.6
Rationale: "speed of the train relative to man = 220 / 20 = 11 m / sec . = 11 x 18 / 5 km / hr = 198 / 5 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 198 / 540.6 km / hr . answer : b"
Answer: b
Problem: the price of a certain painting increased by 10 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 105 % , c ) 95 % , d ) 93.5 % , e ) 90 %
Rationale: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 10 = 110 price at the end of year 2 = 110 - 110 * 0.15 = 110 * 0.85 = 93.5 hence required answer = ( 93.5 / 100 ) * 100 % = 93.5 % answer is d ."
Answer: d
Problem: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 16 seconds . the length of the faster train is
Options: a ) 80 m , b ) 100 m , c ) 120 m , d ) 180 m , e ) none
Rationale: "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 16 ) m = 360 m . answer e"
Answer: e
Problem: a and b began business with rs . 7000 and rs . 15000 after 6 months , a advances rs . 3000 and b withdraws rs . 5000 . at the end of the year , their profits amounted to rs . 2940 find the share of a and b respectively .
Options: a ) 1100 , 1750 , b ) 1140 , 1800 , c ) 940 , 2000 , d ) 1190 , 1750 , e ) 1000 : 1690
Rationale: "7 * 6 + 10 * 6 ) : ( 15 * 6 + 10 * 6 ) = 102 : 150 = 51 : 75 = 17 : 25 17 : 25 a ' s share = 17 / 42 * 2940 = 1190 . b ' s share = 25 / 42 * 2940 = 1750 . a and b shares respectively 1190 and 1750 . answer : d"
Answer: d
Problem: in country z , 10 % of the people do not have a university diploma but have the job of their choice , and 15 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 39 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 40 % not job of choice with diploma = . 15 x not job of choice w / o diploma = . 85 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 15 % of 60 % = 9 % . we can also see that 30 % of the people have their job of choice and a diploma ( 40 % - 10 % = 30 % ) . 30 % + 9 % = 39 % . therefore 39 % of the people in country z have a diploma . ans a"
Answer: a
Problem: the present worth of rs . 676 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 150.50 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 625 , e ) none
Rationale: solution present worth = rs . [ 676 / ( 1 + 4 / 100 ) ² ] = rs . ( 676 x 25 / 26 x 25 / 26 ) = rs . 625 answer d
Answer: d
Problem: a shopkeeper sold an article for rs 2591.36 . approximately what was his profit percent if the cost price of the article was rs 2400
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 8 % , e ) 10 %
Rationale: "explanation : gain % = ( 191.36 * 100 / 2400 ) = 7.97 % = 8 % approx option d"
Answer: d
Problem: dacid obtained 86 , 89 , 82 , 87 and 81 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 99 , c ) 88 , d ) 85 , e ) 75
Rationale: "average = ( 86 + 89 + 82 + 87 + 81 ) / 5 = 425 / 5 = 85 . answer : d"
Answer: d
Problem: the product of two positive integers is 783 and their difference is 2 . what is the bigger number ?
Options: a ) 23 , b ) 25 , c ) 27 , d ) 29 , e ) 31
Rationale: "let ' s use trial and error to find the two numbers . 30 * 28 = 840 ( too high ) 29 * 27 = 783 the answer is d ."
Answer: d
Problem: matt gets a $ 1,000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 700 , how many sales has matt made ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 700 = 150 + x i . e . x = 550 i . e . y = 2 new sales = y + 1 = 3 answer : option a"
Answer: a
Problem: water is poured into a cylindrical well at the rate of 22 cubic meters per hour , the level of water in the tank rises at a rate of 0.7 meters per hour . which of the following best approximates the diameter of the tank in meters ?
Options: a ) √ 10 / 2
b ) √ 10
c ) 2 √ 10
d ) 5
e ) 10
Rationale: here ' s my re - worked solution : volume = 22 = pi ( r ^ 2 ) ( 0.7 ) 22 = 22 / 7 ( 7 / 10 ) ( r ^ 2 ) 10 = r ^ 2 r = sqrt ( 10 ) diameter = 2 * sqrt ( 10 ) ans : c
Answer: c
Problem: how many different 3 - digit multiples of 5 can be composed of digits 1 , 2 , 3 , 4 , and 5 if none of the digits is repeated ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 18
Rationale: can you explain your method . i solved it differently xyz , where z must be 5 . therefore 1 variation of digit in z . y can be any of the 4 possible choices . x can be any of the 3 possible choices . 4 + 3 + 1 = 8 c
Answer: c
Problem: a student finds the sum 1 + 2 + 3 + . . . as his patience runs out . he found the sum as 575 . when the teacher declared the result wrong , the student realized that he missed a number . what was the number the student missed ?
Options: a ) 16 , b ) 18 , c ) 14 , d ) 20 , e ) 22
Rationale: explanation : sum of 1 st 10 natural numbers ( 1 – 10 ) = 1 + 2 + … 10 = 55 . sum of next 10 natural numbers ( 11 – 20 ) = 10 + 11 + 12 + … 20 = 100 + 55 = 155 . sum of next 10 natural numbers ( 31 – 40 ) = 255 . sum of numbers from 31 – 40 = 355 and so on and on . so , we have here 55 + 155 + 255 = 465 . if we add 355 to 465 , it will be way more than 575 . so , we can add one by one . 465 + 31 + 32 + 33 = 561 . 465 + 31 + 32 + 33 + 34 = 595 . thus , the sum should be 595 instead of 575 , and the missing number is 20 . answer : d
Answer: d
Problem: dhoni spends $ 300 buying his favorite dolls . if he buys only small monkey dolls , which are $ 2 cheaper than the large monkey dolls , he could buy 25 more dolls than if he were to buy only large monkey dolls . how much does a large monkey doll cost ?
Options: a ) $ 6.5 , b ) $ 6 , c ) $ 7 , d ) $ 8 , e ) $ 9
Rationale: a is not an integer . so we start with b . if large doll costs $ 6 , then he can buy 300 / 6 = 50 large dolls and 300 / 4 = 75 small dolls . difference is 25 , which is we wanted . answer b .
Answer: b
Problem: set x consists of 5 integers and has median of 20 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 20 , b ) 37 , c ) c . 40 , d ) 43 , e ) 50
Rationale: "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 this is possible . hence it is the greatest such number . answer ( a )"
Answer: a
Problem: find the principle on a certain sum of money at 8 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 939.6 , b ) 928.8 , c ) 927.78 , d ) 926.82 , e ) 902.1
Rationale: "1120 = p [ 1 + ( 8 * 12 / 5 ) / 100 ] p = 939.60 answer : a"
Answer: a
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 21.6 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 28 % , c ) 30 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 121.60 let marked price be rs . x . then , 95 / 100 x = 121.60 x = 12160 / 95 = rs . 128 now , s . p . = rs . 128 , c . p . = rs . 100 profit % = 28 % . answer : b"
Answer: b
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 10 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 22 , b ) 21 , c ) 88 , d ) 30 , e ) 29
Rationale: "explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 10 ) + 6000 ( v - 10 ) < = > 2000 v = 60000 < = > v = 30 answer : d ) 30"
Answer: d
Problem: in a kilometer race , a beats b by 100 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 90 sec , b ) 190 sec , c ) 290 sec , d ) 490 sec , e ) 390 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 100 = 100 sec . time taken by a = 100 - 10 = 90 sec . answer : a"
Answer: a
Problem: a space shuttle orbits the earth at about 4 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 14,400 , c ) 24,200 , d ) 28,800 , e ) 48,000
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 4 * 3600 = 14,400 answer : b"
Answer: b
Problem: what is the remainder when 14452 × 15652 × 16781 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 2 * 2 * 1 = will give units digit as 4 so , whatever be the number , if it ends in 4 , the remainder after dividing with 5 will be 4 . optione
Answer: e