Cheukting/mathqa huggingface dataset:
Question (general): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (physics): 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
Question (geometry): 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
Question (general): 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
Question (other): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (gain): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (other): 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
Question (gain): 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
Question (geometry): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (probability): 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
Question (general): 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
Question (physics): 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
Question (probability): 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
Question (other): 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
Question (other): 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
Question (other): 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
Question (general): 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
Question (physics): 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