Cheukting/mathqa huggingface dataset:
Question (physics): an outlet pipe empties a tank which is full in 8 hours . if the inlet pipe is kept open , which lets water in at the rate of 8 litres / min then outlet pipe would take 4 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 200 litres , c ) 12800 litres , d ) 11520 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 8 * 60 = 480 liters / hour ; net outflow rate when both pipes operate would be x - 480 liters / hour . capacity of the tank = x * 8 hours = ( x - 480 ) * ( 8 + 4 ) hours 8 x = ( x - 480 ) * 12 - - > x = 1440 - - > capacity = 8 x = 11520 liters . answer : d ."
Answer: d
Question (general): how should we mix two rice packets to get one 1 kg packet priced at rs 8 when the prices of 1 kg packets of the two types are rs 7.1 and rs 9.2 .
Options: a ) 4 : 3 , b ) 4 : 7 , c ) 4 : 9 , d ) 4 : 2 , e ) 4 : 1
Rationale: explanation : no explanation is available for this question ! answer : a
Answer: a
Question (physics): car a runs at the speed of 35 km / hr & reaches its destination in 9 hr . car b runs at the speed of 43 km / h & reaches its destination in 10 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 65 : 69 , b ) 56 : 45 , c ) 89 : 71 , d ) 68 : 23 , e ) 63 : 86
Rationale: "sol . distance travelled by car a = 35 × 9 = 315 km distance travelled by car b = 43 × 10 = 430 km ratio = 315 / 430 = 63 : 86 e"
Answer: e
Question (gain): a and b ’ s salaries together amount to rs . 3,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is a ’ s salary ?
Options: a ) 2777 , b ) 2250 , c ) 2789 , d ) 2776 , e ) 2881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 3000 4 b = 3000 = > b = 750 a = 2250 answer b"
Answer: b
Question (general): the average weight of 3 packets a , b and c is 84 kg . another packet d added into the group and the average now becomes 80 kg . if another packet e , whose weight is 3 kg more than that of d , replaces a then the average weight of b , c , d and e becomes 79 kg . the weight of a is :
Options: a ) 70 kg , b ) 72 kg , c ) 75 kg , d ) 80 kg , e ) none of these
Rationale: explanation : a + b + c = ( 84 x 3 ) = 252 kg , a + b + c + d = ( 80 x 4 ) = 320 kg . d = ( 320 - 252 ) = 68 , e = ( 68 + 3 ) = 7 l . b + c + d + e = ( 79 x 4 ) = 316 . ( a + b + c + d ) - ( b + c + d + e ) = ( 320 - 316 ) kg = 4 kg . a - e = 4 = a = ( 4 + e ) = 75 kg answer : c
Answer: c
Question (physics): the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 60 kmph its consumption is 1 litre per hour . if each litre costs $ 30 and other expenses per hous is $ 20 , then what would be the minimum expenditure required to cover a distance of 600 km ?
Options: a ) 500 , b ) 450 , c ) 600 , d ) 650 , e ) 750
Rationale: 60 kmph consumption is 1 lt / hr so 600 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 30 so 10 lt costs $ 300 extra expenses for 1 hr - $ 20 10 hrs - $ 200 total expense - $ 300 + $ 200 = $ 500 answer : a
Answer: a
Question (general): if the average of 10 consecutive integers is 19.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 24 , e ) 25
Rationale: "the average falls between the 5 th and 6 th integers , integer 5 = 19 , integer 6 = 20 . counting up to the tenth integer we get 24 . answer : d"
Answer: d
Question (physics): on the first day of her vacation , louisa traveled 100 miles . on the second day , traveling at the same average speed , she traveled 175 miles . if the 100 - mile trip took 3 hours less than the 175 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 27 , b ) 28 , c ) 25 , d ) 30 , e ) 35
Rationale: "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 100 / t = 175 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 100 / 4 = 25 answer : c"
Answer: c
Question (general): at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 28 liters of forest green to change it to verdant green ?
Options: a ) 28 / 3 , b ) 13 / 6 , c ) 3 , d ) 4 , e ) 14 / 3
Rationale: "28 liter of forset green have 16 liter of blue and 12 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 16 / ( 12 + x ) = ¾ 36 + 3 x = 64 = > x = 28 / 3 answer : a"
Answer: a
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 minutes , then what is the area of the park ( in sq . m ) ?
Options: a ) 153500 , b ) 153650 , c ) 153600 , d ) 153700 , e ) 153750
Rationale: "let length = 3 x km , breadth = 2 x km distance travelled by the man at the speed of 12 km / hr in 8 minutes = 2 ( 3 x + 2 x ) = 10 x therefore , 12 × 860 = 10 xx = 425 km = 160 m area = 3 x × 2 x = 6 x 2 = 6 × 1602 = 153600 m 2 answer is c ."
Answer: c
Question (general): in a office work is distribute between p persons . if 1 / 5 members are absent then work increased for each person is ?
Options: a ) 13.28 % , b ) 14.28 % , c ) 15.28 % , d ) 16.28 % , e ) 25 %
Rationale: "let total % of work is 100 % total person = p 1 / 5 person are absent of total person . so absent person is 1 / 5 p ie p / 5 . left person is , p - p / 5 = 4 p / 5 . p person do the work 100 % 1 person do the work 100 * p % 4 p / 5 person do the work ( 100 * p * 5 ) / 4 p % = 125 % work increased for each person is = ( 125 - 100 ) % = 25 % answer : e"
Answer: e
Question (general): what could be the range of a set consisting of odd multiples of 5 ?
Options: a ) 21 , b ) 24 , c ) 35 , d ) 62 , e ) 60
Rationale: "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 5 * ( 2 n + 1 ) where n is any positive integer . range = 5 * ( 2 m + 1 ) - 5 * ( 2 n + 1 ) = 5 * 2 * ( m - n ) = 10 * ( m - n ) . m , n - any positive integers the answer must be divisible by 10 , which is only 60 . the correct answer is e ."
Answer: e
Question (gain): a book is bought for $ 60 and sold for $ 75 . what is the profit in percentage ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "75 / 60 = 1.25 the answer is d ."
Answer: d
Question (general): how many multiples of 5 are there between 5 to 85 ?
Options: a ) 15 , b ) 18 , c ) 17 , d ) none of these , e ) can not be determined
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 . answer : a"
Answer: a
Question (general): the difference between a number and its two - fifth is 510 . what is 10 % of that number ?
Options: a ) 12.75 , b ) 85 , c ) 204 , d ) 250 , e ) none of these
Rationale: "explanation : let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 10 % of 850 = 85 . answer is b"
Answer: b
Question (general): in a recent election , james received 0.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 45 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 891 , e ) 1,001
Rationale: "james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 45 / 100 ) * total votes + 1 = ( 45 / 100 ) * 2000 + 1 = 901 remaining voted needed to win election = 901 - 10 = 891 answer : option d"
Answer: d
Question (gain): the value of a machine depreciates at 23 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
Options: a ) $ 252935 , b ) $ 432935 , c ) $ 122935 , d ) $ 112935 , e ) $ 152935
Rationale: "the value of the machine after two years = 0.77 * 0.77 * 1 , 50,000 = $ 88,935 sp such that a profit of $ 24,000 is made = 88,935 + 24,000 = $ 1 , 12,935 d"
Answer: d
Question (physics): a train travels 240 km in 3 hours and 450 km in 5 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 60 kmph , c ) 86 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 240 + 450 = 690 km thus , total speed = 8 hrs or , average speed = 690 / 8 or , 86 kmph . answer : c"
Answer: c
Question (general): a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 1,400
Rationale: in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 3,000 - $ 880 = $ 2,120 . answer : b .
Answer: b
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 12 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 200 meter , c ) 156 meter , d ) 168 meter , e ) 154 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 12 = 200 meter answer : b"
Answer: b
Question (physics): two trains of equal lengths take 12 sec and 24 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 18 sec , b ) 12 sec , c ) 17 sec , d ) 21 sec , e ) 16 sec
Rationale: "speed of the first train = 120 / 12 = 10 m / sec . speed of the second train = 120 / 24 = 5 m / sec . relative speed = 10 + 5 = 15 m / sec . required time = ( 120 + 120 ) / 15 = 16 sec . answer : e"
Answer: e
Question (probability): set a contains 4 different positive odd integers and 6 different positive even integers . set b contains two different positive odd integers and 3 different positive even integers . if one integer from set a and one integer from set b are chosen at random , what is the probability that the product of the chosen integers is even ?
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 17 / 25 , d ) 21 / 25 , e ) 43 / 50
Rationale: there can be an odd product only if both integers are odd . p ( odd product ) = 4 / 10 * 2 / 5 = 4 / 25 p ( even product ) = 1 - 4 / 25 = 21 / 25 the answer is d .
Answer: d
Question (physics): a and b can do a piece of work in 16 days , b and c in 24 days , c and a in 12 days . how long will c take to do it ?
Options: a ) 16 days , b ) 55 days , c ) 24 days , d ) 32 days , e ) 22 days
Rationale: "2 c = 1 / 24 + 1 / 12 – 1 / 16 = 1 / 16 c = 1 / 32 = > 32 days answer : d"
Answer: d
Question (gain): population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrement of 35 % and in 2007 there is an increment of 45 % , then find the population of city at theend of the year 2007
Options: a ) 2456789 , b ) 3458009 , c ) 3890043 , d ) 3455048 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1083875 e"
Answer: e
Question (physics): a searchlight on top of the watch - tower makes 3 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "3 revolutions per minute = 1 revolution every 20 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 20 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 5 seconds ) = 1 - p ( man in dark for max of 5 seconds ) = 1 - 5 / 20 = 1 - 1 / 4 = 3 / 4 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 20 seconds because that is the max . in this approach it would be 15 / 20 seconds = 3 / 4 ."
Answer: e
Question (gain): in the first 10 overs of a cricket game , the run rate was only 4.8 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 4.25 , b ) 5.85 , c ) 6.25 , d ) 7 , e ) 7.5
Rationale: "required run rate = 282 - ( 4.8 x 10 ) = 234 234 / 40 = 5.85 b )"
Answer: b
Question (physics): the timing of a college is from 12 p . m to 4.20 p . m . six lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 30 minutes , d ) 39 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 4 hours 20 minutes = 260 minutes as there are 6 lectures , the number of breaks between lectures is 5 . total time of the break = 25 minutes hence , the duration of each lecture is = ( 260 â € “ 25 ) / 6 = 39 minutes answer d"
Answer: d
Question (physics): a man rows his boat 75 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 9
Rationale: "speed downstream = d / t = 75 / ( 2 1 / 2 ) = 30 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 30 - 18 ) / 2 = 6 kmph answer : a"
Answer: a
Question (general): in the land of oz only one or two - letter words are used . the local language has 66 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 132
Rationale: "the seventh letter ( let it be @ ) can be used with other 65 in two type of arrangents one when seventh letter is in 1 st slot @ _ ( 65 ways ) another , when seventh letter is in 2 nd slot _ @ ( 65 ways ) seventh letter ( @ ) itself lost words = 1 + 65 + 65 = 131 answer : d"
Answer: d
Question (general): the sum of the first 100 numbers , 1 to 100 is always divisible by
Options: a ) 2 , b ) 2 and 4 , c ) 2 , 4 and 8 , d ) 2 , 4 and 9 , e ) none of these
Rationale: explanation : the sum of the first 100 natural numbers = ( 100 x 101 ) / 2 = ( 50 x 101 ) as 101 is an odd number and 50 is divisible by 2 , so the sum is always divisible by 2 . answer : option a
Answer: a
Question (geometry): a horse is tethered to one corner of a rectangular grassy field 45 m by 25 m with a rope 22 m long . over how much area of the field can it graze ?
Options: a ) 354 cm 2 , b ) 380 m 2 , c ) 350 m 2 , d ) 407 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 22 ) 2 = 380 m 2 answer b"
Answer: b
Question (gain): p and q started a business investing rs . 85,000 and rs . 35,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 7 , d ) 17 : 2 , e ) 17 : 3
Rationale: p : q = 85000 : 35000 = 17 : 7 . answer : c
Answer: c
Question (physics): a can complete a project in 30 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 27 days , c ) 26.67 days , d ) 5 days , e ) 12 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 30 ) * ( x - 10 ) + ( 1 / 30 ) * ( x ) = 1 ( x / 30 ) + ( x / 30 ) - ( 10 / 30 ) = 1 2 x / 30 = 1 / 3 x = 5 therefore , the answer is d : 5 ."
Answer: d
Question (physics): express a speed of 42 kmph in meters per second ?
Options: a ) 10 mps , b ) 18 mps , c ) 19 mps , d ) 17 mps , e ) 12 mps
Rationale: "42 * 5 / 18 = 12 mps answer : e"
Answer: e
Question (general): a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 5 more blue balls than white balls , and thrice as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 5 more blue balls than white balls . . . equation # 2 : y = 5 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 3 y solve equation # 2 for z : z = y - 5 now , we can replace both x and z with y in equation # 1 3 y + y + ( y - 5 ) = 100 5 y - 5 = 100 5 y = 105 y = 21 there are 21 blue balls . this is 5 more than the number of white balls , so z = 16 . that ' s the answer . just as a check , x = 63 , and 63 + 21 + 16 = 100 . answer = 16 , ( e )"
Answer: e
Question (gain): mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 459 ?
Options: a ) 18 % , b ) 21 % , c ) 20 % , d ) 26.1 % , e ) none of these
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 459 , discount = 621 - 459 = 162 discount % = 162 / 621 * 100 = 26.1 % answer : d"
Answer: d
Question (other): income and expenditure of a person are in the ratio 7 : 6 . if the income of the person is rs . 21000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3000 , e ) rs . 3602
Rationale: "let the income and the expenditure of the person be rs . 7 x and rs . 6 x respectively . income , 7 x = 21000 = > x = 3000 savings = income - expenditure = 7 x - 6 x = x so , savings = rs . 3000 answer : d"
Answer: d
Question (general): a man spends 1 / 3 rd of his salary on food . he spends 1 / 4 th on rent and 1 / 5 th on cloths . if he is left with 1760 , then who much salary does he earn
Options: a ) 8223 , b ) 8123 , c ) 8323 , d ) 8423 , e ) 8523
Rationale: let total salary be x a / q = > x = ( x / 3 ) + ( x / 4 ) + ( x / 5 ) + 1760 = > x - 47 x / 60 = 1760 = > 13 x / 60 = 1760 = > x = 1760 * 60 / 13 = > x = 8123 ( approax ) answer : b
Answer: b
Question (general): what is the largest 4 digit number exactly divisible by 48 ?
Options: a ) 4676 , b ) 4678 , c ) 9984 , d ) 9504 , e ) 9936
Rationale: largest 4 digit number = 9999 9999 ÷ 48 = 208 , remainder = 15 hence largest 4 digit number exactly divisible by 48 = 9999 - 15 = 9984 answer : c
Answer: c
Question (other): the ratio of length of two refill is 9 : 8.2 nd refill got damaged when only half length of 2 nd refill get used . the ratio of total no . of pages written by both refill .
Options: a ) 8 : 3 , b ) 6 : 5 , c ) 9 : 8 , d ) 9 : 4 , e ) 5 : 4
Rationale: the no . of page written is directly proportional to length of refill . so , initial no . of page to be write = 9 x , 8 x . now , 2 nd refill only can write 4 x page so new ratio of page written = 9 x / 4 x = 9 : 4 . answer d
Answer: d
Question (physics): a train running at the speed of 45 km / hr crosses a pole in 16 seconds . find the length of the train .
Options: a ) 200 , b ) 188 , c ) 204 , d ) 288 , e ) 500
Rationale: "speed = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec length of train ( distance ) = speed * time ( 25 / 2 ) * 16 = 200 meter answer : a"
Answer: a
Question (general): he number of times a bucket of capacity 4 liters to be used to fill up a tank is less than number of ties another bucket of capacity 3 liters used for the same purpose by 4 . what is the capacity of the tank ?
Options: a ) 360 liters , b ) 256 , c ) 48 , d ) 525 , e ) 425
Rationale: 4 x = 3 ( x + 4 ) , where x may be number of times 4 l bucket is used . 4 x = 3 ( x + 4 ) - - > 1 . x = 12 , substitute x to lhs or rhs of 1 , which gets you the capacity , and it is 48 . answer : c
Answer: c
Question (gain): a and b start a business , with a investing the total capital of rs . 5000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 500 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) a ) 2500 , b ) b ) 3500 , c ) c ) 5000 , d ) d ) 6000 , e ) e ) 8000
Rationale: interest received by a from b = 10 % of half of rs . 5000 = 10 % * 2500 = 250 . amount received by a per annum for being a working partner = 500 * 12 = rs . 1000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 250 + 1000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 250 + 1000 + p ) = 2 ( p ) p = 1250 total profit = 2 p + 1000 = 2 * 1250 + 1000 = 3500 answer : b
Answer: b
Question (probability): two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability w that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability w = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Question (physics): how many plants will be there in a circular bed whose outer edge measure 35 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 24 , d ) 19 , e ) none of these
Rationale: "circumference of circular bed = 35 cm area of circular bed = ( 35 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 35 ) 2 â  „ 4 ï € ã · 4 = 24.36 = 24 ( approx ) answer c"
Answer: c
Question (other): the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 700 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84 , b ) 1.75 , c ) 3.28 , d ) 2.72 , e ) none of these
Rationale: "here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 700 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 700 * 2 * ( 4 / 5 ) = 1120 2160 + 1120 = 3280 solving for units gives us 3.28 so the answer is c"
Answer: c
Question (general): find the last 3 digit of 443 ^ 443 .
Options: a ) 306 , b ) 307 , c ) 308 , d ) 309 , e ) 310
Rationale: power is 443 = > 443 / 4 rem = 3 so , 443 ^ 3 = 86938307 last 3 digit = 307 answer : b
Answer: b
Question (general): the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 78 , and last 6 numbers is 75 then find 6 th number ?
Options: a ) a ) 258 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48
Rationale: "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 78 + 6 * 75 - 11 * 60 = 258 answer is a"
Answer: a