Cheukting/mathqa huggingface dataset:
Question (physics): tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many q minutes it takes john to reach the station ?
Options: a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min
Rationale: since the question states “ after 15 minutes ” , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john ’ s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , q = 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c .
Answer: c
Question (physics): a student completes a 3 part exam as follows . the student completes section a in 10 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 5 : 2 , b ) 4 : 1 , c ) 4 : 3 , d ) 3 : 2 , e ) 2 : 1
Rationale: the time spent on section b and section c is 25 minutes each . the ratio of c to a is 25 : 10 = 5 : 2 the answer is a .
Answer: a
Question (general): a person ' s present age is two - fifth of the age of his father . after 8 years , he will be one - half of the age of his father . how old is the father at present ?
Options: a ) a ) 40 , b ) b ) 48 , c ) c ) 32 , d ) d ) 45 , e ) e ) 28
Rationale: "let the father ' s present age be x years then the person ' s present age = 2 x / 5 ( 2 x / 5 ) + 8 = 1 / 2 ( x + 8 ) 2 ( 2 x + 40 ) = 5 ( x + 8 ) x = 40 answer is a"
Answer: a
Question (general): a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 21 liters of drink a to convert it to drink b ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "in 21 liters of drink a , there are 12 liters of milk and 9 liters of juice . with 12 liters of milk , we need a total of 16 liters of juice to make drink b . we need to add 7 liters of juice . the answer is e ."
Answer: e
Question (other): the l . c . m . of two numbers is 54 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 32 , c ) 40 , d ) 45 , e ) 54
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 54 or x = 9 . the numbers are 18 and 27 . hence , required sum = ( 18 + 27 ) = 45 . answer : option d"
Answer: d
Question (gain): simple interest on a certain sum of money for 3 years at 8 % per annum is half the compound interest on rs . 4000 for 2 years at 10 % per annum . the sum placed on simple interest is
Options: a ) rs 1650 , b ) rs 1750 , c ) rs 1850 , d ) rs 1950 , e ) none of these
Rationale: "explanation : c . i . = ( 4000 × ( 1 + 10 / 100 ) 2 − 4000 ) = 4000 ∗ 11 / 10 ∗ 11 / 10 − 4000 = 840 so s . i . = 840 / 2 = 420 so sum = s . i . ∗ 100 / r ∗ t = 420 ∗ 100 / 3 ∗ 8 = rs 1750 option b"
Answer: b
Question (gain): a car is purchased on hire - purchase . the cash price is $ 21 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly instalments . interest is charged at 12 % p . a . what is the monthly instalment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 505 , d ) $ 506 , e ) $ 507
Rationale: explanation : cash price = $ 21 000 deposit = 10 % × $ 21 000 = $ 2100 loan amount = $ 21000 − $ 2100 = $ 18900 i = p * r * t / 100 i = 11340 total amount = 18900 + 11340 = $ 30240 regular payment = total amount / number of payments answer : b
Answer: b
Question (physics): in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 12 plants . there are 11 gapes between the two corner trees ( 11 x 2 ) metres and 1 metre on each side is left . therefore length = ( 22 + 2 ) m = 24 m . answer : c"
Answer: c
Question (physics): the radius of a wheel is 25.4 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 724 m , b ) 798.3 m , c ) 287 m , d ) 278 m , e ) 927 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 25.4 = 79829 cm = 798.3 m answer : b"
Answer: b
Question (other): divide $ 2000 among b , c in the ratio 4 : 16 . how many $ that c get ?
Options: a ) $ 1200 , b ) $ 1400 , c ) $ 1600 , d ) $ 1800 , e ) $ 2000
Rationale: sum of ratio terms = 4 + 16 = 20 c = 2000 * 16 / 20 = $ 1600 answer is c
Answer: c
Question (gain): an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 15 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 600 , c ) 887 , d ) 299 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 2.5 % . of x = 15 < = > ( 25 / 10 * 1 / 100 * x ) = 15 < = > x = 600 . answer : b )"
Answer: b
Question (general): what is the smallest integer that is multiple of 5 , 7,8
Options: a ) a ) 70 , b ) b ) 35 , c ) c ) 200 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 5 , 7 and 8 which is 280 . the answer is d ."
Answer: d
Question (general): the smallest 6 digit number exactly divisible by 111 is ?
Options: a ) 100009 , b ) 100010 , c ) 100011 , d ) 100015 , e ) 100017
Rationale: the smallest 6 - digit number 100000 . 111 ) 100000 ( 900 999 - - - - - 100 - - - required number = 100000 + ( 111 - 100 ) = 100011 option c
Answer: c
Question (general): according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 - ounce cans of the concentrate are required to prepare 272 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 67 , e ) 100
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 272 * 6 = 1632 oz so orange juice concentrate : water : : 408 oz : 1224 oz no . of 12 oz can = 408 oz / 12 oz = 34 answer b , 34 cans"
Answer: b
Question (geometry): the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 432 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 432 , 2 ( 7 / 5 ) w + 2 w = 432 solve the above equation to find : w = 90 m and l = 126 m . correct answer e ) 90"
Answer: e
Question (physics): a train 160 m long is running at 30 kmph . in how much time will it pass a platform 120 m long ?
Options: a ) 15.89 seconds , b ) 24.36 seconds , c ) 15.96 seconds , d ) 14.93 seconds , e ) 22.23 seconds
Rationale: distance travelled = 160 + 120 m = 280 m speed = 30 * 5 / 8 = 75 / 4 m time = 280 * 4 / 75 = 14.93 seconds answer : d .
Answer: d
Question (geometry): difference between the length and breadth of a rectangle is 23 m . ifits perimeter is 206 m , then its area is ? ?
Options: a ) 1220 m ^ 2
b ) 1520 m ^ 2
c ) 2520 m ^ 2
d ) 2600 m ^ 2
e ) 3420 m ^ 2
Rationale: we have : ( l - b ) = 23 and 2 ( l + b ) = 206 or ( l + b ) = 103 . solving the two equations , we get : l = 63 and b = 40 . area = ( l x b ) = ( 63 x 40 ) m 2 = 2520 m ^ 2 c
Answer: c
Question (gain): the salaries of a and b together amount to $ 2000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 1500 , e ) $ 1200
Rationale: "let a ' s salary is x b ' s salary = 2000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 2000 - x ) x = $ 1500 answer is d"
Answer: d
Question (general): what is the least value of p , so that 123 p 578 is divisible by 11
Options: a ) 7 , b ) 8 , c ) 6 , d ) 5 , e ) 4
Rationale: "explanation : 123 p 578 1 + 3 + 5 + 8 = 17 2 + p + 7 = 17 = > 9 + p = 17 = > p = 17 - 9 = > p = 8 answer : option b"
Answer: b
Question (physics): a train covers a distance of 12 km in 10 min . if it takes 11 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 177 m , b ) 189 m , c ) 220 m , d ) 178 m , e ) 188 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 11 = 220 m . answer : c"
Answer: c
Question (gain): a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if his company declares 5 % dividend at the end of the year , then how much does he get ?
Options: a ) 234 , b ) 600 , c ) 388 , d ) 278 , e ) 129
Rationale: "explanation : number of shares = = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = = rs . 600 answer : b ) rs . 600"
Answer: b
Question (gain): a man sold 18 toys for rs . 27300 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 1300
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 27300 . gain = sp â € “ cp 3 x = 27300 â € “ 18 x 21 x = 27300 x = rs . 1300 . answer : option e"
Answer: e
Question (other): what is the square root of 3,969 ?
Options: a ) a ) 18 , b ) b ) 9 , c ) c ) 45 , d ) d ) 63 , e ) e ) 81
Rationale: "a square root of a number is a number times itself equals the original number . ex ) the square root of 81 is 9 because 9 times itself ( 9 ) equals the original number ( 81 ) . 63 * 63 = 3,969 3969 divided by x = 63 x = 63 ( d ) 63"
Answer: d
Question (general): if 5 < x < 11 and y = x + 7 , what is the greatest possible integer value of x + y ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: x + y = x + x + 7 = 2 x + 7 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 10.5 then x + y = 10.5 + 17.5 = 28 . the answer is c .
Answer: c
Question (general): having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.75 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.40 , b ) $ 2.80 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80
Rationale: total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.8 therefore , x = $ 2.80 . answer b
Answer: b
Question (general): a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 30,000 , a receives :
Options: a ) s . 12,000 , b ) s . 12,200 , c ) s . 12,400 , d ) s . 12,600 , e ) s . 12,800
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 30000 x 21 / 50 ) = rs . 12,600 . d"
Answer: d
Question (gain): if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2080 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2600 , c ) 2507 , d ) 3200 , e ) 11500
Rationale: "p - 2080 = ( p * 5 * 4 ) / 100 p = 2600 answer : b"
Answer: b
Question (general): a small pool filled only with water will require an additional 600 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 600 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 2000
Rationale: "since pumping in additional 600 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 600 = 0.8 * { total } - - > { total } = 2,000 . answer : e ."
Answer: e
Question (other): the compound ratio of 2 : 3 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 4 : 5 , e ) 1 : 4
Rationale: "2 / 3 * 3 / 2 * 4 / 5 = 4 / 5 = 4 : 5 answer : d"
Answer: d
Question (physics): the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the numbers is 720 , then the other is :
Options: a ) 8 , b ) 10 , c ) 12 , d ) 4 , e ) 6
Rationale: "other number = ( 12 x 600 ) / 720 = 10 . answer : c"
Answer: c
Question (general): david obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) none of these , e ) can not be determined
Rationale: "solution : average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . hence , average = 75 . answer : option c"
Answer: c
Question (other): if the ratio of s . i earned on certain amount on same rate is 4 : 5 . what is the ratio of time ?
Options: a ) 1 : 2 , b ) 6 : 9 , c ) 4 : 5 , d ) 2 : 3 , e ) not possible to calculate
Rationale: s . i 1 / s . i 2 = [ ( p * r * t 1 ) / 100 ] / [ ( p * r * t 2 ) / 100 ] 4 / 5 = t 1 / t 2 ratio = 4 : 5 answer c
Answer: c
Question (general): dick and jane each saved $ 2,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 4,000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "1990 dick saved = $ 2200 jane saved = $ 1800 ( jane saved $ 200 less than she did the prior year ) jane saved approximately $ 200 / 2000 $ ( 10 % ) less in 1990 answer : a"
Answer: a
Question (general): tough and tricky questions : exponents . if 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y , then x + y =
Options: a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 5
Rationale: here is my solution . 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y here rhs 49 ^ x * 27 ^ y = 7 ^ ( 2 x ) * 3 ^ ( 3 y ) equating powers on both sides - - > 3 x - 1 = 2 x , thus x = 1 and 4 y - 3 = 3 y giving y = 3 so , x + y = 4 option : b
Answer: b
Question (gain): a candidate got 35 % of the votes polled and he lost to his rival by 2250 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 2665 , d ) 2888 , e ) 2661
Rationale: 35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2250 100 % - - - - - - - - - ? = > 7500 answer : a
Answer: a
Question (other): find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg .
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 3 : 5 , e ) 4 : 5
Rationale: "req = 60 : 90 = 2 : 3 answer b"
Answer: b
Question (geometry): a volume of 11248 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812 , b ) 8231 , c ) 2734 , d ) 4222 , e ) 4254
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 11248 l can be kept in ( 11248 / 4 ) hemispheres ans . 2812 answer : a"
Answer: a
Question (physics): b completes a work in 6 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.33 days , b ) 4.33 days , c ) 5.33 days , d ) 6.33 days , e ) 7.33 days
Rationale: "1 / 5 + 1 / 10 = 3 / 10 10 / 3 = 3.33 days answer : a"
Answer: a
Question (physics): a man can row upstream at 20 kmph and downstream at 28 kmph , and then find the speed of the man in still water ?
Options: a ) 24 , b ) 37 , c ) 30 , d ) 27 , e ) 18
Rationale: "us = 20 ds = 28 m = ( 28 + 20 ) / 2 = 24 answer : a"
Answer: a
Question (general): if x and y are integers such that x ^ 2 = 2 y and xy = 256 , then x – y = ?
Options: a ) - 30 , b ) - 24 , c ) - 5 , d ) 5 , e ) 20
Rationale: "here x and y are integers . x ^ 2 = 2 y , xy = 256 . substitute ( x ^ 2 ) / 2 = y in xy = > x ^ 3 = 256 * 2 = > x ^ 3 = 512 . here x ^ 3 is positive , x is also positive . x = 8 then y = 32 . x - y = - 24 so option b is correct"
Answer: b
Question (physics): if a tire rotates at 400 revolutions per minute when the car is traveling 144 km / h , what is the circumference of the tire ?
Options: a ) 2 meters , b ) 6 meters , c ) 5 meters , d ) 3 meters , e ) 7 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 144,000 m : c is the circumference c = 6 meters correct answer b"
Answer: b
Question (general): the average of runs of a cricket player of 10 innings was 18 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 16 , c ) 62 , d ) 76 , e ) 17
Rationale: "average after 11 innings = 22 required number of runs = ( 33 * 11 ) - ( 18 * 10 ) = 242 - 180 = 62 . answer : c"
Answer: c
Question (general): if a = 105 and a ^ 3 = 21 * 25 * 15 * b , what is the value of b ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 147 , e ) 54
Rationale: "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 15 = 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 2 * 5 ^ 3 * 7 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 2 * 5 ^ 3 * 7 b = 3 * 7 ^ 2 = 3 * 49 = 147 correct answer d ."
Answer: d
Question (geometry): if the difference of two numbers is 3 and the difference of their square is 39 , then the larger number is :
Options: a ) 9 , b ) 2 , c ) 12 , d ) 14 , e ) 8
Rationale: let the numbers be x and y then x 2 - y 2 = 39 and x - y = 3 we get x + y = 13 solving x - y = 3 , x + y = 13 x = 8 , y = 5 larger number 8 answer e
Answer: e
Question (other): the ratio of two numbers is 3 : 4 and their sum is 21 . the greater of the two numbers is ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 17 , e ) 19
Rationale: 3 : 4 total parts = 7 = 7 parts - - > 21 ( 7 ã — 3 = 21 ) = 1 part - - - - > 3 ( 1 ã — 3 = 4 ) = the greater of the two number is = 4 = 4 parts - - - - > 12 ( 4 ã — 3 = 12 ) a
Answer: a
Question (physics): working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 6 x boxes ?
Options: a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 6 minutes , e ) 12 minutes
Rationale: "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 6 x / 5 x * 10 = 12 min ans : e"
Answer: e
Question (physics): a light flashes every 15 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 600 , c ) 240 , d ) 700 , e ) 750
Rationale: "1 flash = 15 sec for 1 min = 4 flashes so for 1 hour = 4 * 60 = 240 flashes . answer : c"
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 7 seconds . find the length of the train .
Options: a ) 116.67 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 7 = 116.67 meter . answer : a"
Answer: a
Question (physics): in what time will a train 40 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 1.0 sec , c ) 7.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 40 / 40 = 1.0 sec . answer : b"
Answer: b
Question (general): a certain country had a total annual expenditure of $ 1.2 x 10 ^ 12 . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1000 , c ) $ 2000 , d ) $ 3000 , e ) $ 5000
Rationale: "explanation : in scientific notation 240 million is 2.4 x 10 ^ 8 . so the per capita expenditure was : ( $ 1.2 x 10 ^ 12 ) / ( 2.4 x 10 ^ 8 ) = ( $ 1.2 ) / ( 2.4 ) x 10 ^ 12 - 8 = $ 0.5 x 10 ^ 4 = $ 5000 answer : option e"
Answer: e
Question (physics): in a dairy farm , 50 cows eat 50 bags of husk in 50 days . in how many days one cow will eat one bag of husk ?
Options: a ) 34 days , b ) 40 days , c ) 46 days , d ) 50 days , e ) none of these
Rationale: "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 50 bags 50 1 ] : : 50 : x = > x ∗ 50 ∗ 1 = 50 ∗ 1 ∗ 50 = > x = 50 option d"
Answer: d
Question (general): what is the range of all the roots of | x ^ 2 - 1 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 1 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 1 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 2 or x = 1 i guess range is 2 - 1 = 1 d
Answer: d
Question (general): one - third of rahul ’ s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 2 , 50000 as total savings , how much has he saved in public provident fund ?
Options: a ) rs . 30,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 100,000 , e ) none
Rationale: explanation let savings in n . s . c and p . p . f . be rs . x and rs . ( 250000 – x ) respectively . then , 1 / 3 x = 1 / 2 ( 250000 - x ) = > x / 3 + x / 2 = 125000 = > 5 x / 6 = 125000 = > x = 125000 x 6 / 5 = 150000 savings in public provident fund = rs . ( 250000 – 150000 ) = rs . 100000 answer d
Answer: d
Question (physics): roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 2 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 11 , b ) 20 , c ) 77 , d ) 26 , e ) 12
Rationale: "distance = relative speed * time = ( 2 + 3 ) * 4 = 20 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : b"
Answer: b
Question (general): the proportion of water to alcohol in solution a is 4 : 1 and the proportion of water to alcohol in solution b is 3 : 1 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 16.5 % , b ) 18.5 % , c ) 20.5 % , d ) 22.5 % , e ) 24.5 %
Rationale: "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 5 ) ( v / 2 ) + ( 1 / 4 ) ( v / 2 ) = v / 10 + v / 8 = 9 v / 40 . the concentration of alcohol is 9 / 40 = 22.5 % the answer is d ."
Answer: d
Question (geometry): find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm ?
Options: a ) 188 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2
Rationale: "1 / 2 * 20 ( 9 + 6 ) = 150 cm 2 answer : b"
Answer: b
Question (general): how many integers between 0 and 1000 do not contain the integer 1
Options: a ) 727 , b ) 728 , c ) 758 , d ) 748 , e ) 792
Rationale: from 1 to 99 = 19 integers having 1 from 101 to 199 = all are having 1 similarly 201 - 299 , 301 - 399 , 401 - 499 , . . . . . so on , will have 19 integers having 1 answer = 1000 - ( 19 * 9 + 99 + 2 ) / / 2 is added for 100 and 1000 = 728 answer : b
Answer: b