Cheukting/mathqa huggingface dataset:
Question (general): in a box of 8 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 6 / 11 , b ) 8 / 15 , c ) 9 / 20 , d ) 11 / 25 , e ) 15 / 28
Rationale: "p ( neither pen is defective ) = 6 / 8 * 5 / 7 = 15 / 28 the answer is e ."
Answer: e
Question (gain): if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 500 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 512.50 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 25,000 . now , put the value of x = 5000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 5000 + 5 % of 5000 = 5250 . 2 nd year , amount = 5250 + 5 % of 5250 = 5512.50 . we can see after 2 years interest = 5512.50 - 5000 = 512.50 hence , it satisfies the question . hence c is the correct answer"
Answer: c
Question (general): if 2 x + y = 7 and x + 2 y = 5 , then 5 xy / 3 = ?
Options: a ) a ) 5 , b ) b ) 2 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 5 * 3 * 1 ) / 3 = 15 / 3 = 5 a"
Answer: a
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 2880 ?
Options: a ) 8100 , b ) 3388 , c ) 7767 , d ) 2009 , e ) 3645
Rationale: "2880 * 9 / 8 * 9 / 8 = 3645 answer : e"
Answer: e
Question (gain): a man is walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 1250 meters , e ) none of these
Rationale: "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . answer : d"
Answer: d
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 840 grams per kg , what is his percent ?
Options: a ) 19 , b ) 25 , c ) 77 , d ) 88 , e ) 11
Rationale: "840 - - - 160 100 - - - ? = > 19 % answer : a"
Answer: a
Question (physics): a train 500 m long passes a man , running at 9 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is :
Options: a ) 105 , b ) 95 , c ) 90 , d ) 99 , e ) 100
Rationale: "speed of the train relative to man = 500 / 20 m / sec = 25 m / sec . = 25 x 18 / 5 km / hr = 90 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 9 ) km / hr . x - 9 = 90 = 99 km / hr . answer : d"
Answer: d
Question (gain): the cost price of a radio is rs . 4800 and it was sold for rs . 4400 , find the loss % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 4
Rationale: "4800 - - - - 400 100 - - - - ? = > 8 % answer : a"
Answer: a
Question (general): line m lies in the xy - plane . the y - intercept of line m is - 5 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 8 ) . what is the slope of line m ?
Options: a ) - 3 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : a solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 2 ) as we can see that the y axis of intercept point is ( 0 , - 5 ) means line m is parallel to x axis slope m = - 3 ans : a"
Answer: a
Question (physics): a certain machine produces 1,100 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 6 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 40,000 , d ) 100,000 , e ) 158,400
Rationale: since 6 days consist of 24 * 6 hours the total is 144 hours . since every hour the machine produces 1100 units of product p the total product during 144 hours is 144 * 1100 = 158,400 . correct option : e
Answer: e
Question (general): linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 150 , what were her original savings ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900
Rationale: "if linda spent 3 / 4 of her savings on furniture , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 150 . so 1 / 4 of her savings is $ 150 . so her original savings are 4 times $ 150 = $ 600 correct answer b"
Answer: b
Question (physics): if 8 people can eat a gallon of ice cream in 10 days , how long would it take 5 people to eat a gallon of ice cream ?
Options: a ) 12 days , b ) 14 days , c ) 16 days , d ) 18 days , e ) 20 days
Rationale: 8 * 10 = 5 * x x = 16 answer : c
Answer: c
Question (general): 8 x 2.4 - 5 x 1.4 / 1.5 = ?
Options: a ) 9.46 , b ) 2.03 , c ) 50.4 , d ) 14.65 , e ) 12.85
Rationale: "given expression = ( 19.2 - 5 x 1.4 ) / 1.5 = 14.2 / 1.5 = 14.2 / 1.5 = 9.46 answer is a"
Answer: a
Question (physics): in what time will a train 20 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.8 sec , c ) 0.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 20 / 40 = 0.5 sec . answer : c"
Answer: c
Question (general): the sum of number of boys and girls in a school is 150 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 70
Rationale: "we have x + x % of 150 = 150 x + x / 100 * 150 = 150 5 / 2 * x = 150 x = 150 * 2 / 5 = 60 answer is c"
Answer: c
Question (physics): two trains a and b are 175 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 4 s , d ) 8 s , e ) 13 s
Rationale: detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 175 + 150 = 325 m . time taken = 325 / 25 = 13 s . correct answer e .
Answer: e
Question (physics): a train traveling with constant speed crosses a 90 m long platform in 12 seconds and a 120 m long platform in 15 seconds . find the length of the train and its speed .
Options: a ) 30 , b ) 40 , c ) 60 , d ) 50 , e ) none
Rationale: let the length of the train be x m and its speed be y m / sec . then , x / y = 12 = > y = x / 12 ( x + 90 ) / 12 = x + 120 / 15 = > x = 30 m . answer : a
Answer: a
Question (general): if the average ( arithmetic mean ) of a and b is 100 , and c – a = 120 , what is the average of b and c ?
Options: a ) 150 , b ) 140 , c ) 160 , d ) 170 , e ) 180
Rationale: "a + b / 2 = 100 = > a + b = 200 a = c - 120 . . . sub this value c - 120 + b = 200 = > c + b = 320 = > c + b / 2 = 160 answer : c"
Answer: c
Question (physics): how many seconds will a train 130 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 28 sec , b ) 23 sec , c ) 24 sec , d ) 25 sec , e ) 26 sec
Rationale: "d = 130 + 150 = 280 s = 36 * 5 / 18 = 10 mps t = 280 / 10 = 28 sec a"
Answer: a
Question (gain): a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 14 - - > x = $ 17.5 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 17.5 + 21 = $ 38.5 . answer : b ."
Answer: b
Question (general): find the 18 th term of an arithmetic progression whose first term is 4 and the common difference is 5 .
Options: a ) 45 , b ) 38 , c ) 72 , d ) 74 , e ) 78
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 4 + ( 18 - 1 ) * 4 , = 4 + 68 = 72 . answer : c"
Answer: c
Question (general): if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 18 - m ) then m = ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "2 m = 18 - m 3 m = 18 m = 6 the answer is c ."
Answer: c
Question (gain): in a school of 850 boys , 44 % of muslims , 32 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 125 , b ) b ) 119 , c ) c ) 153 , d ) d ) 721 , e ) e ) 159
Rationale: "44 + 32 + 10 = 86 % 100 – 84 = 14 % 850 * 14 / 100 = 119 answer : b"
Answer: b
Question (general): in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 12 years older than b , the present age of b is
Options: a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42
Rationale: "explanation : let b ' s age = x years . then , as age = ( x + 12 ) years . ( x + 12 + 10 ) = 2 ( x — 10 ) hence x = 42 . present age of b = 42 years answer : option e"
Answer: e
Question (general): drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 5 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 3 / 10 , b ) 7 / 10 , c ) 9 / 10 , d ) 9 / 20 , e ) 13 / 20
Rationale: "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 5 ) y = ( 9 / 20 ) y the answer is d ."
Answer: d
Question (general): the average age of 3 boys is 120 years and their ages are in proportion 2 : 6 : 8 . what is the age in years of the youngest boy ?
Options: a ) 10 , b ) 9 , c ) 15 , d ) 6 , e ) 12
Rationale: 2 x + 6 x + 8 x = 120 x = 7.5 2 x = 15 answer : c
Answer: c
Question (general): for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 25000 , my total savings for the two - year is
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 9900 , d ) s . 9990 , e ) s . 10000
Rationale: "sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 25000 + 35000 ) = 66000 - 60000 = rs . 6000 a"
Answer: a
Question (general): rahul played weel in this season . his current batting averagge is 50 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: "50 x + 78 = 54 ( x + 1 ) = > 4 x = 24 = > x = 6 answer : d"
Answer: d
Question (general): in 2 bags , there are to be put together 5 red and 12 white balls , neither bag being empty . how must the balls be divided so as to give a person who draws 1 ball from either bag - the greatest chance of drawing a red ball ?
Options: a ) 1 / 8 , b ) 2 / 8 , c ) 3 / 8 , d ) 4 / 8 , e ) 5 / 8
Rationale: "greatest chance . 1 / 2 * 1 + 1 / 2 * 4 / 16 = 5 / 8 answer : e"
Answer: e
Question (geometry): a circular well with a diameter of 6 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ?
Options: a ) 678.6 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none
Rationale: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 3 × 3 × 24 ) m 3 ‹ = › 678.6 m 3 . answer a"
Answer: a
Question (physics): a man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 12 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 12 , d = 12 b - 12 c ; every 4 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 12 b - 12 c = 4 b + 4 c , - - > b = 2 c , - - > d = 12 b - 6 b = 6 b . interval = \ frac { d } { b } = \ frac { 6 b } { b } = 6 answer : b ( 6 minutes ) ."
Answer: b
Question (general): the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8900 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 2900 , b ) s . 3570 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8900 = 35600 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 3600 salary of may is rs . 6500 salary of january = rs . 2900 answer : a"
Answer: a
Question (general): ( 3 x + 4 ) ( 2 x - 5 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?
Options: a ) 5 , b ) 8 , c ) 9 , d ) 10 , e ) 15
Rationale: "expanding we have 6 x ^ 2 - 15 x + 8 x - 20 6 x ^ 2 - 7 x - 20 taking coefficients , a = 6 , k = - 7 , n = - 20 therefore a - n + k = 6 - ( - 20 ) - 11 = 26 - 11 = 15 the answer is e ."
Answer: e
Question (gain): a shopkeeper has 280 kg of apples . he sells 45 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 27 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 45 x 20 % + 60 x 30 % = 27 this profit will remain same for any total quantity unless the % of products remains the same . hence ' c ' is the answer"
Answer: c
Question (gain): the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 40,000 , how much profit did the business make ?
Options: a ) $ 44,000 , b ) $ 54,000 , c ) $ 64,000 , d ) $ 84,000 , e ) $ 104,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 40000 p = $ 64,000 the answer is c ."
Answer: c
Question (gain): 70 % of the employees of a company are men . 50 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
Options: a ) 4 % , b ) 10 % , c ) 83.33 % , d ) 90.33 % , e ) 20 %
Rationale: "no of employees = 100 ( say ) men = 70 women = 30 men speaking french = 0.5 * 70 = 35 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 35 = 5 and women not speaking french = 30 - 5 = 25 % of women not speaking french = 25 / 30 * 100 = 83.33 % answer c"
Answer: c
Question (gain): a and b are partners in a business . a contributes 1 / 4 of the capital for 15 months and b received 2 / 3 of the profit . for how long b ' s money was used ?
Options: a ) 10 , b ) 37 , c ) 27 , d ) 18 , e ) 19
Rationale: let the total profit be rs . z . then , b ' s share = rs . 2 z / 3 , a ' s share = rs . ( z - 2 z / 3 ) = rs . z / 3 . a : b = z / 3 : 2 z / 3 = 1 : 2 let the total capital be rs , x and suppose b ' s money was used for x months . then . ( 1 ( x ) / 4 * 15 ) / ( 3 x ) / 4 * y ) = 1 / 2 < = > y = ( 15 * 2 / 3 ) = 10 . thus , b ' s money was used for 10 months . answer : a ) 10 months
Answer: a
Question (general): 3 * 15 + 3 * 16 + 3 * 19 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 161
Rationale: "3 * 15 + 3 * 16 + 3 * 19 + 11 = 45 + 48 + 57 + 11 = 161 the answer is e ."
Answer: e
Question (physics): a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 14 hr , e ) 16 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 1 / 3 ) = 1 / 14 leak will empty the tank in 14 hrs . answer : d"
Answer: d
Question (general): right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x - and y - coordinates of p , q and r are to be integers that satisfy the inequalities - 4 < = x < = 5 and 6 < = y < = 16 . how many different triangles with these properties could be constructed ?
Options: a ) 110 , b ) 1100 , c ) 9900 , d ) 10000 , e ) 12100
Rationale: "we know that p , q , r can only lie on a grid 10 x 11 let ' s start by fixing p ' x - coordinate : we have 10 possible places for it then we choose x - coordinate for r : since pr | | x - axis , r ' s x - coordinate can not coincide with p ' s x - coord , so we have only 9 possible choices left . then , we fix p ' s ( and r ' s too ) y - coordinate : 11 possible choices . finally , after we fixed p and r , q ' s x - coordinate must be the same as p ' s ( because p is the right angle and pr | | x - axis ) , so the only choice is for y - coordinate , and we have 10 possible choices left . so , total number of different triangles : 10 * 9 * 11 * 10 = 9,900 answer : c"
Answer: c
Question (geometry): sand is poured into a box so that the box is being filled at the rate of 3 cubic feet per hour . if the empty rectangular box is 5 feet long , 4 feet wide , and 3 feet deep , approximately how many hours does it take to fill the box ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "the volume the box is : length * width * depth = 5 * 4 * 3 = 60 cubic feet . 60 cubic feet / 3 cubic feet per hour = 20 hours . it will take 20 hours to fill the box . the answer is d ."
Answer: d
Question (physics): jack and christina are standing 270 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 4 feet per second and christina walks in a straight line toward jack at a constant speed of 5 feet per second . lindy runs at a constant speed of 8 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 150 , b ) 180 , c ) 210 , d ) 240 , e ) 270
Rationale: "the relative speed of jack and christina is 4 + 5 = 9 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 270 / 7 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 8 * 30 = 240 feet . answer : d ."
Answer: d
Question (gain): how many liters of water must be added to 20 liters of milk and water containing 10 % water to make it 50 % water ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "by rule of alligation : 50 % - 10 % = 40 % 100 % - 50 % = 50 % quantity of pure water : quantity of the mixture = 4 : 5 there are 20 liters of mixture , so we need to add 16 liters of pure water . the answer is d ."
Answer: d
Question (physics): man 1 alone can do a piece of work in 6 days and man 2 alone in 8 days . man 1 and man 2 undertook to do it for rs . 3200 . with the help of man 3 , they completed the work in 3 days . how much is to be paid to man 3 ?
Options: a ) 400 , b ) 200 , c ) 100 , d ) 150 , e ) 500
Rationale: man 3 1 day work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 man 1 : man 2 : man 3 = 1 / 6 : 1 / 8 : 1 / 24 = = > 4 : 3 : 1 man 3 share = 3 * 1 / 24 * 3200 = rs 400 answer a
Answer: a
Question (general): in arun ' s opinion , his weight is greater than 65 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 68 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 16.5 kg , b ) 66.5 kg , c ) 26.5 kg , d ) 56.5 kg , e ) 86.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 65 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 68 . the values satisfying all the above conditions are 66 and 67 . required average = ( 66 + 67 ) / 2 = 66.5 kg answer : b"
Answer: b
Question (gain): shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 500 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 555 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 2,000 , b ) 2,500 , c ) 4,000 , d ) 5,000 , e ) 6,000
Rationale: "so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 250 , thus 0.2 x = $ 250 - - > x = $ 1,250 . since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,250 = $ 2,500 . answer : b"
Answer: b
Question (gain): ramesh purchased a refrigerator for rs . 15500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 2899 , d ) 17600 , e ) 21725
Rationale: "price at which the tv set is bought = rs . 15,500 discount offered = 20 % marked price = 15500 * 100 / 80 = rs . 19375 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 19375 + 375 = rs . 19750 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 19750 * 110 / 100 = rs . 21725 answer : e"
Answer: e
Question (general): how many numbers from 10 to 1000000 are exactly divisible by 9 ?
Options: a ) 900 , b ) 8000 , c ) 1100 , d ) 111110 , e ) 14
Rationale: "10 / 9 = 1 and 1000000 / 9 = 111111 = = > 111111 - 1 = 111110 . answer : d"
Answer: d
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 150 , b ) 872 , c ) 287 , d ) 288 , e ) 212
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 9 = 150 meter answer : a"
Answer: a
Question (physics): a rectangular plot measuring 30 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 46 m , b ) 66 m , c ) 26 m , d ) 56 m , e ) 32 m
Rationale: "perimeter of the plot = 2 ( 30 + 50 ) = 160 m no of poles = 160 / 5 = 32 m answer : e"
Answer: e
Question (general): a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 4 * x hence , a 1 + a 2 + . . + a 20 + n = 24 x so , the fraction asked = 4 x / 24 x = 1 / 6 ; answer : b ."
Answer: b