regisss/math_qa huggingface dataset:
Problem: a 250 m long train is running at a speed of 55 km / hr . it crossed a platform of length 300 m in ?
Options: a ) 41.1 sec , b ) 20.2 sec , c ) 36 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 250 m + 300 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 550 m time = distance / speed = 550 x 18 / ( 5 x 55 ) = 36 sec ans is : c"
Answer: c
Problem: arjun started a business with rs . 20,000 and is joined afterwards by anoop with rs . 40 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: suppose anoop joined after 3 months . then , 20000 * 12 = 40000 * ( 12 – x ) = > = > x = 6 . answer : d
Answer: d
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 36 ?
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 5
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 36 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 5 more to make it 36 m + 36 answer - e"
Answer: e
Problem: a cubical block of metal weighs 5 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48
b ) 40
c ) 24
d ) 18
e ) 12
Rationale: for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 5 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 5 pounds = 40 pounds so answer is b and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 5 * 8 = 40 so answer is b
Answer: b
Problem: a box contains 3 red balls and 3 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 2 , e ) 2 / 3
Rationale: "my complicated version of your simple approach let the 3 black balls be bbb and 3 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 6 ! ) / ( 3 ! x 3 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 5 slots and 2 black ( bb ) and 3 red ( rrr ) they can be arranged in ( 5 ! ) / ( 2 ! x 3 ! ) hence required probability = [ ( 6 ! ) / ( 3 ! x 3 ! ) ] / [ ( 5 ! ) / ( 2 ! x 3 ! ) ] = 2 d"
Answer: d
Problem: 3 candidates in an election and received 1136 , 5636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 40 % , b ) 55 % , c ) 57 % , d ) 63.2 % , e ) 62 %
Rationale: "total number of votes polled = ( 1136 + 5636 + 11628 ) = 18400 so , required percentage = 11628 / 18400 * 100 = 63.2 % d"
Answer: d
Problem: the population of a town increased from 1 , 75,000 to 2 , 62,500 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 262500 - 175000 ) = 87500 . increase % = ( 87500 / 175000 × 100 ) % = 50 % . required average = ( 50 / 10 ) % = 5 % . answer b"
Answer: b
Problem: there are 14 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?
Options: a ) 87 , b ) 91 , c ) 95 , d ) 99 , e ) 103
Rationale: "14 c 2 = 91 the answer is b ."
Answer: b
Problem: the decimal 0.1 is how many times greater than the decimal ( 0.0001 ) ^ 3 ?
Options: a ) 10 ^ 9 , b ) 10 ^ 10 , c ) 10 ^ 11 , d ) 10 ^ 12 , e ) 10 ^ 13
Rationale: "0.1 = 10 ^ - 1 ( 0.0001 ) ^ 3 = ( 10 ^ - 4 ) ^ 3 = 10 ^ - 12 10 ^ 11 * 10 ^ - 12 = 10 ^ - 1 the answer is c ."
Answer: c
Problem: when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.168 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8
Rationale: "for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 4 digits after decimal total no . of decimals = 6 req . no . of digits = ( n - 1 ) = ( 6 - 1 ) = 5 answer : a"
Answer: a
Problem: two employees a and b are paid a total of rs . 450 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?
Options: a ) 130 , b ) 140 , c ) 150 , d ) 170 , e ) 180
Rationale: "let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 450 but x = 150 % of y = 150 y / 100 = 15 y / 10 ∴ 15 y / 10 + y = 450 ⇒ y [ 15 / 10 + 1 ] = 450 ⇒ 25 y / 10 = 450 ⇒ 25 y = 4500 ⇒ y = 4500 / 25 = rs . 180 e"
Answer: e
Problem: what is the probability of getting only 1 head in a single throw of four fair coins ?
Options: a ) 1 / 2 , b ) 3 / 8 , c ) 1 / 4 , d ) 1 / 5 , e ) 5 / 8
Rationale: "one possible case is httt . p ( httt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 there are 4 c 1 = 4 possible cases . p ( 1 head ) = 4 * 1 / 16 = 1 / 4 the answer is c ."
Answer: c
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 18 sec , c ) 36 sec , d ) 72 sec , e ) none
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 120 = 360 m . time taken = 360 / 10 = 36 sec answer : c"
Answer: c
Problem: 4 is what percent of 50 ?
Options: a ) 0.2 % , b ) 8 % , c ) 10 % , d ) 20 % , e ) 500 %
Rationale: "4 = x * 50 / 100 x = 8 % ans ; b"
Answer: b
Problem: the ratio of the radius of two circles is 2 : 3 , and then the ratio of their areas is ?
Options: a ) 1 : 7
b ) 2 : 9
c ) 4 : 9
d ) 3 : 7
e ) 3 : 4
Rationale: r 1 : r 2 = 2 : 3 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 4 : 9 answer : c
Answer: c
Problem: the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 55 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 992 , d ) $ 870 , e ) $ 660
Rationale: "c let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 155 % of $ 640 = 150 / 100 * 640 = $ 992 ."
Answer: c
Problem: what is the units digit of the expression 14 ^ 7 − 18 ^ 4 ?
Options: a ) 0 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "units digit of 14 ^ 7 − 18 ^ 4 : consider the following unit digits : 4 ^ 1 : 4 4 ^ 2 : 6 4 ^ 3 : 4 4 ^ 4 : 6 ⇒ unit digit of 4 ^ 7 is : 4 the unit digit of 14 ^ 7 will also be 4 also : 8 ^ 1 : 8 8 ^ 2 : 4 8 ^ 3 : 2 8 ^ 4 : 6 ⇒ unit digit of 8 ^ 4 is : 6 the unit digit of 18 ^ 4 will also be 6 finally , 4 - 6 ( or 14 - 6 ) = 8 answer : e )"
Answer: e
Problem: for 6 - digit integer 46 x , y 12 , when x and y are drawn at random from { 3 , 58 } , what is the probability w that the integer drawn is divisible by 8 ? * a solution will be posted in two days .
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: in general , the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8 . thus , in order for 46 , x , y 12 to be divided by 8 , y 12 should be divided by 8 . amongst 3 , 5,8 , 3 and 5 can be divided by 8 . therefore , w = two out of three can be divided and the answer is d .
Answer: d
Problem: the average of 10 numbers is calculated as 46 . it is discovered later on that while calculating the average , the number 75 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 48 , b ) 51 , c ) 60 , d ) 71 , e ) 96
Rationale: "the total sum of the numbers should be increased by 50 . then the average will increase by 50 / 10 = 5 . the correct average is 51 . the answer is b ."
Answer: b
Problem: a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "otal time for travelling 80 miles @ 60 mph = 80 / 60 = 4 / 3 hour = 80 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 80 minutes it will use = 2 gallons . thus , full tank = 2 + 8 = 10 gallons - - - > 2 / 10 = 20 % of the fuel used . b is the correct answer ."
Answer: b
Problem: all the students of class are told to sit in circle shape . here the boy at the 10 th position is exactly opposite to 40 th boy . total number of boys in the class ?
Options: a ) 50 , b ) 45 , c ) 60 , d ) 55 , e ) 53
Rationale: "as half the circle shape consist of 40 - 10 = 30 boys , so total number of boys in full circle = 2 * 30 = 60 answer : c"
Answer: c
Problem: in what time will a train 120 metres long cross an electric pole , if its speed be 72 km / hr ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 9 sec , e ) 5 sec
Rationale: "solution speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec time taken = ( 120 / 20 ) sec = 6 sec . answer b"
Answer: b
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1850 ?
Options: a ) s . 125 , b ) s . 108 , c ) s . 100 , d ) s . 103 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1850 74 x = 1850 = > x = 25 5 x = 125 rs . answer : a"
Answer: a
Problem: a worker ' s daily wage is increased by 50 % and the new wage is $ 42 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 22 , b ) $ 24 , c ) $ 28 , d ) $ 32 , e ) $ 36
Rationale: "let x be the daily wage before the increase . 1.5 x = $ 42 x = $ 28 the answer is c ."
Answer: c
Problem: 5 ltr of water is added with 15 ltr of a solution containing 26 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 17.25 % , b ) 19 , c ) 19.5 % , d ) 21.5 % , e ) 22 %
Rationale: we have a 15 litre solution containing 26 % alcohol in water . = > quantity of alcohol in the solution = 15 ã — 26 / 100 now 5 litre of water is added to the solution . = > total quantity of the new solution = 15 + 5 = 20 percentage of alcohol in the new solution = 15 ã — 26 / 100 20 ã — 100 = 15 ã — 26 / 10020 ã — 100 = 15 ã — 1.3 / 100 = 19.5 % c
Answer: c
Problem: a 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 177 , b ) 166 , c ) 350 , d ) 198 , e ) 161
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 39 = 50 / 3 3 ( x + 300 ) = 1950 è x = 350 m . answer : c"
Answer: c
Problem: anne bought doughnuts for a class breakfast party . she bought 15 chocolate doughnuts , 12 coconut doughnuts , and 14 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 41 , b ) 36 , c ) 39 , d ) 21 , e ) 11
Rationale: add the numbers of doughnuts . 15 + 12 + 14 = 41 . answer is a .
Answer: a
Problem: following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 12 , c ) 13 , d ) 14 , e ) 14.5
Rationale: "let the candy and soda before the increase be c and s respectively so increased price of can = c ( 1 + 25 / 100 ) = 10 - - - - - - - - - - - > c = 8 increase price of soda : s ( 1 + 1 / 2 ) = 6 - - - - - - - - - - - > s = 4 hence total = 8 + 4 = 12 . . hence answer : b"
Answer: b
Problem: if a boat is rowed downstream for 500 km in 5 hours and upstream for 240 km in 6 hours , what is the speed of the boat and the river ?
Options: a ) 70 , 30 , b ) 30 , 70 , c ) 70 , 70 , d ) 30 , 30 , e ) 80 , 50
Rationale: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 100 ; us = 40 x = ( 100 + 40 ) / 2 = 140 / 2 = 70 km / hr y = ( 100 - 40 ) / 2 = 60 / 2 = 30 km / hr answer : a"
Answer: a
Problem: the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8215 for a computer table , then what was the cost price of the computer table ?
Options: a ) 7297 , b ) 6625 , c ) 2871 , d ) 6725 , e ) 2981
Rationale: "explanation : cp = sp * ( 100 / ( 100 + profit % ) ) = 8215 ( 100 / 124 ) = rs . 6625 . answer : b"
Answer: b
Problem: set d consists of all the prime numbers between 10 and 25 . what is the range of set d ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23
Rationale: answer of set d is 12 = a
Answer: a
Problem: an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2800 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 3500 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: "4 - - - 2800 5 - - - ? = > 3500 answer : b"
Answer: b
Problem: the price of a mobile was increased by 25 percent . the new price was then decreased by 10 percent . a single increase of what percent is equivalent to these two successive changes ?
Options: a ) 10 % , b ) 15 % , c ) 17.5 % , d ) 25 % , e ) 12.5 %
Rationale: "consider base price - $ 100 25 % increase = 1.25 * 100 = $ 125 then a 10 % decrease on new price = 0.9 * 125 = $ 112.5 so final price of radio - $ 112.5 therefore a 12.5 % increase correct option - e"
Answer: e
Problem: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 26,000 is made ?
Options: a ) rs . 1 , 10,000 , b ) rs . 1 , 20,000 , c ) rs . 1 , 22,000 , d ) rs . 1 , 21,000 , e ) none of these
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 24,000 is made = 96,000 + 26,000 = rs . 1 , 22,000 answer : c"
Answer: c
Problem: caleb spends $ 64.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 29 , b ) 10 , c ) 20 , d ) 40 , e ) 45
Rationale: "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 64.50 . by solving the equations y = 29 . ans a ."
Answer: a
Problem: if two integers x , y ( x > y ) are selected from - 10 to 4 ( inclusive ) , how many possible cases are there ?
Options: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 105
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 15 c 2 = 15 * 14 / 2 = 105 . therefore , the answer is e ."
Answer: e
Problem: in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 30800 . how many times did he participate in the competition ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "30800 = 2 * 2 * 2 * 2 * 5 * 5 * 7 * 11 john participated 8 times . the answer is d ."
Answer: d
Problem: a rectangular plot measuring 40 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 ) 36 m , c ) 26 m , d ) 56 m , e ) 25 m
Rationale: "perimeter of the plot = 2 ( 40 + 50 ) = 180 m no of poles = 180 / 5 = 36 m answer : b"
Answer: b
Problem: the no 2.52 , when written as a fraction and reduced to lowest terms , the sum of the numeratr n denominator is :
Options: a ) 7 , b ) 141 , c ) 29 , d ) 349 , e ) 359
Rationale: the actual question has bar on decimal part . hence the number is 2.5252525252 . . . . . . so let x = 2.525252 . . then 100 x = 252.525252 100 x - x = 250 x = 250 / 99 so ans = num + den = 349 answer : d
Answer: d
Problem: if sharon ' s weekly salary increased by 15 percent , she would earn $ 575 per week . if instead , her weekly salary were to decreased by 12 percent , how much would she earn per week ?
Options: a ) rs . 540 , b ) rs . 580 , c ) rs . 560 , d ) rs . 620 , e ) rs . 650
Rationale: "soln : - ( 575 / 115 ) 112 = 560 in this case long division does not take much time . ( 23 / 5 ) = 4.6 4.6 * 112 = rs . 560 answer : c"
Answer: c
Problem: of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 20 percent was planted with potato and 70 percent of the cleared land was planted with tomato . if the remaining 630 acres of cleared land was planted with corn , how many acres did the farmer own ?
Options: a ) 7000 , b ) 6800 , c ) 8000 , d ) 5400 , e ) 7100
Rationale: 20 % od 90 % = 18 % , 70 % 0 f 90 % = 63 % so the remaining 90 - 18 - 63 = 9 % = 630 acres or 10 % of 90 % = 9 % - - > 630 / 9 * 100 = 7000 acres answer ( a )
Answer: a
Problem: a , band c can do a piece of work in 11 days , 20 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 20 = 31 / 220 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 day ' s = 31 / 220 + 6 / 55 = 55 / 220 = 1 / 4 1 / 4 th work done in 2 days work done = 4 * 2 = 8 days answer : b"
Answer: b
Problem: a man buys an article for $ 10 . and sells it for $ 30 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 150 % , e ) 300 %
Rationale: "c . p . = $ 10 s . p . = $ 30 gain = $ 20 gain % = 20 / 10 * 100 = 300 % answer is e"
Answer: e
Problem: a man buys 56 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 7.6 % , b ) 7.7 % , c ) 20.52 % , d ) 23.62 % , e ) 27.82 %
Rationale: "explanation : let marked price be re . 1 each c . p . of 56 pens = rs . 46 s . p . of 56 pens = 99 % of rs . 56 = rs . 55.44 profit % = ( profit / c . p . ) x 100 profit % = ( 9.44 ) x 100 = 20.52 % answer : c"
Answer: c
Problem: a train running at the speed of 58 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 145 , b ) 272 , c ) 278 , d ) 277 , e ) 112
Rationale: "speed = 58 * ( 5 / 18 ) m / sec = 145 / 9 m / sec length of train ( distance ) = speed * time ( 145 / 9 ) * 9 = 145 meter answer : a"
Answer: a
Problem: what is the least common multiple of 812 , 3214
Options: a ) 672 , b ) 682 , c ) 328 , d ) 964 , e ) 285
Rationale: the given numbers are 8,12 , 32,14 thus the l . c . m is 2 * 2 * 2 * 1 * 3 * 4 * 7 = 672 the answer is a
Answer: a
Problem: a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 1.1 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 1.0 , b ) 1.2 , c ) 1.4 , d ) 1.6 , e ) 1.8
Rationale: "72 km / hr = 1.2 km / min the total distance is 1.2 km . 1.2 / 1.2 = 1 minute the answer is a ."
Answer: a
Problem: the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 20 , what is the perimeter of the garden in feet ?
Options: a ) 32
b ) 36
c ) 40
d ) 44
e ) 48
Rationale: let x be the length of one side of the square garden . x ^ 2 = 8 x + 20 x ^ 2 - 8 x - 20 = 0 ( x - 10 ) ( x + 2 ) = 0 x = 10 , - 2 p = 4 ( 10 ) = 40 the answer is c .
Answer: c
Problem: a student is ranked 13 th from right and 8 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: from right 13 , from left 8 total = 13 + 8 - 1 = 20 answer : c
Answer: c
Problem: a train crosses a platform of 200 m in 20 sec , same train crosses another platform of length 350 m in 25 sec . then find the length of the train ?
Options: a ) 150 m , b ) 180 m , c ) 400 m , d ) 250 m , e ) 155 m
Rationale: "length of the train be ‘ x ’ x + 200 / 20 = x + 350 / 25 5 x + 1000 = 4 x + 1400 x = 400 m answer : c"
Answer: c
Problem: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 30 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 8 , c ) 14 , d ) 16 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.30 * 8 = 0.2 ( x + 8 ) - - > x = 8 . answer : b ."
Answer: b
Problem: 8 + 8
Options: a ) 5 , b ) 17 , c ) 16 , d ) 23 , e ) 19
Rationale: c
Answer: c
Problem: on dividing a number by 357 , we get 40 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 6 , b ) 5 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 40 = ( 17 * 21 * y ) + ( 17 * 2 ) + 6 = 17 * ( 21 y + 2 ) + 6 . required number = 6 . answer is a"
Answer: a
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 14 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 105
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 5 x + 2 / 3 x + 14 x - 13 / 15 x = 14 2 / 15 x = 14 = > so x = ( 15 / 2 ) * 14 = 105 km answer e"
Answer: e
Problem: a certain protective additive increases from 30 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 100 % , d ) 66 2 / 3 % , e ) 75 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by ( 60 − 30 ) / 30 ∗ 100 = 100 answer : c"
Answer: c
Problem: the present worth of rs . 1404 due in two equal half - yearly instalments at 8 % per annum . simple interest is :
Options: a ) 1320 , b ) 1300 , c ) 1325 , d ) 120 , e ) none of these
Rationale: "explanation : required sum = pw of rs . 702 due 6 months hence + pw of rs . 702 due 1 year hence = rs . [ 100 × 702 / 100 + ( 8 × 12 ) + 100 × 702 / 100 + ( 8 × 1 ) ] = rs . 1325 answer : c"
Answer: c
Problem: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 19 , what was the price before the first discount ?
Options: a ) $ 45.10 , b ) $ 34.31 , c ) $ 28.44 , d ) $ 67.54 , e ) $ 33.77
Rationale: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 19 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 19 solve for x x = $ 33.77 correct answer e"
Answer: e
Problem: sum of two numbers is 40 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) 26 , 14 , b ) 23 , 17 , c ) 17 , 23 , d ) 14 , 26 , e ) 15 , 25
Rationale: "explanation : x + y = 15 3 y ã ¢ â ‚ ¬ â € œ 2 x = 5 x = 23 y = 17 answer : b"
Answer: b
Problem: a cab driver 5 days income was $ 600 , $ 250 , $ 450 , $ 400 , $ 800 . then his average income is ?
Options: a ) $ 460 , b ) $ 480 , c ) $ 500 , d ) $ 520 , e ) $ 540
Rationale: "avg = sum of observations / number of observations avg income = ( 600 + 250 + 450 + 400 + 800 ) / 5 = 500 answer is c"
Answer: c
Problem: what is the units digit of ( 3 ^ 10 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 10 = 3 ^ 4 * 2 + 2  3 ^ 2 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 10 ) ( 4 ^ 13 )  ( 3 ^ 2 ) ( ~ 4 ) = ( ~ 9 ) ( ~ 4 ) = ~ 6 . therefore , the answer is c ."
Answer: c
Problem: two trains of equal are running on parallel lines in the same direction at 52 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 50 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 52 - 36 = 16 km / hr . = 16 * 5 / 18 = 40 / 9 m / sec . 2 x / 36 = 40 / 9 = > x = 80 . answer : c"
Answer: c
Problem: a volume of 11780 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 ) 2945
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 11780 l can be kept in ( 11780 / 4 ) hemispheres ans . 2945 answer : e"
Answer: e
Problem: when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.2 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.2 then x = 0.2 / 1000 = 0.0002 . the answer is e"
Answer: e
Problem: square x is inscribed in circle y . if the perimeter of x is 64 , what is the circumference of y ?
Options: a ) 16 √ 2 π
b ) 8 √ 2 π
c ) 22 √ 2 π
d ) 12 √ 2 π
e ) 9
Rationale: square forms two right angled triangles . any time we have a right angle triangle inside a circle , the hypotenuse is the diameter . hypotenuse here = diagonal of the square = 16 sqrt ( 2 ) = diameter = > radius = 8 sqrt ( 2 ) circumference of the circle = 2 pi r = 16 pi sqrt ( 2 ) answer is a .
Answer: a
Problem: two trains of length 210 m and 120 m are 160 m apart . they start moving towards each other on parallel tracks , at speeds 74 kmph and 92 kmph . after how much time will the trains meet ?
Options: a ) 35 / 10 , b ) 31 / 10 , c ) 31 / 10 , d ) 36 / 10 , e ) 37 / 10
Rationale: they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 74 + 92 ) * 5 / 18 = 46.1 mps . the time required = d / s = 160 / 46.1 = 35 / 10 sec . answer : a
Answer: a
Problem: a man can row 8 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.98 , b ) 7.98 , c ) 7.96 , d ) 5.87 , e ) 5.82
Rationale: "m = 8 s = 1.2 ds = 9.6 us = 6.8 x / 9.6 + x / 6.8 = 1 x = 3.98 d = 3.98 * 2 = 7.96 answer : c"
Answer: c
Problem: after getting 2 successive discounts , a shirt with a list price of rs 150 is available at rs 105 . if the second discount is 12.55 , find the first discount
Options: a ) 22 % , b ) 23 % , c ) 21 % , d ) 20 % , e ) 17 %
Rationale: let the first discount be x % then , 87.5 % of ( 100 - x ) % of 150 = 105 87.5 / 100 * ( 100 - x ) / 100 * 450 = 150 = > 105 = > 100 - x = ( 105 * 100 * 100 ) / ( 150 * 87.5 ) = 80 x = ( 100 - 80 ) = 20 first discount = 20 % option d
Answer: d
Problem: from a pack of 52 cards , two cards are drawn together at random . what is the probability of one is a spade and one is a heart ?
Options: a ) 102 / 102 , b ) 5 / 102 , c ) 1 / 102 , d ) 8 / 102 , e ) 13 / 102
Rationale: solution let s be the sample space . then , n ( s ) = 52 c 2 = ( 52 × 51 ) / ( 2 × 1 ) = 1326 . let e = event of getting 1 spade and 1 heart . n ( e ) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = ( 13 c 1 * 13 c 1 ) = 169 . p ( e ) = n ( e ) / n ( s ) = 169 / 1326 = 13 / 102 . answer e
Answer: e
Problem: 10 is added to a certain number , the sum is multiplied by 2 , the product is divided by 2 and 2 is subtracted from the quotient . the remainder left is half of 88 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 25 , d ) 36 , e ) 45
Rationale: "let number is x . when 10 added to it , = ( x + 10 ) 2 multiplied to sum , = 2 * ( x + 10 ) now , = [ { 2 * ( x + 10 ) } / 2 ] and , = [ { 2 * ( x + 10 ) } / 2 ] - 2 according to question , [ { 2 * ( x + 10 ) } / 2 ] - 2 = half of 88 [ ( 2 x + 20 ) / 2 ) = 44 + 2 x + 10 = 46 x + 10 = 46 x = 46 - 10 x = 36 so , required number is : 36 . answer : d"
Answer: d
Problem: four dice are thrown simultaneously . find the probability that all of them show the same face .
Options: a ) 1 / 216 , b ) 1 / 215 , c ) 5 / 300 , d ) 1 / 415 , e ) 1 / 500
Rationale: "total no of elementary events = 6 ^ 4 n ( s ) = 6 ^ 4 x = { ( 1,1 , 1,1 ) ( 2,2 , 2,2 ) . . . . . ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) / n ( s ) = 6 / 6 ^ 4 = 1 / 216 answer a"
Answer: a
Problem: when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 2 of the remaining balance , what will be the final balance in her bank account ?
Options: a ) 300 , b ) 375 , c ) 450 , d ) 500 , e ) 575
Rationale: "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 2 of 300 = 150 total amount in her account = 450 answer c"
Answer: c
Problem: the simple form of the ratio 8 / 5 : 2 / 3 is ?
Options: a ) 12 : 5 , b ) 12 : 7 , c ) 7 : 12 , d ) 5 : 7 , e ) 4 : 7
Rationale: "8 / 5 : 2 / 3 = 12 : 5 answer : a"
Answer: a
Problem: in measuring the sides of a rectangle , one side is taken 16 % 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 ) 10.2 % , 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 116 * 95 = 11,020 , which is 10.2 % greater than the actual area . answer : c ."
Answer: c
Problem: a can do a work in 6 days . b can do the same work in 8 days . both a & b together will finish the work and they got $ 1000 from that work . find their shares ?
Options: a ) 600,800 , b ) 500,500 , c ) 300,700 , d ) 800,200 , e ) 550,450
Rationale: "ratio of their works a : b = 6 : 8 ratio of their wages a : b = 3 : 4 a ' s share = ( 3 / 5 ) 1000 = 600 b ' s share = ( 4 / 5 ) 1000 = 800 correct option is a"
Answer: a
Problem: what is the sum of all the multiples of 12 between 30 and 200 ?
Options: a ) 1648 , b ) 1632 , c ) 1626 , d ) 1612 , e ) 1800
Rationale: "you first have to know all the multiples of 12 between 30 and 200 . they are 12 , 24,36 , 48,60 , 72,84 , 96,108 , 120,132 , 144,156 , 168,180192 . if you add all these numbers together , you get 1632 . final answer : b"
Answer: b
Problem: what is the least number should be added to 1100 , so the sum of the number is completely divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 4 , e ) 8
Rationale: "( 1100 / 23 ) gives remainder 19 19 + 4 = 23 , so we need to add 4 answer : d"
Answer: d
Problem: ritesh and co . generated revenue of rs . 1,250 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 1,250 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1250 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1250 . = > 10,000 . hence , the total revenue by end of 2007 is rs . 10,000 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 10000 ) × 100 . = > 25 % . answer : c"
Answer: c
Problem: if p ( a ) = 4 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 8 / 25 , b ) 1 / 25 , c ) 2 / 25 , d ) 3 / 14 , e ) 25 / 8
Rationale: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 4 / 5 . 2 / 5 p ( a n b ) = 8 / 25 . a"
Answer: a
Problem: a making a cube with dimension 5 * 5 * 5 using 1 * 1 * 1 cubes . what is the number of cubes needed to make hollow cube looking of the same shape .
Options: a ) 98
b ) 99
c ) 100
d ) 101
e ) 102
Rationale: 125 1 * 1 * 1 small cubes = 5 * 5 * 5 cubes because hallow in inner we do n ' t have 3 * 3 * 3 cubes so 125 - 27 = 98 cubes required answer : a
Answer: a
Problem: how many 4 digit numbers have no repeat digits , do not contain zero , and have a sum of digits f equal to 28 ?
Options: a ) 14 , b ) 24 , c ) 28 , d ) 48 , e ) 96
Rationale: first , look for all 4 digits without repeat that add up to 28 . to avoid repetition , start with the highest numbers first . start from the largest number possible 9874 . then the next largest number possible is 9865 . after this , you ' ll realize no other solution . clearly the solution needs to start with a 9 ( cuz otherwise 8765 is the largest possible , but only equals 26 ) . with a 9 , you also need an 8 ( cuz otherwise 9765 is the largest possible , but only equals 27 ) . with 98 __ only 74 and 65 work . so you have two solutions . each can be rearranged in 4 ! = 24 ways . so f = 24 + 24 = 48 . d
Answer: d
Problem: tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many q kilometers per hour did tammy walk on the second day ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6
Rationale: "ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5"
Answer: c
Problem: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 580 ?
Options: a ) rs . 500 , b ) rs . 5100 , c ) rs . 530 , d ) rs . 540 , e ) none of these
Rationale: "explanation : 580 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 500 answer : option a"
Answer: a
Problem: of 300 surveyed students , 20 % of those who read book a also read book b and 50 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
Options: a ) 120 , b ) 125 , c ) 130 , d ) 135 , e ) 150
Rationale: "say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 50 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.5 b - - > a = 2.5 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 300 = 2.5 b + b - 0.5 b - - > b = 100 , a = 2.5 b = 250 and { both } = 0.5 b = 50 . the number of students who read only book a is { a } - { both } = 250 - 50 = 200 ; the number of students who read only book b is { b } - { both } = 100 - 50 = 50 ; the difference is 200 - 50 = 150 . answer : e ."
Answer: e
Problem: a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 3 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 12 : 15 , b ) 1 : 4 , c ) 1 : 5 , d ) 2 : 5 , e ) 1 : 3
Rationale: "say theratio of cats to dogs is a / b . then the numberof cats would be ax and the number of dogs bx , for some positive integer x . we are told that ax - bx = 3 - - > x ( a - b ) = 3 . since 3 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 13 . the above implies that either x = 1 and ( a - b ) = 3 or x = 3 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13 . for the original question only option which fits is e , 4 : 5 . cats = 3 * 4 = 12 and dogs = 3 * 5 = 15 . answer : a ."
Answer: a
Problem: in one hour , a boat goes 13 km / hr along the stream and 9 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 11 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "explanation : let the speed downstream be a km / hr and the speed upstream be b km / hr , then speed in still water = 1 / 2 ( a + b ) km / hr rate of stream = 1 / 2 ( a − b ) km / hr speed in still water = 1 / 2 ( 13 + 9 ) kmph = 11 kmph . answer : option a"
Answer: a
Problem: 6 mat - weavers can weave 6 mats in 6 days . at the same rate , how many mats would be woven by 8 mat - weavers in 8 days ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "let the required number of mats be x more mat - weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) hence we can write as ( mat - weavers ) 6 : 8 } : : 6 : x ( days ) 6 : 8 ⇒ 6 × 6 × x = 8 × 8 × 6 ⇒ x = 10 answer : b"
Answer: b
Problem: if the cost price is 80 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 11 % , c ) 13 % , d ) 25 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 80 profit = $ 20 profit % = 20 / 80 * 100 = 25 / 6 = 25 % answer is d"
Answer: d
Problem: dacid obtained 81 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 29 , b ) 38 , c ) 76 , d ) 37 , e ) 75
Rationale: "average = ( 81 + 65 + 82 + 67 + 85 ) / 5 = 76 . answer : c"
Answer: c
Problem: he average of 30 numbers is zero . of them , at the most , how many may be greater than zero ?
Options: a ) 29 , b ) 1 , c ) 10 , d ) 30 , e ) 8
Rationale: average of 30 numbers = 0 . sum of 30 numbers ( 0 x 30 ) = 0 . it is quite possible that 29 of these numbers may be positive and if their sum is a the 30 th number is ( - a ) . answer : option a
Answer: a
Problem: in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 11 and 200 , then the least and greatest integer on the card would be
Options: a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 13 , d ) 4 and 14 , e ) 5 and 14
Rationale: "given : 11 < x ( x + 1 ) < 200 . now , it ' s better to test the answer choices here rather than to solve : if x = 3 then x ( x + 1 ) = 12 > 11 - - > so , the least value is 4 . test for the largest value : if x = 15 then x ( x + 1 ) = 15 * 16 = 240 > 200 - - > discard b . answer : a ."
Answer: a
Problem: a number when divided by 342 gives a remainder 47 . when the same number if it divided by 19 , what would be the remainder ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 9 , e ) 11
Rationale: "on dividing the given number by 342 , let k be the quotient and 47 as remainder . then , number – 342 k + 47 = ( 19 x 18 k + 19 x 2 + 9 ) = 19 ( 18 k + 2 ) + 9 .  the given number when divided by 19 , gives ( 18 k + 2 ) as quotient and 9 as remainder . answer d"
Answer: d
Problem: √ ( 36 ) ^ 2
Options: a ) 6 , b ) 14 , c ) 36 , d ) 21 , e ) none of these
Rationale: explanation √ ( 36 ) ^ 2 = ? or , ? = 36 answer c
Answer: c
Problem: a and b start a business , with a investing the total capital of rs . 100000 , 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 . 10000 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 ) 2520000 , b ) b ) 2620000 , c ) c ) 2820000 , d ) d ) 2920000 , e ) e ) 2420000
Rationale: "interest received by a from b = 10 % of half of rs . 100000 = 10 % * 50000 = 5000 . amount received by a per annum for being a working partner = 10000 * 12 = rs . 120000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 5000 + 120000 + 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 ( 5000 + 120000 + p ) = 2 ( p ) p = 125000 total profit = 2 p + 120000 = 2 * 125000 + 120000 = 2620000 answer : b"
Answer: b
Problem: double of quarter of 1 percent written as a decimal is :
Options: a ) 0.003 , b ) 0.0005 , c ) 0.25 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 1 % = 2 * ( 1 / 4 * 1 / 100 ) = 1 / 400 = 2 * 0.0025 = 0.005 . answer : d"
Answer: d
Problem: 15 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 30 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 15 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 15 * 21 * 8 = 14 * x * 6 x = 30 answer : c"
Answer: c
Problem: the number 49 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 11 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 49 : 1 , 4 , 9 , 16 , 25 , 36 , 49 . . now , 49 should be the sum of 3 of those 7 numbers . also to simplify a little bit trial and error , we can notice that as 49 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 49 equals to 4 + 9 + 36 = 2 ^ 2 + 3 ^ 2 + 6 ^ 2 = 49 - - > 2 + 3 + 6 = 11 . answer : a ."
Answer: a
Problem: he total marks obtained by a student in physics , chemistry and mathematics is 140 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 70 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 140 + p c + m = 140 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 140 / 2 = 70 . answer : b"
Answer: b
Problem: 4 men can check exam papers in 8 days working 5 hours regularly . what is the total hours when 2 men will check the double of the papers in 20 days ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 1 , e ) 5
Rationale: let a man can do 1 unit of work in 1 hour . total units of work = 4 x 8 x 5 = 160 units . now work = 2 x 160 = 320 units . now 2 men work for 20 days . let in x hours they have to work per day . now total work = 2 × x × 20 = 40 x 40 x = 320 so x = 320 / 40 = 8 hours . answer : a
Answer: a
Problem: given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 1 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > only in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . i . e 0 , 1,5 or 6 intersection of values is 6 , thus the units digit of p + 1 is 6 + 1 = 9 . answer : a ."
Answer: a
Problem: the population of a town is 10000 . it increases annually at the rate of 30 % p . a . what will be its population after 2 years ?
Options: a ) 14000 , b ) 14400 , c ) 14500 , d ) 14600 , e ) 16900
Rationale: "formula : 10000 × 130 / 100 × 130 / 100 = 16900 answer : e"
Answer: e
Problem: find the area of a parallelogram with base 18 cm and height 16 cm ?
Options: a ) 423 cm 2 , b ) 122 cm 2 , c ) 420 cm 2 , d ) 251 cm 2 , e ) 288 cm 2
Rationale: "area of a parallelogram = base * height = 18 * 16 = 288 cm 2 answer : e"
Answer: e
Problem: evaluate : 50 - 12 ÷ 2 × 2 =
Options: a ) a ) 36 , b ) b ) 38 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
Rationale: "according to order of operations , 12 ÷ 2 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 2 × 2 = 6 × 2 = 12 hence 50 - 12 ÷ 6 × 2 = 50 - 12 = 38 correct answer is b ) 38"
Answer: b
Problem: when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 5 , the remainder is 5 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 0 . . a"
Answer: a
Problem: 16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 24 girls will take to construct ?
Options: a ) 4 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 24 girls = 8 ã — 6 / 4 + 12 = 12 + 24 = 36 girls 4 days to complete the work answer : option a"
Answer: a
Problem: the incomes of two persons a and b are in the ratio 3 : 4 . if each saves rs . 100 per month , the ratio of their expenditures is 1 : 2 . find their incomes ?
Options: a ) 150,287 , b ) 150,219 , c ) 150,200 , d ) 150,298 , e ) 150,217
Rationale: the incomes of a and b be 3 p and 4 p . expenditures = income - savings ( 3 p - 100 ) and ( 4 p - 100 ) the ratio of their expenditure = 1 : 2 ( 3 p - 100 ) : ( 4 p - 100 ) = 1 : 2 2 p = 100 = > p = 50 their incomes = 150 , 200 answer : c
Answer: c
Problem: a certain country is divided into 6 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 9 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 5
Rationale: let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 9 the total number of traditionalists is 6 p / 9 = 2 p / 3 . the total population is p + 2 p / 3 = 5 p / 3 p / ( 5 p / 3 ) = 3 / 5 the answer is e .
Answer: e
Problem: a tradesman sold an article at a loss of 10 % . if the selling price had been increased by $ 50 , there would have been a gain of 10 % . what was the cost price of the article ?
Options: a ) $ 150 , b ) $ 200 , c ) $ 250 , d ) $ 120 , e ) $ 100
Rationale: "let c . p . be $ x then 110 % of x - 90 % of x = 50 20 % of x = 50 x / 5 = 50 x = 250 answer is c"
Answer: c
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.20 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 799.2 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.2 = 799.2 answer : c"
Answer: c