regisss/math_qa huggingface dataset:
Problem: a man can row 6 kmph in still water . when the river is running at 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 ) 5.32 , b ) 5.7 , c ) 5.76 , d ) 5.74 , e ) 5.71
Rationale: "m = 6 s = 2 ds = 8 us = 4 x / 8 + x / 4 = 1 x = 2.66 d = 2.66 * 2 = 5.32 answer : a"
Answer: a
Problem: if 8 workers can build 8 cars in 8 days , then how many days would it take 6 workers to build 6 cars ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: "8 workers can build 1 car per day on average . 1 worker can build 1 / 8 of a car per day . 6 workers can build 6 / 8 car per day . the time required to build 6 cars is 6 / ( 6 / 8 ) = 8 days the answer is d ."
Answer: d
Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 31 !
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "solution - consider multiples of 25 ! = > 3,6 , 9,12 , 15,18 , 21,24 , 27,30 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 21 = 3 x 7 - > 1 24 = 3 x 8 - > 1 27 = 3 x 3 x 3 - > 3 30 = 3 x 10 - > 1 - - - - count 3 ' s = 14 so answer is 14 answer : d"
Answer: d
Problem: a person can swim in still water at 12 km / h . if the speed of water 10 km / h , how many hours will the man take to swim back against the current for 8 km ?
Options: a ) 4 , b ) 7 , c ) 5 , d ) 9 , e ) 6
Rationale: "m = 12 s = 10 us = 12 - 10 = 2 d = 8 t = 8 / 2 = 4 answer : a"
Answer: a
Problem: the moon revolves around the earth at a speed of approximately 0.2 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 720 , c ) 62.5 , d ) 3,600 , e ) 3,672
Rationale: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 0.2 * 3600 = 720 kilometers per hour . option b is correct"
Answer: b
Problem: if 1.5 cm of a pencil is purple , 0.5 cm of the remaining is black and the remaining 2 cm is blue , what is the total length of the pencil ?
Options: a ) 5 cm , b ) 3 cm , c ) 1 cm , d ) 4 cm , e ) 2 cm
Rationale: purple is 1.5 cm black is 0.5 cm blue is 2 cm 1.5 + 0.5 + 2 = 4 cm answer is d ) 4 cm
Answer: d
Problem: of the 130 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 30 answer : option b
Answer: b
Problem: what is the rate percent when the simple interest on rs . 810 amount to rs . 155 in 4 years ?
Options: a ) 4.78 , b ) 4.68 , c ) 4.58 , d ) 4.48 , e ) 4.38
Rationale: "155 = ( 810 * 4 * r ) / 100 r = 4.78 % answer : a"
Answer: a
Problem: a pharmaceutical company received $ 4 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 58 %
Rationale: "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 4 / 20 = 1 / 5 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 4 / 20 ) x 60 = 12 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 12 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 12 ) / 12 ] x 100 - 175 / 3 x 100 at this point we can stop and consider the answer choices . since we know that 175 / 3 is just a bit less than ½ , we know that - 175 / 3 x 100 is about a 58 % decrease . answer e ."
Answer: e
Problem: a father said to his son , ` ` i was as old as you are at the present at the time of your birth ' ' . if the father ' s age is 52 years now , the son ' s age 5 years back was :
Options: a ) a ) 14 , b ) b ) 67 , c ) c ) 56 , d ) d ) 21 , e ) e ) 34
Rationale: let the son ' s present age be x years . then , ( 52 - x ) = x 2 x = 52 . x = 26 . son ' s age 5 years back ( 26 - 5 ) = 21 years . answer : d
Answer: d
Problem: at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 20 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 20 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "let number of apples = a number of oranges = b a + b = 20 - - - 1 . 56 = ( . 4 a + . 6 b ) / 20 = > 56 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 4 b = 16 let the number of oranges put back = c 52 * ( 20 - c ) = 40 * 4 + 60 ( 16 - c ) = > c = 10 answer e"
Answer: e
Problem: there are 20 cm , 21 cm , 22 cm , 23 cm , 24 cm , 25 cm rods of quantities 23 , 64 , 32 respectively . find average of this data .
Options: a ) 32.25 , b ) 21.45 , c ) 45 , d ) 22.45 , e ) 22
Rationale: average = ( 20 * 2 + 21 * 3 + 22 * 6 + 23 * 4 + 24 * 3 + 25 * 2 ) / 20 = 22.45 answer : d
Answer: d
Problem: a can finish a work in 18 days and b can do the same work in half the time taken by a . then , working together what part of the same work they can finish in a day ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 6 , d ) 2 / 5 , e ) 2 / 9
Rationale: 1 days work of a + b = ( 18 + 9 ) / 18 * 9 = 1 / 6 answer is c
Answer: c
Problem: if n is a positive integer and n ^ 2 is divisible by 18 , then what is the largest positive integer that must divide n ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "18 = 2 * 3 ^ 2 if 18 divides n ^ 2 , then n must be divisible by 2 * 3 = 6 the answer is c ."
Answer: c
Problem: an employee ’ s annual salary was increased $ 25000 . if her new annual salary now equals $ 90000 , what was the percent increase ?
Options: a ) 15 % , b ) 162 ⁄ 3 % , c ) 20 % , d ) 38.46 % , e ) 24 %
Rationale: new annual salary = $ 90,000 salary increase = $ 25,000 . original salary = $ 90,000 - $ 25,000 . = $ 75,000 % increase = ( $ 25,000 / $ 65,000 ) * 100 = 38.46 % hence d .
Answer: d
Problem: in a class of 45 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?
Options: a ) 30 , b ) 10 , c ) 18 , d ) 23 , e ) 32
Rationale: "total = english + german - both + neither - - > 45 = english + 22 - 12 + 0 - - > english = 35 - - > only english = english - both = 35 - 12 = 23 . answer : d ."
Answer: d
Problem: mr . parkin invested in fund z and fund b . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund z paid 23 % and fund b paid 17 % . the interest earned in fund b was exactly $ 200 greater than the interest earned in fund z . how much did ms . morris invest in fund z ?
Options: a ) $ 32000 , b ) $ 36000 , c ) $ 40000 , d ) $ 42000 , e ) $ 45000
Rationale: 0.17 b - 0.23 z = 200 | * 100 17 b - 23 z = 20000 z + b = 100000 b = 100000 - z 17 ( 100000 - z ) - 23 z = 20000 1 , 700000 - 17 z - 23 z = 20000 1 , 680000 = 40 z divide by 40 first two digits : 42 . . . so answer is d .
Answer: d
Problem: a train 100 meters long completely crosses a 300 meters long bridge in 36 seconds . what is the speed of the train is ?
Options: a ) 32 kmph , b ) 76 kmph , c ) 34 kmph , d ) 43 kmph , e ) 40 kmph
Rationale: "s = ( 100 + 300 ) / 36 = 400 / 36 * 18 / 5 = 40 answer : e"
Answer: e
Problem: a school has 11 maths 8 physics and 5 chemistry teachers each teacher can teach 3 subjects max what is he minimum number of teachers required
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "total subjects = 11 + 8 + 5 = 24 max subjects by 1 teacher = 3 so , min of teachers required = 24 / 3 = 8 answer : d"
Answer: d
Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 3 , – 4 ) , k = ( – 3 , 1 ) , l = ( 5 , 7 ) , and m = ( 5 , – 4 ) . what is its perimeter ?
Options: a ) 34 , b ) 36 , c ) 38 , d ) 40 , e ) ( f ) 42
Rationale: jk = 5 lm = 11 kl = using distance formula 10 jm = using distance formula 8 sum of all is 34 a
Answer: a
Problem: | - 2 | ( | - 25 | - | 5 | ) = ? ? source : preparation material mba center
Options: a ) 40 , b ) – 60 , c ) 60 , d ) 75 , e ) 100
Rationale: absolute value will turn negatives into their positive ' equivalents ' , and will leave positives unchanged , so | - 2 | = 2 , | - 25 | = 25 , and | 5 | = 5 . getting rid of our absolute values we have : | - 2 | ( | - 25 | - | 5 | ) = ( 2 ) ( 25 - 5 ) = 2 * 20 = 40
Answer: a
Problem: at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 30 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 30 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 14 , e ) 15
Rationale: "let number of apples = a number of oranges = b a + b = 30 - - - 1 . 56 = ( . 4 a + . 6 b ) / 30 = > 56 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 6 b = 24 let the number of oranges put back = c 52 * ( 30 - c ) = 40 * 6 + 60 ( 24 - c ) = > c = 15 answer e"
Answer: e
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 12 % while buying and by 30 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 60 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 112 kg ; the owner sells 100 kg but actually gives 70 kg ; profit : ( 112 - 70 ) / 70 * 100 = ~ 60 % answer : d ."
Answer: d
Problem: a train covers a distance of 12 km in 16 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 80 , b ) 90 , c ) 60 , d ) 75 , e ) 85
Rationale: "speed = ( 12 / 16 * 60 ) km / hr = ( 45 * 5 / 18 ) m / sec = 12.5 m / sec . length of the train = 12.5 * 6 = 75 m . answer : d"
Answer: d
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 180 kg . in the first week 28 percent is cut away . in the second week 18 percent of the remainder is cut away . in the third week the statue is completed when 20 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 85 kg , c ) 108 kg , d ) 125 kg , e ) 117 kg
Rationale: "b 85 kg 180 ã — 0.72 ã — 0.82 ã — 0.8 = 85 kg ."
Answer: b
Problem: there are 22 kids in a classroom . 12 kids are wearing socks and 8 are wearing shoes . 6 kids are wearing both . how many are bare feet ?
Options: a ) 10 , b ) 2 , c ) 4 , d ) 5 , e ) 8
Rationale: 12 kids wear socks 8 kids wear shoes 6 wear both . 12 â € “ 6 = 6 ( wear only socks ) 8 â € “ 6 = 2 ( wear only shoes ) 6 ( wear both ) hence , 22 - 14 = 8 8 kids are with bare feet . e
Answer: e
Problem: a and b together can do a piece of work in 6 days and a alone can do it in 13 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 15 days , c ) 78 / 7 days , d ) 21 days , e ) 22 / 7 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 13 work in 1 day b alone can do ( 1 / 6 - 1 / 13 ) = 7 / 78 work in 1 day = > complete work can be done in 78 / 7 days by b answer : option c"
Answer: c
Problem: a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 5 for a dollar and the other at a rate of 5 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
Options: a ) 1 : 1 , b ) 1 : 5 , c ) 2 : 3 , d ) 1 : 2 , e ) 2 : 5
Rationale: "the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 5 - 1 / 5 = 0 dollars . the selling price of a mango from the second stack = 1 / 5 dollars - - > the loss from one mango = 1 / 5 - 1 / 5 = 0 dollars . no profit as whole 1 : 1 answer : a ."
Answer: a
Problem: what is the units digit of 26 ! + 50 ! + 4 ! + 4 ! ?
Options: a ) 8 , b ) 6 , c ) 4 , d ) 2 , e ) 0
Rationale: "let us first write down the factorials of different numbers : 1 ! = 1 2 ! = 2 3 ! = 6 4 ! = 24 5 ! = 120 6 ! = 720 and so on . if we notice here , all the numbers after 4 ! will end with a 0 . here is why : if we multiply any number by 10 , a 0 is added to that number and a 10 is formed by a 5 and a 2 , 10 = 5 * 2 till 4 ! , we do not have a ` ` 5 ' ' in multiplication . but after that , we will have atleast one ` ` 5 ' ' in the multiplication . coming back to the question , units digit of 26 ! + 50 ! + 4 ! + 4 ! = ? by the logic above , 26 ! and 50 ! will end in a ` ` 0 ' ' 4 ! will end in a 4 hence the units digit = 0 + 0 + 4 + 4 = 8 correct option : a"
Answer: a
Problem: the h . c . f of two numbers is 13 and their l . c . m is 2200 . if one of the numbers is 286 , then the other is ?
Options: a ) 85 , b ) 90 , c ) 95 , d ) 100 , e ) 105
Rationale: "other number = ( 13 * 2200 ) / 286 = 100 . answer : d"
Answer: d
Problem: the length of a side of a hexagon is 4 inches . what is the perimeter ?
Options: a ) 22
b ) 23
c ) 24
d ) 25
e ) 26
Rationale: hexagon . it means 6 equal sides . p = 6 ( 4 ) = 24 inches answer c
Answer: c
Problem: 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 . 23000 , my total savings for the two - year is
Options: a ) s . 8000 , 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 ) - ( 23000 + 35000 ) = 66000 - 58000 = rs . 8000 a"
Answer: a
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 112 m length ?
Options: a ) 82.1 sec , b ) 12.1 sec , c ) 16.1 sec , d ) 11.1 sec , e ) 12.15 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 112 = 222 m . required time = 222 / 20 = 11.1 sec . answer : d"
Answer: d
Problem: ketchup , mustard and mayo bottles at a hot dog stand are in the ratio of 3 : 3 : 2 . if there are 6 ketchup bottles , the number of mayo bottles at the hot dog stand is :
Options: a ) 12 , b ) 6 , c ) 3 , d ) 1 , e ) 4
Rationale: explanation : let ketchup = 3 x , mustard = 3 x & mayo = 2 x . now , 3 x = 6 hence x = 2 . number of mayo bottles = 2 x which is 4 . answer : e
Answer: e
Problem: the average of first 10 odd numbers is ?
Options: a ) 22 , b ) 10 , c ) 98 , d ) 66 , e ) 88
Rationale: "sum of 10 odd no . = 100 average = 100 / 10 = 10 answer : b"
Answer: b
Problem: at a certain university , 65 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
Options: a ) 25 , b ) 37.5 , c ) 50 , d ) 62.5 , e ) 75
Rationale: "total women = 65 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 25 % but question wants to know the percent of men that are tenured 25 % / 40 % = 62.5 % d"
Answer: d
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is
Options: a ) 8 / 17 , b ) 7 / 15 , c ) 3 / 15 , d ) 5 / 12 , e ) 1 / 4
Rationale: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 5 days they work 35 * 5 = 175 remaining work is 300 - 175 = 125 remaining fraction of work is = 125 / 300 = 5 / 12 answer d"
Answer: d
Problem: if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 16,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 750 , c ) $ 850 , d ) $ 800 , e ) $ 900
Rationale: "- > 250 / 5,000 = 5 % and 16,000 * 5 % = 800 . thus , d is the answer ."
Answer: d
Problem: of the 200 stamps in a collection , 90 are foreign and 80 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 50 , b ) 80 , c ) 100 , d ) 130 , e ) 150
Rationale: "20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 60 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 60 ) = 50 the answer is a ."
Answer: a
Problem: find the volume & curved surface area of a cylinder with diameter of base 14 cm and height 60 cm .
Options: a ) 260 cm 2
b ) 2610 cm 2
c ) 2600 cm 2
d ) 2640 cm 2
e ) 264 cm 2
Rationale: volume = pier 2 h = pie x 72 x 60 = 9240 cm 3 curved surface area = 2 pierh = ( 2 x 3.14 x 7 x 60 ) cm 2 = 2640 cm 2 answer : d
Answer: d
Problem: a car traveled 560 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 9 , b ) 16 , c ) 21 , d ) 22 , e ) 27
Rationale: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 462 miles will be covered in 462 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 560 / h = > 336 / c = 560 / ( c + 6 ) = > 336 c + 336 * 6 = 560 c = > c = 336 * 6 / 224 = 9 answer a ."
Answer: a
Problem: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 2 dm by 5 dm . the number of stones required is :
Options: a ) 180
b ) 1800
c ) 5400
d ) 18000
e ) 1.8
Rationale: area of the hall = 3600 * 1500 area of each stone = ( 20 * 50 ) therefore , number of stones = ( 3600 * 1500 / 20 * 50 ) = 5400 answer : c
Answer: c
Problem: by selling an article at rs . 900 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 600 , b ) s . 480 , c ) s . 500 , d ) s . 540 , e ) s . 550
Rationale: "sp = 900 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 900 * [ 100 / 125 ] = 720 loss = 25 % = 25 % of 720 = rs . 180 sp = cp - loss = 720 - 180 = rs . 540 answer : d"
Answer: d
Problem: a train 220 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 12 , e ) 9
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 220 * 3 / 55 ] sec = 12 sec answer : option d"
Answer: d
Problem: assume that f ( 1 ) = 0 and f ( m + n ) = f ( m ) + f ( n ) + 4 ( 9 mn - 1 ) . for all natural numbers ( integers > 0 ) m and n . what is the value of f ( 17 ) ?
Options: a ) 4832 , b ) 4855 , c ) 4825 , d ) 4895 , e ) 4862
Rationale: explanation : f ( 1 ) = 0 f ( 2 ) = f ( 1 + 1 ) = f ( 1 ) + f ( 1 ) + 4 ( 9 × 1 × 1 – 1 ) = 0 + 0 + 4 × 8 = 32 f ( 4 ) = f ( 2 + 2 ) = f ( 2 ) + f ( 2 ) + 4 ( 9 × 2 × 2 – 1 ) = 32 + 32 + 4 × 35 = 204 f ( 8 ) = f ( 4 + 4 ) = f ( 4 ) + f ( 4 ) + 4 ( 9 × 4 × 4 – 1 ) = 204 + 204 + 4 × 143 = 980 f ( 16 ) = f ( 8 + 8 ) = f ( 8 ) + f ( 8 ) + 4 ( 9 × 8 × 8 – 1 ) = 980 + 980 + 4 × 575 = 4260 f ( 17 ) = f ( 1 + 16 ) = f ( 16 ) + f ( 1 ) + 4 ( 9 × 16 × 1 – 1 ) = 4260 + 0 + 4 × 143 = 4832 answer : a
Answer: a
Problem: allay ' s internet provider offers unlimited traffic which costs $ 0.5 per day charged off at 12 a . m . the service is discontinued when client ' s debt exceeds $ 5 . if today in the morning allay makes a payment of $ 7 , for how many days , including today , will she be connected to the internet without any additional payments , given her initial balance was $ 0 ?
Options: a ) 15 , b ) 24 , c ) 25 , d ) 26 , e ) 13
Rationale: day 0 - payment of $ 7 is made in the morning ( after 12 am midnight ) day 1 onwards ( after 12 am midnight ) internet service will begin and will run for 7 * 2 = 14 days i . e . at the end of day 15 balance will be zero . now allay can still use the internet till her debt reaches $ 5 which means total of 5 * 2 = 10 days . now the question states for how many days , including today , will she be connected to the internet without any additional paymentsi . e . we will have to include day 0 also in our final answer . therefore total no . of days = 1 + 14 + 10 = 25 = c
Answer: c
Problem: the smallest value of n , for which n + 3 is not a prime number , is
Options: a ) 1 , b ) 2 , c ) 6 , d ) 8 , e ) 3
Rationale: "( 1 + 3 ) = 3 . ( 2 + 3 ) = 5 . ( 3 + 3 ) = 6 . ( 4 + 3 ) = 7 . which is not prime , n = 3 . answer : e"
Answer: e
Problem: a man swims downstream 72 km and upstream 45 km taking 6 hours each time ; what is the speed of the current ?
Options: a ) 2.28 , b ) 2.24 , c ) 2.27 , d ) 2.25 , e ) 2.23
Rationale: "72 - - - 6 ds = 12 ? - - - - 1 45 - - - - 6 us = 7.5 ? - - - - 1 s = ? s = ( 12 - 7.5 ) / 2 = 2.25 answer : d"
Answer: d
Problem: if ( 2 ^ 16 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
Options: a ) 7 , b ) 8 , c ) 15 , d ) 16 , e ) 23
Rationale: given 2 ^ 16 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 16 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans d on comparing the power of 2 = > m = 16
Answer: d
Problem: 90 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 91 , e ) 81
Rationale: "explanation : 90 + 5 * 12 / ( 180 / 3 ) = 90 + 5 * 12 / ( 60 ) = 90 + ( 5 * 12 ) / 60 = 90 + 1 = 91 . answer : d"
Answer: d
Problem: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is
Options: a ) 289 , b ) 231 , c ) 200 , d ) 288 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"
Answer: c
Problem: a can finish a work in 20 days , b in 15 days and c in 12 days . b and c start the work but are forced to leave after 2 days . the remaining work was done by a in :
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "( b + c ) ’ s one day ’ s work = 1 / 15 + 1 / 12 = 3 / 20 work done by b and c in 2 days = 3 * 2 / 20 = 3 / 10 remaining work = 1 - 3 / 10 = 7 / 10 1 / 20 work is done by a in 1 day . so , 7 / 10 work is done by a in 20 * 7 / 10 = 14 days answer : e"
Answer: e
Problem: when positive integer n is divided by positive integer j , the remainder is 8 . if n / j = 150.25 , what is value of j ?
Options: a ) 16 , b ) 26 , c ) 32 , d ) 132 , e ) 20
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 150.25 here 150 is the quotient . given that remainder = 8 so , 150.25 = 150 + 8 / j so , j = 32 answer : c"
Answer: c
Problem: a welder received an order to make a 1 million liter cube - shaped tank . if he has only 2 x 3 meter sheets of metal that can be cut , how many metal sheets will be required for this order ? ( 1 cubic meter = 1000 liters )
Options: a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 100
Rationale: the question say : a welder received an order to make a 1 million liter cube - shaped tank . ( 1 cubic meter = 1,000 liters ) in other words , the tank is going to have a volume of 1000 cubic meters . that would equal 1 million liters . a cube with a volume of 1000 cubic meters must be ( 10 meters ) x ( 10 meters ) x ( 10 meters ) . the question does n ' t specify whether this tank should have a closed top or an open top . ( the real gmat is good about specifying things like that . ) here , we are going to assume a closed top , only because if the top is open , we do n ' t use enough metal - - - we get an answer smaller than any of the answer choices . a closed - top cube , a full cube , has 6 sides , each of which is ( 10 meters ) x ( 10 meters ) . that ' s a total surface area of 600 sq m . the question tells us : he has only 2 x 3 meter sheets of metal that can be cut . each sheet has an area of 6 sq m . how many of these need to fill up 600 sq m ? 600 / 6 = 100 . he needs 100 sheets . answer = e
Answer: e
Problem: if 18 persons can build a wall 140 m long in 42 days , the number of days that 30 persons will take to complete a similar wall 100 m long , is .
Options: a ) 18 , b ) 21 , c ) 24 , d ) 28 , e ) 30
Rationale: explanation : ( length 140 : 100 ) : ( persons 30 : 18 ) : : 42 : x = > 140 * 30 * x = 100 * 18 * 42 = > or x = 18 answer : a
Answer: a
Problem: when x is multiplied by 3 , the result is 10 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) - 4 , b ) 9 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 10 = 26 - x or , 4 x = 36 or , x = 9 . b answer ."
Answer: b
Problem: if the l . c . m of two numbers is 560 and their product is 42000 , find the h . c . f of the numbers .
Options: a ) 50 , b ) 30 , c ) 75 , d ) 25 , e ) none of these
Rationale: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 42000 / 560 = 75 . answer : c"
Answer: c
Problem: 1,000 ^ 2 + 1,001 ^ 2 + 1,002 ^ 2 + 1,003 ^ 2 + 1,004 ^ 2 =
Options: a ) 6 , 030,053 , b ) 6 , 030,054 , c ) 6 , 030,055 , d ) 6 , 020,030 , e ) 6 , 030,057
Rationale: interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 . . . 1004 ^ 2 - > 16 total - > * 30 answer d .
Answer: d
Problem: in a room filled with 6 people , all 6 people have exactly 1 sibling in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 5 / 6 , d ) 5 / 12 , e ) 7 / 12
Rationale: the 6 people consist of three sets of 2 siblings . the number of ways to choose 2 people is 6 c 2 = 15 . the number of ways to choose 2 from the first group of siblings is 2 c 2 = 1 . the number of ways to choose 2 from the second group of siblings is 2 c 2 = 1 . the number of ways to choose 2 from the third group of siblings is 2 c 2 = 1 . the number of ways to choose 2 people who are siblings is 1 + 1 + 1 = 3 . the number of ways to choose 2 people who are not siblings is 15 - 3 = 12 . p ( the two people are not siblings ) = 12 / 15 = 4 / 5 the answer is b .
Answer: b
Problem: find the least number of complete years in which a sum of money put out at 50 % compound interest will be more than double of itself ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 2 years answer : a
Answer: a
Problem: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 18 min , b ) 17 min , c ) 19 min , d ) 20 min , e ) 21 min
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 60 - 40 ) km i . e 20 km at 60 km / hr . stoppage time = 20 / 60 hrs = 20 min . answer : d"
Answer: d
Problem: in an office , 50 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a ) 8 , b ) 64 , c ) 50 , d ) 144 , e ) 160
Rationale: ( 10 / 100 ) workers = 16 = > number of workers = 160 ( 50 / 100 ) * workers = x + 16 = > x = 8 answer a
Answer: a
Problem: a certain roller coaster has 6 cars , and a passenger is equally likely to ride in any 1 of the 6 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 6 times , what is the probability that the passenger will ride in each of the 6 cars ?
Options: a ) 3 / 1944 , b ) 1 / 96 , c ) 2 / 96 , d ) 1 / 1944 , e ) 1
Rationale: if he is to ride 6 times and since he can choose any of the 6 cars each time , total number of ways is = 6 * 6 * 6 * 6 * 6 * 6 = 46656 now the number of ways if he is to choose a different car each time is = 6 * 5 * 4 * 3 * 2 * 1 = 720 so the probability is = 720 / 46656 = 3 / 1944 answer : a
Answer: a
Problem: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many d hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in d = 3 hours ) solving these 2 equations we can find b as 12 so , d"
Answer: d
Problem: the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 8 ?
Options: a ) 96 , b ) 200 , c ) 128 , d ) 116 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 8 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 640 = 200 answer : b"
Answer: b
Problem: a 9 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 1 / 6 , b ) 1 / 5 , c ) 2 / 9 , d ) 1 / 3 , e ) 2 / 5
Rationale: "a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 1 meters from either end . the probability of this is 2 / 9 . the answer is c ."
Answer: c
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 17 , the how old is b ? a . 7 b . 8 c . 9 d . 10 explanation :
Options: a ) 6 , b ) 7 , c ) 9 , d ) 10 , e ) 11
Rationale: let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 17 5 x = 15 x = 3 . hence , b ' s age = 2 x = 6 years . answer : option a
Answer: a
Problem: two pipes can fill a tank in 12 minutes and 20 minutes respectively . both pipes are opened together and after some time the first pipe is closed and the tank is full in totally 10 minutes . for how many minutes was first pipe open ?
Options: a ) 8 minutes , b ) 6 minutes , c ) 7 minutes , d ) 10 minutes , e ) 9 minutes
Rationale: second pipe is opened for 10 minutes . so , part of tank filled by the second pipe = 10 / 20 = 1 / 2 . so , 1 - 1 / 2 = 1 / 2 tank is filled by first pipe . first pipe can fill 1 / 2 of tank in 1 * 12 / 2 = 6 minutes . so , the first pipe is opened for 6 minutes . answer : b
Answer: b
Problem: what is the area inscribed by the lines y = 6 , x = 3 , y = 2 x - 4 on an xy - coordinate plane ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 8 , e ) e ) 16
Rationale: "first , let ' s graph the lines y = 6 and x = 3 at this point , we need to find the points where the line y = 2 x - 4 intersects the other two lines . for the vertical line , we know that x = 3 , so we ' ll plug x = 3 into the equation y = 2 x - 4 to get y = 2 ( 3 ) - 4 = 2 perfect , when x = 3 , y = 2 , so one point of intersection is ( 3,2 ) for the horizontal line , we know that y = 6 , so we ' ll plug y = 6 into the equation y = 2 x - 4 to get 6 = 2 x - 4 . solve to get : x = 5 so , when y = 6 , x = 5 , so one point of intersection is ( 5,6 ) now add these points to our graph and sketch the line y = 2 x - 4 at this point , we can see that we have the following triangle . the base has length 2 and the height is 4 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 2 ) ( 4 ) = 4 answer : c"
Answer: c
Problem: the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - fourth of the males and three - fourths of the females in the class ?
Options: a ) 186 , b ) 192 , c ) 198 , d ) 204 , e ) 210
Rationale: "1 / 4 * 2 / 5 + 3 / 4 * 3 / 5 = 2 / 20 + 9 / 20 = 11 / 20 the number of degrees is 11 / 20 * 360 = 198 degrees the answer is c ."
Answer: c
Problem: the average of 50 numbers id 20 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.75 , b ) 33.25 , c ) 22.25 , d ) 11.75 , e ) 18.75
Rationale: "explanation : total of 50 numbers = ( 50 × 20 ) = 1000 total of 48 numbers = ( 1000 - ( 45 + 55 ) ] = 900 required average = 900 / 48 = 18.75 answer : e"
Answer: e
Problem: the area of a triangle is with base 10 m and height 10 m ?
Options: a ) 11 , b ) 10 , c ) 50 , d ) 122 , e ) 12
Rationale: "1 / 2 * 10 * 10 = 50 m 2 answer : c"
Answer: c
Problem: in what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 3 sec , b ) 4 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec
Rationale: "t = 40 / 36 * 18 / 5 = 4 sec answer : b"
Answer: b
Problem: find remainder if ( 67 ^ 67 + 67 ) is divided by 68
Options: a ) 60 , b ) 62 , c ) 66 , d ) 72 , e ) 78
Rationale: = > ( 6767 + 1 ) is divisible by ( 67 + 1 ) = > ( 6767 + 1 ) is divisible by 68 = > ( 6767 + 1 ) ÷ 68 gives a remainder of 0 = > [ ( 6767 + 1 ) + 66 ] ÷ 68 gives a remainder of 66 = > ( 6767 + 67 ) ÷ 68 gives a remainder of 66 c
Answer: c
Problem: last year a worker saved 6 % of her annual salary . this year , she made 20 % more money than last year and she saved 5 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?
Options: a ) 90 % , b ) 100 % , c ) 110 % , d ) 120 % , e ) 130 %
Rationale: let x be the worker ' s salary last year . last year , she saved 0.06 x . this year , she saved 0.05 ( 1.2 x ) = 0.06 x 0.06 x / 0.06 x = 100 % the answer is b .
Answer: b
Problem: a walks at 10 kmph and 4 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 150 km , c ) 80 km , d ) 120 km , e ) 200 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 4 hours . x / 10 - x / 20 = 4 x = 80 km answer is c"
Answer: c
Problem: a and b can do a piece of work in 10 days and 10 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 30 days , b ) 40 days , c ) 50 days , d ) 60 days , e ) 70 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 10 + 1 / 10 ] = 10 [ 1 + 1 / 10 ] = 2 a complete remaining work in 2 * 10 = 20 total work = 10 + 20 = 30 days answer : option a"
Answer: a
Problem: one hour before john started walking from p to q , a distance of 33 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 9 miles , d ) 9,6 miles , e ) 21 miles
Rationale: "ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 33 - 3 = 30 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 30 miles so it will take them 30 / 5 = 6 hours to meet . in 6 hrs , ann would have covered 6 hrs * 3 miles per hour = 18 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 18 = 21 miles . answer ( e )"
Answer: e
Problem: kim finds a 2 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ?
Options: a ) 3 / 5 , b ) 2 / 5 , c ) 7 / 5 , d ) 1 / 2 , e ) 8 / 15
Rationale: "3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is a"
Answer: a
Problem: two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 216 marks in the second test and failed by 36 marks in that test . find the pass mark in the first test ?
Options: a ) 277 , b ) 266 , c ) 111 , d ) 121 , e ) 224
Rationale: "let the maximum mark in each test be m . the candidate failed by 36 marks in the second test . pass mark in the second test = 216 + 36 = 252 45 / 100 m = 252 pass mark in the first test = 40 / 100 m = 40 / 45 * 252 = 224 . answer : e"
Answer: e
Problem: a man can swim in still water at 12 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 2.67 , c ) 1.2 , d ) 1.5 , e ) 4
Rationale: "m = 12 s = x ds = 12 + x us = 12 + x 12 + x = ( 12 - x ) 2 12 + x = 24 - 2 x 3 x = 12 x = 4 answer : e"
Answer: e
Problem: nitin ranks 24 th in a class of 58 students . what is rank from the last ?
Options: a ) 33 , b ) 34 , c ) 32 , d ) 28 , e ) 19
Rationale: "explanation : number students behind the nitin in rank = ( 58 - 24 ) = 34 nitin is 34 nd from the last answer : b ) 34"
Answer: b
Problem: a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 4 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: if average of 3 is 4 so sum of 3 should be 12 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 5 and 5 so a has to be 2 a
Answer: a
Problem: 5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 12 days . how many additional pipes q , each draining water at the same constant rate , will be needed to drain the pool in 4 days ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: this is an inverse proportional problem . . . . . . 5 pipes in 12 days ; so for 4 days , it will be = 12 x 5 / 4 = 15 so , q = 15 - 5 = 10 . c
Answer: c
Problem: set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 3 ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 3 , e ) e ) 16
Rationale: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d"
Answer: d
Problem: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 45 % . staff are allowed a further 40 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.35 d , b ) 0.76 d , c ) 0.65 d , d ) 0.77 d , e ) 0.33 d
Rationale: effective discount = a + b + ab / 100 = - 45 - 40 + ( - 45 ) ( - 40 ) / 100 = - 67 sale price = d * ( 1 - 67 / 100 ) sale price = . 33 * d answer ( e )
Answer: e
Problem: convert 300 miles into km ?
Options: a ) 360 km , b ) 480 km , c ) 510 km , d ) 320 km , e ) 500 km
Rationale: "1 mile = 1.6 km approximately 300 mile = 300 * 1.6 = 480 km answer is b"
Answer: b
Problem: difference of 2 numbers is 100 . if 5 % of one number is 10 % of the other number , find the addition of 2 numbers ?
Options: a ) 150 , b ) 300 , c ) 210 , d ) 290 , e ) 180
Rationale: "let the numbers be x and y 5 % of x = 10 % of y x = 2 y x - y = 100 2 y - y = 100 y = 100 x = 2 y = 200 x + y = 300 answer is b"
Answer: b
Problem: in a room with 6 people , 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 15
Rationale: "( 4 / 6 ) ( 5 / 5 ) + ( 3 / 6 ) ( 4 / 5 ) if you choose one of the 4 with one other friend , then you have a 5 / 5 chance of not picking their friend 2 nd . if you choose one of the 3 with 2 friends , you have a 4 / 5 chance of not picking one of their friends second . add them up . 20 / 30 + 12 / 30 32 / 30 = 16 / 15 e . 16 / 15"
Answer: e
Problem: the average weight of 4 person ' s increases by 8.5 kg when a new person comes in place of one of them weighing 95 kg . what might be the weight of the new person ?
Options: a ) 129 kg , b ) 134 kg , c ) 180 kg , d ) 185 kg , e ) 190 kg
Rationale: "total weight increased = ( 4 x 8.5 ) kg = 34 kg . weight of new person = ( 95 + 34 ) kg = 129 kg option a"
Answer: a
Problem: the s . i . on a certain sum of money for 2 years at 8 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 2197 , b ) 1267 , c ) 1750 , d ) 2267 , e ) 2625
Rationale: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 2 * 8 ) = rs . 2625 answer : e"
Answer: e
Problem: two trains 120 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 , b ) 10.7 , c ) 10.3 , d ) 10.08 , e ) 10.2
Rationale: relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 120 + 160 = 280 m . required time = 280 * 9 / 250 = 252 / 25 = 10.08 sec . ' answer : d
Answer: d
Problem: a , b and c start a business each investing 20,000 . after 6 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 67,600 was recorded . find the share of b .
Options: a ) 20,000 , b ) 21,200 , c ) 21,600 , d ) 20,500 , e ) none of these
Rationale: "ratio of the capitals of a , b and c = 20000 ã — 6 + 15000 ã — 6 : 20000 ã — 6 + 16000 ã — 6 : 20000 ã — 6 + 26000 ã — 6 = 210000 : 216000 : 250000 = 210 : 216 : 250 b â € ™ s share = ( 67600 ã — 216 â  „ 676 ) = 21600 answer c"
Answer: c
Problem: in the first 20 overs of a cricket game , the run rate was only 4.6 . what should be the run rate in the remaining 30 overs to reach the target of 396 runs ?
Options: a ) 10.13 , b ) 9.13 , c ) 8.13 , d ) 11.13 , e ) 13.13
Rationale: required run rate = 396 - ( 4.6 x 20 ) / 30 = 304 / 30 = 10.13 option a
Answer: a
Problem: a club wants to mix 10 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 10 * 8 + 5 * w ) / ( 10 + w ) = > 60 + 6 w = 80 + 5 w = > w = 20 answer a"
Answer: a
Problem: a ferry can transport 50 tons of vehicles . automobiles range in weight from 1,800 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 23 , b ) 55 , c ) 48 , d ) 62 , e ) 70
Rationale: "to get maximum vehicles we must take into consideration the minimum weight i . e 1800 pounds here since , 1 ton = 2000 pounds 50 tons will be 100,000 pounds from the answer choices : let max number of vehicles be total weight will be = 55 * 1800 = 99000 pounds , which is lesser than the maximum weight allowed . ans : b"
Answer: b
Problem: if the annual increase in the population of a town is 10 % and the present number of people is 15000 , what will the population be in 2 years ?
Options: a ) 12100 , b ) 15240 , c ) 18150 , d ) 18452 , e ) 19002
Rationale: "the required population is = 15000 ( 1 + 10 / 100 ) ^ 2 = 15000 * 11 / 10 * 11 / 10 = 18150 answer is c"
Answer: c
Problem: a plant manager must assign 8 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ?
Options: a ) 243 , b ) 336 , c ) 350 , d ) 486 , e ) 540
Rationale: "whatever : my take selecting team of 2 out of 8 to assign to the shifts = 8 c 2 = 28 ways . now 2 out of 8 means total of 4 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 4 * 3 * 2 * 1 = 24 here alt and alt are the same : so 24 / 2 = 12 ways . total ways of selecting = ( selecting 2 out of 8 ) * arranging those teams in shifts = 28 * 12 = 336 ans : b"
Answer: b
Problem: 1 = 62 = 363 = 3634 = 3645 = 365 , then 36 = ?
Options: a ) 1 , b ) 2 , c ) 345 , d ) 445 , e ) 235
Rationale: 1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ? 36 = 2 check the second eqn . answer : b
Answer: b
Problem: a and b can do a piece of work in 7 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 33 days , b ) 77 days , c ) 30 days , d ) 17 days , e ) 18 days
Rationale: "c = 1 / 5 – 1 / 6 = 1 / 30 = > 30 days answer : c"
Answer: c
Problem: convert the 13 / 36 m / s into kilometers per hour ?
Options: a ) 2.9 , b ) 2.2 , c ) 1.3 , d ) 1.2 , e ) 1.8
Rationale: 13 / 36 m / s = 13 / 36 * 18 / 5 = 13 / 10 = 1.3 kmph . answer : c
Answer: c
Problem: a man has some hens and cows . if the number of heads be 100 and the number of feet equals 240 , then the number of cows will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 20 , e ) 28
Rationale: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 100 . . . . ( i ) and 2 x + 4 y = 240 x + 2 y = 120 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 26 , y = 20 . the required answer = 20 . answer : d"
Answer: d