regisss/math_qa huggingface dataset:
Problem: the total age of a and b is 12 years more than the total age of b and c . c is how many year younger than a
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : given that a + b = 12 + b + c = > a – c = 12 + b – b = 12 = > c is younger than a by 12 years answer : option b"
Answer: b
Problem: if the diameter of circle r is 40 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 16 % , b ) 18 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: "let diameter of circle r , dr = 40 and diameter of circle s , ds = 100 radius of circle r , rr = 20 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 20 / 50 ) ^ 2 = ( 4 / 10 ) ^ 2 = 16 % answer : a"
Answer: a
Problem: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Problem: mary can do a piece of work in 26 days . rosy is 30 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
Options: a ) 22 , b ) 20 , c ) 24 , d ) 26 , e ) 30
Rationale: "ratio of times taken by mary and rosy = 130 : 100 = 13 : 10 suppose rosy takes x days to do the work . 13 : 10 : : 26 : x = > x = 20 days . hence , rosy takes 20 days to complete the work . answer : b"
Answer: b
Problem: if 2 ^ 4 , 3 ^ 3 , and 13 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 198 , b ) 288 , c ) 363 , d ) 396 , e ) 468
Rationale: i will go with e ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 13 ^ 1 = 468
Answer: e
Problem: during a certain two - week period , 58 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 10 a , b ) 9 a , c ) 8 2 / 3 a , d ) 11 a , e ) 12 a
Rationale: "total movies = 100 . comedies = 58 . action + drama = 42 . since there were 5 times as many dramas as action movies , then action + 5 * action = 42 - - > action = a = 7 . comedies = = 8 2 / 3 a answer : c ."
Answer: c
Problem: a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 56 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 500 , d ) 610 , e ) 700
Rationale: "let the maximum marks be x then , 33 % of x = 175 + 56 33 x / 100 = 231 x = 700 answer is e"
Answer: e
Problem: if s and t are both odd prime numbers ands < t , then how many different positive integer factors does 2 sthave ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: s and t are both odd prime numbers - it means either s or t is not 2 and since prime numbers have only two factors - 1 and the number itself s and t each will have ( 1 + 1 ) = 2 factors hence 2 st will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer
Answer: d
Problem: the maximum number of student amoung them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 910 , c ) 1001 , d ) 1911 , e ) none of these
Rationale: "solution required number of student = h . c . f of 1001 and 910 = 91 . answer a"
Answer: a
Problem: a class of 20 students took a science test . 10 students had an average ( arithmetic mean ) score of 80 . the other students had an average score of 60 . what is the average score of the whole class ?
Options: a ) 70 , b ) 60 , c ) 55 , d ) 65 , e ) 85
Rationale: hear , 10 students had average score of 80 , so , 80 x 10 = 800 and 10 students had average score of 60 , so , 60 x 10 = 600 total no of student are 20 ( 800 + 600 ) / 20 = 70 correct ans is a
Answer: a
Problem: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 900 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 922.50 . what is the value of x ?
Options: a ) 9000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: simple way to solve this question is to use options . from si , we know that x * y = 45,000 . now , put the value of x = 9000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 9000 + 5 % of 9000 = 9450 . 2 nd year , amount = 9450 + 5 % of 9450 = 9922.50 . we can see after 2 years interest = 9922.50 - 9000 = 922.50 . hence , it satisfies the question . hence a is the correct answer
Answer: a
Problem: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 153 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 175.50 , d ) rs . 258.50 , e ) none of these
Rationale: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 153 ) / \ x − 153 22.50 = > x − ( 153 / 22.50 ) = 1 . = > x − 153 = 22.50 . = > x = 175.50 rs . answer : c"
Answer: c
Problem: the number of boxes in a warehouse can be divided evenly into 7 equal shipments by boat or 28 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 28 , b ) 33 , c ) 54 , d ) 81 , e ) 162
Rationale: "answer is the lcm of 7 and 28 = 28 answer a"
Answer: a
Problem: in what time will a railway train 50 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 5 sec , b ) 4 sec , c ) 3 sec , d ) 6 sec , e ) 1 sec
Rationale: "t = 50 / 36 * 18 / 5 = 5 sec answer : a"
Answer: a
Problem: the marks obtained by vijay and amith are in the ratio 8 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 12 : 5 , b ) 12 : 1 , c ) 6 : 5 , d ) 12 : 2 , e ) 6 : 3
Rationale: 8 : 5 3 : 2 - - - - - - - 24 : 15 : 10 24 : 10 12 : 5 answer : a
Answer: a
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 22 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 11.36 , c ) 7.4 , d ) 5 , e ) 6
Rationale: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 22 run rate needed = 250 / 22 = 11.36 answer : option b"
Answer: b
Problem: x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 9 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9
Rationale: "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 9 ^ 2 = 1 / 9 answer : c"
Answer: c
Problem: a train running at the speed of 90 km / hr crosses a pole in 5 seconds . find the length of the train .
Options: a ) 150 meter , b ) 145 meter , c ) 140 meter , d ) 125 meter , e ) none of these
Rationale: "explanation : speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time = 25 * 5 = 125 meter option d"
Answer: d
Problem: find the mean proportional between 64 & 81 ?
Options: a ) a ) 59 , b ) b ) 61 , c ) c ) 63 , d ) d ) 72 , e ) e ) 67
Rationale: "formula = √ a × b a = 64 and b = 81 √ 64 × 81 = 8 × 9 = 72 d"
Answer: d
Problem: if ( a + b ) = 12 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 6 . , e ) - 2 .
Rationale: "given a + b = 12 = > a = 12 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 12 - b + 3 - c = > 15 - ( b + c ) = > 15 - 9 = 6 . option d . . ."
Answer: d
Problem: if the area of a circle is 64 pi square feet , find its circumference .
Options: a ) 65 pi feet , b ) 43 pi feet , c ) 42 pi feet , d ) 18 pi feet , e ) 16 pi feet
Rationale: "the area is given by pi * r * r . hence pi * r * r = 64 pi r * r = 64 ; hence r = 8 feet the circumference is given by 2 * pi * r = 2 * pi * 8 = 16 pi feet correct answer e"
Answer: e
Problem: what is the lowest positive integer that is divisible by each of the integers 1 through 8 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 5020
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , and 2 ^ 3 . the lcm is 1 * 2 ^ 3 * 3 * 5 * 7 = 840 the answer is b ."
Answer: b
Problem: what is the perimeter of an isosceles right angled triangle . the area of the isosceles right angled triangle is 50 .
Options: a ) 25
b ) 36
c ) 25
d ) 30
e ) 34.14
Rationale: an isosceles right angled triangle has both the base and height same . the area of an isosceles triangle = 1 / 2 * base * height since height = base 1 / 2 * height * height = 1 / 2 * height ^ 2 = 50 height ^ 2 = 100 height = 10 = base since we know the base and height . we will calculate the hypotenuse using pythagoras base ^ 2 + height ^ 2 = hypotenuse ^ 2 10 ^ 2 + 10 ^ 2 = hypotenuse ^ 2 hypotenuse ^ 2 = 200 hypotenuse = 14.14 perimeter of the triangle = 10 + 10 + 14.14 = 34.14 ans : e
Answer: e
Problem: here 10 programmers , type 10 lines within 10 minutes then 60 lines can type within 60 minutes . how many programmers are needed ?
Options: a ) 16 , b ) 10 , c ) 6 , d ) 60 , e ) 50
Rationale: 10 10 programmer 10 line 10 mins . 10 programmer 20 line 20 mins . . . . . 10 programmer 60 line 60 mins . answer : d
Answer: d
Problem: in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are strategy majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 13
Rationale: "pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are strategy majors is s = 13 . the answer is e ."
Answer: e
Problem: in a store , the total price for 25 shirts is $ 400 and the total price for 75 sweaters is $ 1500 . by how much does the average ( arithmetic mean ) price of a sweater exceed that of a shirt in this store ?
Options: a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 5
Rationale: the average price of a shirt is : $ 400 / 25 = $ 16 . the average price of a sweater is : $ 1500 / 75 = $ 20 . the difference in price is : $ 20 - $ 16 = $ 4 . the answer is d .
Answer: d
Problem: jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 6 hours . how long would it take taimour to paint the fence alone ?
Options: a ) 6 hours , b ) 8 hours , c ) 18 hours , d ) 24 hours , e ) 32 hours
Rationale: "i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 6 = > 1 / 18 working alone taimour can do the job in 1 = 1 / 18 * hours = > 18 answer c"
Answer: c
Problem: if the least common multiple of two prime numbers x and y is 10 , where x < y , then the value of 3 x + y is
Options: a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 21
Rationale: "lcm ( x , y ) = 10 and both x an y are prime . the only values of x and y can be 2 and 5 ( x = 2 and y = 5 ) 3 x + y = 3 * 2 + 5 = 11 correct option : c"
Answer: c
Problem: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 800 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 820 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 40,000 . now , put the value of x = 8000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 8000 + 5 % of 8000 = 8400 . 2 nd year , amount = 8400 + 5 % of 8400 = 8820 . we can see after 2 years interest = 8820 - 8000 = 820 . hence , it satisfies the question . hence a is the correct answer"
Answer: a
Problem: i had 30 donuts when i left home this morning but only 9 when i came back home . what percentage of the donuts are missing ?
Options: a ) 70 , b ) 65 , c ) 55 , d ) 75 , e ) 60
Rationale: 30 - 9 = 21 21 / 30 or 7 / 10 7 / 10 = 70 / 100 = 70 % answer is a
Answer: a
Problem: a semicircle has a radius of 10 . what is the approximate perimeter of the semicircle ?
Options: a ) 27 , b ) 33 , c ) 39 , d ) 45 , e ) 51
Rationale: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 10 + 2 * 10 which is about 51 . the answer is e ."
Answer: e
Problem: find the average of the first 19 natural numbers ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: average of the first ' n ' natural numbers = ( n + 1 ) / 2 we get ( 19 + 1 ) / 2 = 10 answer : c
Answer: c
Problem: if the remainder is 11 when positive integer n is divided by 18 , what is the remainder when n is divided by 9 ?
Options: a ) 0 , b ) 2 , c ) 1 , d ) 3 , e ) 4
Rationale: "assume x is quotient here , n = 18 x + 11 - - - - - - - - - - ( 1 ) and n = 9 x + ? we can also write equation ( 1 ) as : n = ( 18 x + 9 ) + 2 . ie 9 ( 2 x + 1 ) + 2 ie the first term is perfectly divisible by 6 . so , the remainder left is 2 . so , answer ( b ) is right choice ."
Answer: b
Problem: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 88,000 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "b - > 1 g - > 5 p - > x ; 5 < x < 11 r - > 11 now , 88000 = 11 * 8 ^ 2 * 5 ^ 4 * 1 ^ n hence no of balls drawn , b = cant be determined g = 4 p = 2 ( only possible value is 8 ) r = 1 hence b"
Answer: b
Problem: if n = 16 × 10 ^ ( - p ) and − 4 < p < 4 , how many different integer values of p will make n a perfect square ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 5 , e ) 7
Rationale: i think the answer should be c . thoose are p - values that satisfy given restriction : - 2 , 0 , 2 ( note , a fraction can be also a perfect square ) - - > 16 * 100 , 16 * 1 , 16 / 100
Answer: c
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 40 , e ) 41
Rationale: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 9 = > 2 b - b - 9 = 30 b = 39 so the present age of b is 39 years answer : c"
Answer: c
Problem: a reduction of 15 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 2.8 , b ) 2.3 , c ) 1.8 , d ) 2.1 , e ) 2.9
Rationale: "100 * ( 15 / 100 ) = 15 - - - 10 ? - - - 1 = > rs . 1.5 100 - - - 85 ? - - - 1.5 = > rs . 1.8 answer : c"
Answer: c
Problem: on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.5 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 22.04 % , b ) 16.12 % , c ) 8 % , d ) 18.25 % , e ) 10.5 %
Rationale: per quarter , interest = 2.5 % so for a year , interest = 10 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 10 % answer = 10.5 % = answer : e
Answer: e
Problem: a train which has 250 m long , is running 40 kmph . in what time will it cross a person moving at 4 kmph in same direction ?
Options: a ) 30 sec , b ) 28 sec , c ) 29 sec , d ) 35 sec , e ) 25 sec
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 250 / ( ( 40 - 4 ) ( 5 / 18 ) = 250 / 36 * ( 5 / 18 ) = 250 / 10 = 25 sec answer : e"
Answer: e
Problem: two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 20 , e ) 18
Rationale: "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 15 ] m / sec = 8 m / sec . relative speed = ( 12 + 8 ) = m / sec = 20 m / sec . ∴ required time = ( 120 + 120 ) / 20 secc = 12 sec . answer a"
Answer: a
Problem: if x is a positive number and 2 the square root of x is equal to x / 2 , then x =
Options: a ) 1 / 16 , b ) 4 , c ) 1 , d ) 2 , e ) 8
Rationale: "2 of sqrt ( x ) = x / 2 , which means that sqrt ( x ) = x or x = x ^ 2 - > divide by x 1 = x x = 1 c ."
Answer: c
Problem: two trains of length 100 m and 200 m are 100.00001 m apart . they start moving towards each other on parallel tracks , at speeds 108 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 8 , b ) 7 , c ) 9 , d ) 2 , e ) 1
Rationale: "relative speed = ( 108 + 72 ) * 5 / 18 = 50 mps . the time required = d / s = ( 100 + 100 + 200 ) / 50 = 400 / 50 = 8 sec . answer : a"
Answer: a
Problem: in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 82 per kg ?
Options: a ) 5 : 8 , b ) 4 : 7 , c ) 3 : 7 , d ) 1 : 1 , e ) 9 : 8
Rationale: "( 96 - 82 ) / ( 82 - 68 ) = 14 / 14 = 1 / 1 answer : d"
Answer: d
Problem: if a ( a + 2 ) = 48 and b ( b + 2 ) = 48 , where a ≠ b , then a + b =
Options: a ) - 10 , b ) - 9 , c ) - 5 , d ) - 4 , e ) - 2
Rationale: "i . e . if a = 6 then b = - 8 or if a = - 8 then b = 6 but in each case a + b = - 8 + 6 = - 2 answer : b"
Answer: b
Problem: an article with cost price of 240 is sold at 20 % profit . what is the selling price ?
Options: a ) 288 , b ) 200 , c ) 204 , d ) 207 , e ) 210
Rationale: "sp = 1.20 * 240 = 288 answer : a"
Answer: a
Problem: how many seconds will it take for a car that is traveling at a constant rate of 120 miles per hour to travel a distance of 77 yards ? ( 1 mile = 1,160 yards )
Options: a ) 1.25 , b ) 1.31 , c ) 1.58 , d ) 1.87 , e ) 2.3
Rationale: "speed = 120 miles / hr = 58.67 yard / s distance = 77 yards time = distance / speed = 77 / 58.67 = 1.31 sec ans - b"
Answer: b
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability r that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability r is 2 / 3 . d"
Answer: d
Problem: a store reported total sales of $ 460 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 44 % , d ) 65 % , e ) 83 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 460 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 460 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 460 – 320 ) / 320 ] x 100 ≈ 44 % . the answer is c ."
Answer: c
Problem: water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 55 ° c , what is the temperature of the pot of water in ° f ?
Options: a ) 116 ° f , b ) 125 ° f , c ) 131 ° f , d ) 138 ° f , e ) 145 ° f
Rationale: "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 55 ) / 5 + 32 = 131 ° f the answer is c ."
Answer: c
Problem: what distance will be covered by a bus moving at 126 kmph in 10 seconds ?
Options: a ) 287 , b ) 600 , c ) 350 , d ) 276 , e ) 207
Rationale: "126 kmph = 126 * 5 / 18 = 35 mps d = speed * time = 35 * 10 = 350 m . answer : c"
Answer: c
Problem: the dimensions of a room are 10 m x 7 m x 5 m . there are 2 doors and 3 windows in the room . the dimensions of the doors are 1 m x 3 m . one window is of size 2 m x 1.5 m and the other 2 windows are of size 1 m x 1.5 m . the cost of painting the walls at rs . 3 per sq m is
Options: a ) 2488 , b ) 378 , c ) 739 , d ) 474 , e ) 291
Rationale: explanation : area of 4 walls = 2 ( l + b ) h = 2 ( 10 + 7 ) x 5 = 170 sq m area of 2 doors and 3 windows = 2 ( 1 x 3 ) + ( 2 x 1.5 ) + 2 ( 1 x 1.5 ) = 12 sq m area to be planted = 170 - 12 = 158 sq m cost of painting = rs . 158 x 3 = rs . 474 answer : d
Answer: d
Problem: o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 5.3 ) + e ( – 6.7 ) + o ( – 7.3 ) + e ( 6.6 ) is :
Options: a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4
Rationale: o ( 5.3 ) + e ( – 6.7 ) + o ( – 7.3 ) + e ( 6.6 ) = 7 + ( - 6 ) + ( - 9 ) + 6 = - 2 the answer is b .
Answer: b
Problem: a quadratic function f ( x ) attains a maximum of 3 at x = 1 . the value of the function at x = 0 is 1 . what is the value of f ( x ) at x = 10 ?
Options: a ) - 119 , b ) - 159 , c ) - 110 , d ) - 180 , e ) - 105
Rationale: explanation : let , the quadratic equation be ax 2 + bx + c . so , f ( x ) = ax 2 + bx + c at x = 0 , the value of function is 1 . x = 0 , f ( x ) = 1 ax 2 + bx + c = a * 0 + b * 0 + c = c c = 1 . at x = 1 , f ( x ) = 3 x = 1 , f ( x ) = 3 a * 1 + b * 1 + c = 3 since c = 1 , a + b = 2 . also , we know that f ( x ) is maximum when x = 1 . if f ( x ) is maximum , ( dx / dt ) ( f ( x ) ) = 0 differentiating f ( x ) , we have d / dt ( ax 2 + bx + c ) = 2 ax + b at x = 1 , 2 ax + b = 0 . 2 a + b = 0 . b = - 2 a . substituting we have a + b = 2 , or a + - 2 a = 2 . a = - 2 . so , b = 4 . so the equation is - 2 x 2 + 4 x + 1 . at x = 10 , the value is - 2 * 100 + 4 * 10 + 1 i . e - 159 . answer : b
Answer: b
Problem: in a certain company , a third of the workers do not have a retirement plan . 40 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 137
Rationale: "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,6 * 1 / 3 * x 120 = 14 / 30 x x = 257 257 - 120 = 137 answer e"
Answer: e
Problem: the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 48.0 billion from $ 72.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 30.4 , c ) 31.8 , d ) 32.5 , e ) 33.3
Rationale: "$ 72 - $ 48 = 24 $ ( 24 / 72 ) * 100 = 33.33 % answer : e"
Answer: e
Problem: a trader bought a car at 10 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 62 % , c ) 12 % , d ) 19 % , e ) 22 %
Rationale: "original price = 100 cp = 90 s = 90 * ( 180 / 100 ) = 162 100 - 162 = 62 % answer : b"
Answer: b
Problem: sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 40 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 16.7 % , b ) 23.33 % , c ) 25 % , d ) 33.3 % , e ) 46.7 %
Rationale: "40 % is 10 % - points above 30 % and 20 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 2 : 1 . 2 / 3 * 70 % = 140 % / 3 = 46.7 % the answer is e ."
Answer: e
Problem: a man buys a cycle for rs . 2800 and sells it at a loss of 25 % . what is the selling price of the cycle ?
Options: a ) s . 2090 , b ) s . 2160 , c ) s . 2100 , d ) s . 2202 , e ) s . 2092
Rationale: "s . p . = 75 % of rs . 2800 = rs . 75 x 2800 / 100 = rs . 1190 answer : option c"
Answer: c
Problem: if 42.12 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "42.12 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.12 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.12 = km / 50 . . . . . . 12 / 100 = 3 m / 50 . . . . . . m = 2 k + m = 3 + 2 = 5 answer : a"
Answer: a
Problem: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 40 percent of b , what is the value of m / x ?
Options: a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 5
Rationale: a / b = 4 / 5 m / x = ( 3 / 5 ) * 5 / ( 5 / 4 ) * 4 = 3 / 5 the answer is e .
Answer: e
Problem: a , b and c rents a pasture for rs . 730 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 199 , c ) 676 , d ) 156 , e ) 227
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 730 = 227 answer : e"
Answer: e
Problem: the area of a triangle is with base 10 m and height 5 m ?
Options: a ) 11 , b ) 25 , c ) 787 , d ) 122 , e ) 12
Rationale: "1 / 2 * 10 * 5 = 25 m 2 answer : b"
Answer: b
Problem: a certain fraction is equivalent to 2 / 5 . if the numerator of the fraction is increased by 4 and the denominator is doubled , the new fraction is equivalent to 1 / 4 . what is the sum of the numerator and denominator of the original fraction ?
Options: a ) 49 , b ) 35 , c ) 56 , d ) 26 , e ) 21
Rationale: "x / y = 2 / 5 - > 1 ( x + 4 ) / 2 y = 1 / 4 - > 2 divide 1 by 2 : = > 2 x / ( x + 4 ) = 8 / 5 = > 5 x = 4 x + 16 = > x = 16 = > y = 5 / 2 * 16 = 40 so x + y = 56 the answer is c"
Answer: c
Problem: how many diagonals does a polygon with 13 sides have , if one of its vertices does not connect to any diagonal ?
Options: a ) 65 , b ) 62 , c ) 58 , d ) 54 , e ) 60
Rationale: "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 13 - 1 then 12 * ( 12 - 3 ) / 2 = 54 correct option : d"
Answer: d
Problem: a car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 38 miles per hour , how many hours long is the trip ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "let t be the total time of the trip . 30 * 5 + 42 ( t - 5 ) = 38 t 4 t = 210 - 150 t = 15 the answer is c ."
Answer: c
Problem: in a certain country 1 / 5 of 8 = 4 . assuming the same proportion , what would be the value of 1 / 4 of 16 ?
Options: a ) 13 , b ) 12 , c ) 10 , d ) 16 , e ) 14
Rationale: c 10
Answer: c
Problem: in what ratio must a grocer mix two varieties of pulses costing rs . 15 and rs . 20 per kg respectively so as to get a mixture worth rs . 16.50 per kg ?
Options: a ) 3 : 7 , b ) 5 : 7 , c ) 7 : 3 , d ) 7 : 5 , e ) none
Rationale: solution required ratio = 3.50 : 1.50 = 35 : 15 = 7 : 3 . answer c
Answer: c
Problem: a can do a piece of work in 4 days . b can do it in 10 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 22 days , b ) 20 / 3 days , c ) 67 days , d ) 17 / 6 days , e ) 18 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 10 = 3 / 20 = > 20 / 3 days answer : b"
Answer: b
Problem: a and b invests rs . 1500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 5 , b ) 9 : 8 , c ) 9 : 2 , d ) 9 : 9 , e ) 9 : 16
Rationale: "( 1.5 * 6 + 3 * 6 ) : ( 4 * 12 ) 27 : 48 = > 9 : 16 answer : e"
Answer: e
Problem: the length of a rectangular garden is 2 feet longer than 3 times its width . if the perimeter of the garden is 100 feet , find the length of the garden .
Options: a ) 42
b ) 38
c ) 28
d ) 57
e ) 49
Rationale: let l and w be the length and width of the garden . the statement ` ` the length of a rectangular garden is 2 feet longer than 3 times its width ' ' may be formulated by l = 2 + 3 w the formula for the perimeter is given by p = 2 l + 2 w substitute p and l in the above equation by 100 and 2 + 3 w respectively to obtain 100 = 2 ( 2 + 3 w ) + 2 w solve for w and l w = 12 and l = 2 + 3 w = 38 . check that the perimeter of the rectangular garden is 100 p = 2 l + 2 w = 76 + 24 = 100 correct answer b
Answer: b
Problem: calculate 24 x 99
Options: a ) 2673 , b ) 2763 , c ) 2637 , d ) 2736 , e ) 2376
Rationale: "= 24 - 1 = 23 = ( decrement each digit of the number obtained from 9 ) here we got 23 . now = 9 - 2 = 7 and 9 - 3 = 6 . so we have 76 just write these numbers together . that is we have 23 and 76 . hence answer is 2376 answer is e ."
Answer: e
Problem: a fill pipe can fill 1 / 4 of cistern in 16 minutes . in how many minutes , it can fill 3 / 4 of the cistern ?
Options: a ) 24 min , b ) 30 min , c ) 48 min , d ) 26 min , e ) 16 min
Rationale: "required time = 16 * 4 * 3 / 4 = 48 minutes answer is c"
Answer: c
Problem: a reduction of 40 % in the price of oil enables a house wife to obtain 8 kgs more for rs . 2400 , what is the reduced price for kg ?
Options: a ) rs . 120 , b ) rs . 125 , c ) rs . 130 , d ) rs . 135 , e ) rs . 140
Rationale: "explanation : 2400 * ( 40 / 100 ) = 960 - - - - 8 ? - - - - 1 = > rs . 120 answer : a"
Answer: a
Problem: a trail mix company keeps costs down by employing the peanuts : cashews : almonds ratio of 10 : 4 : 1 in each bag of up to 75 total nuts . what is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts ?
Options: a ) 40 % , b ) 48 % , c ) 49 % , d ) 50 % , e ) 58 %
Rationale: peanuts = 50 cashews = 20 almonds = 5 we want to remove as many peanuts as possible while still having peanuts represent more than half of the mixture . . . the number of cashews and almonds will stay the same though , so we have 20 + 5 = 25 of those non - peanuts in total . if we had 25 peanuts and 25 non - peanuts , then that would be 50 % exactly . we want more than 50 % though , so we need to add in 1 more peanut . this gives us . . . peanuts = 26 cashews = 20 almonds = 5 the question asked for the decrease in the number of peanuts as a percentage . we started with 50 peanuts and removed 24 = 24 / 50 = 48 % ; answer : b
Answer: b
Problem: there is a 30 % chance that tigers will not win at all during the whole season . there is a 30 % chance that portugeese will not play at all in the whole season . what is the greatest possible probability that the tigers will win and portugeese will play during the season ?
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 80 %
Rationale: "there is a 30 % chance that tigers will not win at all during the whole season we can infer that there is 70 % chance tigers will win . similarly there is a 30 % chance that portugeese will not play at all in the whole season we can also infer that there is 70 % chance that portugeese will play . answer c"
Answer: c
Problem: we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 390 . how many math books did we buy ?
Options: a ) 57 , b ) 60 , c ) 63 , d ) 66 , e ) 69
Rationale: "m + h = 90 h = 90 - m 4 m + 5 h = 390 4 m + 5 * ( 90 - m ) = 390 m = 60 the answer is b ."
Answer: b
Problem: the sum of three consecutive even numbers is 60 . find the middle number of the three ?
Options: a ) 14 , b ) 60 , c ) 18 , d ) 70 , e ) 45
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 60 6 p = 60 = > p = 10 . the middle number is : 10 p = 60 . answer : b"
Answer: b
Problem: a number when divided by 133 leaves 16 as a remainder . what will be the remainder if the number is divided by 50 ?
Options: a ) 51 , b ) 56 , c ) 49 , d ) 17 , e ) 7
Rationale: "133 + 16 = 149 dividing 149 evenly into whole numbers is 2 and leaves 49 remaining . the correct answer is c ."
Answer: c
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 240 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?
Options: a ) 65 , b ) 44 , c ) 18 , d ) 15.49 , e ) 14
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 240 / 3 = 80 sq m l b = 80 i . e . , l * l / 3 = 240 l 2 = 240 = > l = 15.49 answer : d"
Answer: d
Problem: a train 100 m long crosses a platform 125 m long in 15 sec ; find the speed of the train ?
Options: a ) 91.2 kmph , b ) 61.9 kmph , c ) 45.9 kmph , d ) 61.2 kmph , e ) 71.2 kmph
Rationale: "d = 100 + 155 = 255 t = 15 s = 255 / 15 * 18 / 5 = 61.2 kmph answer : d"
Answer: d
Problem: john has 10 pairs of matched socks . if he loses 3 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 7 , b ) 8 , c ) 5 , d ) 4 , e ) 3
Rationale: "because we have to maximize the pair of matched socks , we will remove 1 pairs ( 2 socks ) out of 10 pairs 1 sock from the 2 th pair . thus the no of matching socks pair remaining = 10 - 2 = 8 answer b"
Answer: b
Problem: a train 250 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 6 sec . , b ) 7 sec . , c ) 9 sec . , d ) 15 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 250 m at ( 50 / 3 ) m / sec = ( 250 x 3 / 50 ) sec = 15 sec . answer d"
Answer: d
Problem: a garrison of 400 men had a provision for 31 days . after 26 days 275 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 16 days , b ) 45 days , c ) 10 days , d ) 17 days , e ) 18 days
Rationale: "400 - - - 31 400 - - - 5 125 - - - ? 400 * 5 = 125 * x = > x = 16 days . answer : a"
Answer: a
Problem: if the cost price of 50 articles is equal to the selling price of 40 articles , then the gain or loss percent is ?
Options: a ) 33 % , b ) 29 % , c ) 25 % , d ) 55 % , e ) 39 %
Rationale: "c 25 % given that , cost price of 50 article is equal to selling price of 40 articles . let cost price of one article = rs . 1 selling price of 40 articles = rs . 50 but cost price of 40 articles = rs . 40 therefore , the trader made profit . \ percentage of profit = 10 / 40 * 100 = 25 %"
Answer: c
Problem: if two dice are thrown together , the probability of getting an even number on both dice is
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 2
Rationale: "the number of exhaustive outcomes is 36 . let e be the event of getting an even number on both dies is 9 / 36 = 1 / 4 p ( e ) = 1 / 4 . a )"
Answer: a
Problem: an alloy of copper and zinc contains copper and zinc in the ratio 8 : 2 . another alloy of copper and zinc contains copper and zinc in the ratio 4 : 6 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 5 : 1 , b ) 4 : 1 , c ) 3 : 1 , d ) 6 : 1 , e ) 8 : 1
Rationale: "let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 8 x / 10 , and fraction of zinc in alloy _ 1 = 2 x / 10 similarly , fraction of copper in alloy _ 2 = 4 y / 10 , and fraction of zinc in alloy _ 2 = 6 y / 10 . mixing them , we get copper = 8 x / 10 + 4 y / 10 ; zinc = 2 x / 10 + 6 y / 10 so , 8 x + 4 y = 2 x + 6 y - > 6 x = 2 y - > x / y = 6 / 2 = 3 / 1 so , they must be mixed in the ratio 3 : 1 answer : c"
Answer: c
Problem: the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is rs . 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p + q + r is :
Options: a ) 16100 , b ) 15700 , c ) 17500 , d ) 16000 , e ) 16500
Rationale: "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) ( p + q + r ) ' s monthly income = rs . 16500 . answer : e"
Answer: e
Problem: if 1 / ( x + 1 ) + 1 / ( x - 1 ) = 1 / ( x - 1 ) , what is the value of x ?
Options: a ) 2 , b ) - 2 , c ) 1 , d ) - 1 , e ) 5
Rationale: if we solve the question , we get x = 1 . option : c
Answer: c
Problem: evaluate 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 = ?
Options: a ) 3043 , b ) 5050 , c ) 5176 , d ) 9356 , e ) 4890
Rationale: b 5050 you must have noticed that 50 pairs of n ^ 2 – ( n - 1 ) ^ 2 exist . n ^ 2 – ( n - 1 ) ^ 2 = n + ( n – 1 ) in such case , we may as well write 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 as 100 + 99 + 98 + . . . + 2 + 1 = ( 100 x 101 ) / 2 = 5050
Answer: b
Problem: what percent of 14 is 14 percent of 1 ?
Options: a ) 0.001 , b ) 0.01 , c ) 0.1 , d ) 101 , e ) 1
Rationale: "14 % of 1 = ( 14 / 100 ) * 1 = 14 / 100 to determine what percentage of 14 this is : [ 14 ] [ / 100 * 14 ] * 100 = 1 % ans : e"
Answer: e
Problem: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years r in which the population would be doubled assuming there is no emigration or immigration is
Options: a ) 20 , b ) r = 25 , c ) r = 30 , d ) r = 35 , e ) 40
Rationale: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."
Answer: d
Problem: there are 15 balls in a jar . you take out 3 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 3 . how many blue balls were there in the beginning ?
Options: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .
Rationale: "7 = 3 blue balls + 12 / 3 answer : d"
Answer: d
Problem: the average ( arithmetic mean ) of 8 numbers is 43.1 . if the sum of half of these numbers is 158.4 , what is the average of the other half ?
Options: a ) 12.8 , b ) 24.2 , c ) 46.6 , d ) 72.1 , e ) 96.8
Rationale: arithmetic mean = sum / total numbers sum = 43.1 * 8 = 344.8 sum of half of these numbers is 158.4 . so , 4 numbers sum is 158.4 . rest 4 numbers sum = 344.8 - 158.4 = 186.4 arithmetic mean of the 4 nos = 186.4 / 4 = 46.6 hence , c is the answer .
Answer: c
Problem: 12.5 * 6.2 * 8.8 = ?
Options: a ) 352 , b ) 435 , c ) 224 , d ) 682 , e ) 742
Rationale: "d 682 ? = 12.5 * 6.2 * 8.8 = 682"
Answer: d
Problem: if 5 and 8 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 14 , e ) 56
Rationale: "60 n / 7 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 5 * 2 * 2 * 2 = 3 * n / 2 must be an integer for this to be true n must multiple of 2 , thus min of n = 2 hence a"
Answer: a
Problem: what is the probability of getting exactly 2 heads in a single throw of four fair coins ?
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16
Rationale: "one possible case is hhtt . p ( hhtt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 there are 4 c 2 = 6 possible cases . p ( 2 heads ) = 6 * 1 / 16 = 3 / 8 the answer is c ."
Answer: c
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 45 kms . what was the total distance traveled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 672 kms , d ) 752 kms , e ) 152 kms
Rationale: explanation : total distance travelled in 12 hours = ( 45 + 47 + 49 + . . . . . upto 12 terms ) this is an a . p with first term , a = 45 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 45 + { 12 - 1 ) x 2 ] = 6 ( 112 ) = 672 kms . answer : c
Answer: c
Problem: n denotes the number obtained when n is rounded to the nearest tenth . for example 4.31 = 4.3 0.089 - 1.135 =
Options: a ) 1.05 , b ) 1.04 , c ) - 1.05 , d ) - 1.0 , e ) - 0.1
Rationale: here let the first quantity be a = > a rounded to nearest tenths = > 0.1 similarly let the second quantity be b = > b rounded to nearest tenths = > 1.1 = > a - b = 0.1 - 1.1 = - 1 hence a - b = - 1 answer : d
Answer: d
Problem: if x , y , and z are positive real numbers such that x + y - z = 50 , y - z + x = 60 , and z - x + y = 80 , then find the z value ?
Options: a ) 10 , b ) 20 , c ) 5 , d ) 15 , e ) 25
Rationale: "x + y - z = 50 , - - - - - - 1 ) y - z + x = 60 , - - - - - - 2 ) z - x + y = 80 - - - - - - 3 ) from ( 1 ) & ( 2 ) 2 z = 10 z = 5 correct option is c"
Answer: c
Problem: initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many w women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"
Answer: d
Problem: 12.5 * 3.2 * 7.8 = ?
Options: a ) 312 , b ) 435 , c ) 224 , d ) 646 , e ) 742
Rationale: "a 312 ? = 12.5 * 3.2 * 7.8 = 312"
Answer: a
Problem: a certain protective additive increases from 30 days to 45 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 ) 50 % , 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 45 − 30 / 30 ∗ 100 = 50 answer : c .
Answer: c
Problem: an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1,220 , what was the total number of pairs of contact lenses that she sold ?
Options: a ) 9 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "( x + 5 ) * 150 + x * 85 = 1220 = > x = 2 total lens = 2 + ( 2 + 5 ) = 9 answer a"
Answer: a
Problem: a bus trip of 660 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "the time is the distance / speed . the time difference is 1 hour . 660 / v - 660 / ( v + 5 ) = 1 660 ( v + 5 ) - 660 v = ( v ) ( v + 5 ) 3300 = ( v ) ( v + 5 ) 55 * 60 = ( v ) ( v + 5 ) v = 55 mph the answer is d ."
Answer: d
Problem: a man can row downstream at 35 kmph and upstream at 25 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 35 , 3 , b ) 25 , 5 , c ) 35 , 4 , d ) 5 , 30 , e ) 30 , 5
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 35 - - - ( 1 ) and x - y = 25 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 60 = > x = 30 , y = 5 . answer : e"
Answer: e
Problem: in an examination , 300 students appeared . out of these students ; 30 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 33 , b ) 37 , c ) 54 , d ) 99 , e ) 48
Rationale: the number of students with first division = 30 % of 300 = 30 / 100 × 300 = 9000 / 100 = 90 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 90 + 162 ) = 48 answer : e
Answer: e
Problem: if two dice are thrown together , the probability of getting an even number on one die and an odd number on the other is ?
Options: a ) 1 / 9 , b ) 1 / 2 , c ) 1 / 1 , d ) 1 / 5 , e ) 1 / 8
Rationale: "the number of exhaustive outcomes is 36 . let e be the event of getting an even number on one die and an odd number on the other . let the event of getting either both even or both odd then = 18 / 36 = 1 / 2 p ( e ) = 1 - 1 / 2 = 1 / 2 . answer : b"
Answer: b
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 45 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 7 rs , c ) 8 rs , d ) 4 rs , e ) 3 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 45 rs . 5 m + 5 m + 5 m - - - - - 45 rs . 15 m - - - - - - 45 rs . = > 1 m = 3 rs . answer : e"
Answer: e
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 34 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 132 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 34 = > 4 / x = 1 / 34 x = 34 ∗ 4 = 136 mins option c"
Answer: c
Problem: two dice are rolled . what is the probability that the sum on the top face of both the dice will be greater than 9 ?
Options: a ) 3 / 8 , b ) 2 / 3 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 6
Rationale: total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) hence , total number of outcomes possible two dice are rolled , n ( s ) = 6 × 6 = 36 e = getting a sum greater than 9 when the two dice are rolled = { ( 4 , 6 ) , { 5 , 5 } , { 5 , 6 } , { 6 , 4 } , { 6 , 5 } , ( 6 , 6 ) } hence , n ( e ) = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 36 = 1 / 6
Answer: e
Problem: let a be the event that a randomly selected two digit number is divisible by 3 and let b be the event that a randomly selected two digit number is divisible by 10 . what is p ( a and b ) ?
Options: a ) 1 / 30 , b ) 1 / 15 , c ) 1 / 5 , d ) 1 / 3 , e ) 1 / 2
Rationale: "p ( a and b ) = 1 / 3 * 1 / 10 = 1 / 30 the answer is a ."
Answer: a