regisss/math_qa huggingface dataset:
Problem: a container holding 9 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 5 : 12 , e ) 7 : 3
Rationale: "container 1 has 9 ounces in the ratio 1 : 2 or , x + 2 x = 9 gives x ( alcohol ) = 3 and remaining water = 6 container 2 has 8 ounces in the ratio 1 : 3 or , x + 3 x = 8 gives x ( alcohol ) = 2 and remaining water = 6 mixing both we have alcohol = 3 + 2 and water = 6 + 6 ratio thus alcohol / water = 5 / 12 answer d"
Answer: d
Problem: if the ratio of apples to bananas is 3 to 2 and the ratio of bananas to cucumbers is 1 to 3 , what is the ratio of apples to cucumbers ?
Options: a ) 2 : 3 , b ) 1 : 2 , c ) 3 : 5 , d ) 2 : 5 , e ) 5 : 6
Rationale: "the ratio of bananas to cucumbers is 1 to 3 which equals 2 to 6 . the ratio of apples to bananas to cucumbers is 3 to 2 to 6 . the ratio of apples to cucumbers is 3 to 6 which equals 1 : 2 . the answer is b ."
Answer: b
Problem: if k and w are the dimensions of a rectangle that has area 60 , and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: "kw = 60 = 60 * 1 = 30 * 2 = 15 * 4 = 20 * 3 = 12 * 5 = 10 * 6 - - > k can take 6 values answer : e"
Answer: e
Problem: a candidate appearing for an examination has to secure 42 % marks to pass paper i . but he secured only 60 marks and failed by 20 marks . what is the maximum mark for paper i ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 190
Rationale: "he secured 60 marks nd fail by 20 marks so total marks for pass the examinatn = 80 let toal marks x x * 42 / 100 = 80 x = 190 answer : e"
Answer: e
Problem: the market value of a certain machine decreased by 30 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 2,400 , e ) $ 800
Rationale: "market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 30 / 100 ) = 8000 - 2400 = $ 5600 market value in 1984 = market value in 1983 - ( 30 % of $ 8000 ) = 5600 - 2400 = $ 3200 answer : c"
Answer: c
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : 2550 + ( 100 * 50 ) = 7550 ; answer : b
Answer: b
Problem: ratio between rahul and deepak is 4 : 3 , after 22 years rahul age will be 26 years . what is deepak present age
Options: a ) 10 , b ) 3 , c ) 5 , d ) 7 , e ) 8
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 22 = 26 = > x = 1 so deepak age is = 3 ( 1 ) = 3 answer : option b"
Answer: b
Problem: which of the options is a two - digit number , which has a unit ' s digit that exceeds its 10 ' s digit by 4 and the product of the given number and the sum of its digits is equal to 208 .
Options: a ) 15 , b ) 37 , c ) 55 , d ) 26 , e ) 73
Rationale: using the elimination method the option that fits this description is 26 6 - 2 = 4 ( unit ' s digit that exceeds its ten ' s digit by 3 ) 26 * 8 = 208 ( the product of the given number and the sum of its digits is equal to 175 ) answer : d
Answer: d
Problem: 2 , 4 , 6 , 8 , 10 , . . . ?
Options: a ) 8 , b ) 5 , c ) 7 , d ) 3 , e ) 12
Rationale: "each number increases by 2 . 2 + 2 = 4 4 + 2 = 6 6 + 2 = 8 8 + 2 = 10 10 + 2 = 12 answer : e"
Answer: e
Problem: the hcf and lcm of two numbers m and n are respectively 5 and 210 . if m + n = 75 , then 1 / m + 1 / n is equal to
Options: a ) 1 / 14 , b ) 3 / 35 , c ) 5 / 37 , d ) 2 / 35 , e ) none
Rationale: "answer we have , m x n = 5 x 210 = 1050 â ˆ ´ 1 / m + 1 / n = ( m + n ) / mn = 75 / 1050 = 1 / 14 correct option : a"
Answer: a
Problem: two trains are moving in the same direction at 54 kmph and 36 kmph . the faster train crosses a man in the slower train in 27 seconds . find the length of the faster train ?
Options: a ) 135 , b ) 277 , c ) 187 , d ) 257 , e ) 271
Rationale: "relative speed = ( 54 - 36 ) * 5 / 18 = 5 mps . distance covered in 27 sec = 27 * 5 = 135 m . the length of the faster train = 135 m . answer : a"
Answer: a
Problem: drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 4 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 5 / 6 , e ) 7 / 8
Rationale: ( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 4 ) y = ( 1 / 2 ) y the answer is a .
Answer: a
Problem: the ratio of three numbers is 1 : 2 : 3 and the sum of their squares is 2744 . the sum of the numbers is ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 14 , e ) 9
Rationale: "let the numbers be x , 2 x , 3 x then , x ^ 2 + 4 x ^ 2 + 9 x ^ 2 = 2744 14 x ^ 2 = 2744 x ^ 2 = 196 x = 14 answer is d"
Answer: d
Problem: 0.6 of a number is equal to 0.08 of another number . the ratio of the numbers will be
Options: a ) 3 : 4 , b ) 4 : 3 , c ) 2 : 15 , d ) 2 : 9 , e ) 3 : 8
Rationale: let the numbers be x and y 0.6 x = 0.08 y = > x / y = 0.08 / 0.6 = 2 : 15 answer c .
Answer: c
Problem: if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on all 6 flips ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 32 , d ) 1 / 2 , e ) 1 / 64
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 64 answer : e
Answer: e
Problem: the perimeter of one face a of cube is 20 cm . its volume must be
Options: a ) 125 cm 3
b ) 400 cm 3
c ) 1000 cm 3
d ) 8000 cm 3
e ) none
Rationale: solution edge of the cube = ( 20 / 4 ) cm ‹ = › 5 cm . volume = ( 5 × 5 × 5 ) cm 3 ‹ = › 125 cm 3 . answer a
Answer: a
Problem: a train 660 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 640 , b ) 277 , c ) 500 , d ) 297 , e ) 435
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 660 + x ) / 60 = 65 / 3 x = 640 m . answer : a"
Answer: a
Problem: two goods trains each 850 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 sec , b ) 81.6 sec , c ) 48 sec , d ) 18.3 sec , e ) 9.32 sec
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 850 + 850 = 1700 m . required time = 1700 * 6 / 125 = 81.6 sec . answer : b"
Answer: b
Problem: the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 8400 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6725 , b ) rs . 6727 , c ) rs . 6908 , d ) rs . 6725 , e ) rs . 7000
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8400 ( 100 / 120 ) = rs . 7000 . answer : e"
Answer: e
Problem: what is 92 % of 3 / 4 ?
Options: a ) 6.9 , b ) 69.0 , c ) 0.6845 , d ) 0.6859 , e ) 0.69
Rationale: "soln : - 120 % = 12 / 10 5 / 8 * 12 / 10 = 60 / 80 = 6 / 8 = 3 / 4 = 0.69 answer : e ."
Answer: e
Problem: the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 30 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 960 , d ) $ 832 , e ) $ 660
Rationale: "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 130 % of $ 640 = $ 832 . d"
Answer: d
Problem: a 140 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 228 , b ) 108 , c ) 84 , d ) 188 , e ) 211
Rationale: "s = 140 / 6 * 18 / 5 = 84 kmph answer : c"
Answer: c
Problem: a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 18 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 7 / 25 , e ) 9 / 10
Rationale: "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 18 - 2 cmb = 100 b - cb - mb - 2 cmb = 28 hence the probability = 28 / 100 = 7 / 25 . d"
Answer: d
Problem: if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 5 m of the same rod ?
Options: a ) 22.8 kg , b ) 25.6 kg , c ) 19 kg , d ) 26.5 kg , e ) none of these
Rationale: "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 5 : : 42.75 : x = > 11.25 x x = 5 x 42.75 = > x = ( 5 x 42.75 ) / 11.25 = > x = 19 answer : c"
Answer: c
Problem: the area of a rectangle is 460 square metres . if the length is 15 % more than the breadth , what is the breadth of the rectangular field ?
Options: a ) 20
b ) 27
c ) 26
d ) 188
e ) 11
Rationale: explanation : let breadth = x meters . then , length = meters given that , = > x = 20 breadth = 20 answer : a ) 20 m
Answer: a
Problem: find the product of the local value and absolute value of 6 in 564823
Options: a ) 8000 , b ) 16000 , c ) 12000 , d ) 18000 , e ) 360000
Rationale: "explanation : place value = local value face value = absolute value the place value of 6 in 564823 is 6 x 10000 = 60000 the face value of 6 in 564823 is nothing but 6 . = > 60000 x 6 = 360,000 answer : option e"
Answer: e
Problem: find the compound interest on $ 100000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 824.32 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 8243.21
Rationale: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 100000 * ( 1 + 2 / 100 ) ^ 4 = 100000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 108243.21 c . i . = 108243.21 - 100000 = $ 8243.21 answer is e"
Answer: e
Problem: rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 135 . how much was lent at 5 % ?
Options: a ) 2333 , b ) 2777 , c ) 2688 , d ) 1500 , e ) 2871
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 135 x = 1500 answer : d"
Answer: d
Problem: ( 0.66 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.66 ) ( power 2 ) + 0.066 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.86 , b ) 0.56 , c ) 0.96 , d ) 0.69 , e ) 0.76
Rationale: "given expression = ( 0.66 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.66 ) ( power 2 ) + ( 0.66 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.66 - 0.1 ) = 0.56 answer is b"
Answer: b
Problem: a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 10 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 50 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .
Options: a ) 80 % , b ) 65 % , c ) 28.33 % , d ) 19.109 % , e ) 50 %
Rationale: "anyways , one can infer that he ' steals ' 10 % from suppliers and then charges 50 % extra to customers so basically 1.1 * 1.5 = 1.65 given that 1 is start point , we get 65 % more hence answer is b"
Answer: b
Problem: when the no . 7 y 86038 is exactly divisible by 11 , then the smallest whole no . in place of y ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the given number = 7 y 86038 sum of the odd places = 8 + 0 + 8 + 7 = 23 sum of the even places = 3 + 6 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 23 - ( 9 + y ) = divisible by 11 14 � y = divisible by 11 . y must be 3 , to make given number divisible by 11 . b
Answer: b
Problem: set i consists of integers { 3 , - 8 , y , 19 , - 6 } and set b consists of integers { k , - 3 , 0 , 16 , - 5 , 9 } . number l represents the median of set i , number m represents mode of set b and number z = l ^ m . if y is an integer greater than 21 , for what value of k will z be a divisor of 26 ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: i = { 3 , - 8 , y , 19 , - 6 } b = { k , - 3 , 0,16 , - 5,9 } y > 21 so l = median of i = 3 m = mode of set b z = ( 3 ) ^ m if z is a divisor of 26 , ( 3 ) ^ m = 1 because 26 does not have 3 as a factor = > m = 0 hence k = 0 , as m is mode and 0 will be the most frequently occuring number in set b . answer - c
Answer: c
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 12 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 25 , b ) 23 , c ) 22 , d ) 20 , e ) 10
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 12 w = 120 = > w = 10 answer e"
Answer: e
Problem: a rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . feet , how many feet of fencing will be required ?
Options: a ) 80 feet
b ) 85 feet
c ) 83 feet
d ) 88 feet
e ) 90 feet
Rationale: given that area of the field = 680 sq . feet = > lb = 680 sq . feet length ( l ) = 20 feet = > 20 × b = 680 = > b = 680 / 20 = 34 feet required length of the fencing = l + 2 b = 20 + ( 2 × 34 ) = 88 feet answer is d .
Answer: d
Problem: simple interest on a certain sum of money for 2 years at 12 % per annum is half the compound interest on rs . 6000 for 2 years at 15 % per annum . the sum placed on simple interest is
Options: a ) rs . 6000 , b ) rs . 7935 , c ) rs . 8265.63 , d ) rs . 3967.5 , e ) none
Rationale: "solution c . i . = rs [ 6000 x ( 1 + 15 / 100 ) â ² - 4000 ] rs . ( 4000 x 115 / 100 x 115 / 100 - 6000 ) = rs . 7935 . sum = rs . [ 3967.5 x 100 / 4 x 12 ] = rs . 8265.63 . answer c"
Answer: c
Problem: 10 men working 12 hours daily finish a work in 24 days . in how many days will they finish 1 / 4 th of the work working 8 hours daily ?
Options: a ) 9 days , b ) 10 days , c ) 11 days , d ) 12 days , e ) 18 days
Rationale: the number of days needed to finish 1 / 4 of the work = 1 / 4 * 12 / 8 * 24 = 9 days . answer : a
Answer: a
Problem: 65 % of x = 20 % of 747.50 . find the value of x ?
Options: a ) 100 , b ) 230 , c ) 150 , d ) 180 , e ) 199
Rationale: "65 % of x = 20 % of 747.50 then , 65 / 100 * x = 20 / 100 * 7475 / 10 x = 230 answer is b"
Answer: b
Problem: what is the remainder wen 2 ^ 35 is divided by 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2 ^ 35 / 5 = > ( 2 ^ 4 ) ^ 8 * 2 ^ 3 / 5 = > ( 5 * 3 + 1 ) ^ 8 * ( 5 + 3 ) / 5 = > ( 1 * 3 ) / 5 = > 3 / 5 = > remainder = 3 answer : c"
Answer: c
Problem: a certain car can travel 40 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 78 , d ) 91 , e ) 104
Rationale: "fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 40 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 40 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : c ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 40 x 3.9 x 3.8 / 5.7 x 1.6 = 65 b"
Answer: b
Problem: each side of a rectangle is increased by 100 % . by what percentage does the area increase ?
Options: a ) 300 % , b ) 400 % , c ) 500 % , d ) 200 % , e ) 600 %
Rationale: original area = a * b where a and b are sides after increase in side increase in area will be = ( ( ( 2 a * 2 b ) - ( a * b ) ) * 100 ) / ( a * b ) = 300 % answer : a
Answer: a
Problem: the average monthly salary of 20 employees in an organisation is rs . 1300 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) 3600 , b ) 3890 , c ) 88798 , d ) 3400 , e ) 2891
Rationale: "explanation : manager ' s monthly salary rs . ( 1400 * 21 - 1300 * 20 ) = rs . 3400 . answer : d"
Answer: d
Problem: convert 2.0 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 200 ares . , e ) 250 ares .
Rationale: "2.0 hectares in ares 1 hectare = 100 ares therefore , 2.0 hectares = 2.0 × 100 ares = 200 ares . answer - d"
Answer: d
Problem: seller selling an apple for rs . 19 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 20 , d ) 18 , e ) 21
Rationale: sp = 19 loss = cp 20 loss = cp − sp = cp − 19 ⇒ cp 20 = cp − 19 ⇒ 19 cp 20 = 19 ⇒ cp 20 = 1 ⇒ cp = 20 c
Answer: c
Problem: what is the difference between the largest and the smallest number written with 7 , 7 , 0 , 7 ?
Options: a ) 6893 , b ) 6993 , c ) 6093 , d ) 693 , e ) none
Rationale: "7770 7077 - - - - - - - - - - - - - 693 answer : d"
Answer: d
Problem: if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 3 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 5 / 3 , b ) 5 / 4 , c ) 10 / 3 , d ) 15 / 4 , e ) 15 / 2
Rationale: "n = 2 d / 5 j = n / 3 = 2 d / 15 the average of november and january is ( n + j ) / 2 = 8 d / 15 / 2 = 4 d / 15 d is 15 / 4 times the average of november and january . the answer is d ."
Answer: d
Problem: a man bring 2 cats to his home to eliminate all the mice . they do a half of the work in 5 days , then the man brings 3 more cats . if they hunt at the same rate , how many days will take to hunt all the mice , since the first day ?
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days
Rationale: we have that : 2 cats - - - - - 5 days , ( 2 + 3 ) c - - - - - x d , that is : ( x d / 2 c ) = ( 5 d / 5 p ) , then : x d = ( 5 d / 5 c ) 2 c = 2 d . is to say , the 5 cats hunt the same quantity in 2 days ; as it is only 1 / 2 of the work , all the mice would be hunt in : m = 5 d + 2 d = 7 days . answer a .
Answer: a
Problem: a sum of money lent out at s . i . amounts to rs . 720 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) 600 , b ) 288 , c ) 2768 , d ) 287 , e ) 191
Rationale: "s . i for 5 years = ( 1020 - 720 ) = rs . 300 . s . i . for 2 years = 300 / 5 * 2 = rs . 120 . principal = ( 720 - 120 ) = rs . 600 . answer : a"
Answer: a
Problem: there are 15 members in a family . it takes 180 days for a women to complete the work , however man completes in 120 days . they take 17 days to complete the work if men work on alternate days and women work every third day . if all of them started together on the 1 st day , then how many women are there in the family
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: let the number of men be m and so the number of women = 15 - m out of 17 days , men and women work together on 1,4 , 7,10 , 13,16 th days ( total of 6 days ) from the start . men work on alternate days , that is 1 , 3,5 , 7,9 , 11,13 , 15,17 th days ( total of 9 days ) . let the total work be 360 units ( lcm of 180 and 120 ) . 1 man does 360 / 120 = 3 units per day 1 woman does 360 / 180 = 2 units per day based on above facts , total work by men + women in these 17 days = 360 units m * 9 * 3 + ( 15 - m ) * 6 * 2 = 360 , 27 m + 180 - 12 m = 360 , solving m = 12 . num of men = 12 and number of women = 15 - 12 = 3 answer : c
Answer: c
Problem: how many integers between 1000 and 10000 have no digits other than 4 , 5 or 6 ?
Options: a ) 91 , b ) 51 , c ) 81 , d ) 71 , e ) 61
Rationale: any number between 1000 and 10000 is of 4 digits . the unit ’ s place can be filled up by 45 or 6 , that is , in 3 ways . similarly , the ten ’ s place can be filled up by 4 or 5 or 6 , that is in 3 ways . the hundred ’ s place can be filled up by 4 , 5 or 6 , that is in 3 ways and the thousand ’ s place can . be filled up by 4 or 5 or 6 , that is , in 3 ways . hence the required numbers = 3 x 3 x 3 x 3 = 81 answer : c
Answer: c
Problem: john completes a piece of work in 8 days , rose completes the same work in 16 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 6 days , b ) 5.33 days , c ) 10 days , d ) 12 days , e ) 14 days
Rationale: if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 8 × 16 / 24 = 5.33 days answer : b
Answer: b
Problem: what is the area of a triangle with the following vertices l ( 2 , 3 ) , m ( 5 , 1 ) , and n ( 3 , 5 ) ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: there is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem . though if you make a diagram minimum simple calculations will be needed : answer : b .
Answer: b
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and b quits 5 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 5 days , a can do 1 / 4 of the project . thus a and b must complete 3 / 4 of the project , which takes 9 days . the total number of days is 9 + 5 = 14 . the answer is c ."
Answer: c
Problem: how long does a train 140 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?
Options: a ) 13.6 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 16.8 sec , e ) 14.9 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 140 + 132 = 272 m . required time = 272 / 20 = 13.6 sec . answer : a"
Answer: a
Problem: in kaya ' s teacher ' s desk there are 10 pink highlighters , 15 yellow highlighters , and 8 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 10 + 15 + 8 = 33 . answer is d ."
Answer: d
Problem: income and expenditure of a person are in the ratio 9 : 8 . if the income of the person is rs . 18000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 3603 , c ) rs . 2000 , d ) rs . 3632 , e ) rs . 3602
Rationale: "let the income and the expenditure of the person be rs . 9 x and rs . 8 x respectively . income , 9 x = 18000 = > x = 2000 savings = income - expenditure = 9 x - 8 x = x so , savings = rs . 2000 answer : c"
Answer: c
Problem: a gambler has won 40 % of his 40 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 80 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let x be the number of additional games the gambler needs to play . 0.4 ( 40 ) + 0.8 x = 0.6 ( x + 40 ) 0.2 x = 8 x = 40 the answer is e ."
Answer: e
Problem: x , y , and z are consecutive numbers and x > y > z . also , 2 x + 3 y + 3 z = 5 y + 8 . what is the value of z ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: if x , y , and z are consecutive numbers and x > y > z , then y = z + 1 and x = z + 2 . 2 x + 3 y + 3 z = 5 y + 8 2 z + 4 + 3 z + 3 + 3 z = 5 z + 5 + 8 3 z = 6 z = 2 the answer is a .
Answer: a
Problem: in the coordinate plane , points ( x , 6 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x * y =
Options: a ) 52 , b ) 46 , c ) 60 , d ) 50 , e ) 35
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 6 ) = ( 12 , 6 ) and ( 10 , y ) = ( 10,5 ) - - > x * y = 12 * 5 = 60 . answer : c"
Answer: c
Problem: a vessel of capacity 3 litre has 25 % of alcohol and another vessel of capacity 5 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 27.5 % . , d ) 29 % . , e ) 51 % .
Rationale: "25 % of 3 litres = 0.75 litres 40 % of 5 litres = 2 litres therefore , total quantity of alcohol is 2.75 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 27.5 % c"
Answer: c
Problem: a jar contains 18 balls . 3 blue balls are removed from the jar and not replaced . now the probability of getting a blue ball is 1 / 5 then how many blue balls jar contains initially ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: x / 15 = 1 / 5 x = 3 3 + 3 ( removed 3 blue balls ) = 6 answer : e
Answer: e
Problem: a rectangular grassy plot 110 m by 65 cm has a gravel path . 5 cm wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . mt ?
Options: a ) 680 rs , b ) 540 rs , c ) 480 rs , d ) 640 rs , e ) 280 rs
Rationale: area of theplot = 110 * 65 = 7150 sq m area of the plot excluding the path = ( 110 - 5 ) * ( 65 - 5 ) = 6300 sq m area of the path = 7150 - 6300 = 850 sq m cost of gravelling the path = 850 * 80 / 100 = 680 rs answer : a
Answer: a
Problem: a motorcyclist goes from nagpur to delhi , a distance of 600 kms at an average of 60 kmph speed . another man starts from nagpur by car 5 â ½ hours after the first , and reaches delhi â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 7 , c ) 1 : 9 , d ) 1 : 5 , e ) 2 : 5
Rationale: t = 600 / 60 = 10 h t = 10 - 6 = 4 time ratio = 10 : 4 = 5 : 2 speed ratio = 2 : 5 answer : e
Answer: e
Problem: according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 120 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? d"
Answer: d
Problem: there are 20 balls in a jar . you take out 2 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ?
Options: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .
Rationale: "12 = 3 blue balls + 18 / 2 answer : a"
Answer: a
Problem: the volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is :
Options: a ) 3 / 4 ∏
b ) 4 / 3 ∏
c ) 5 ∏
d ) 5 / 9 ∏
e ) none
Rationale: sol . required volume = volume of a sphere of radius 1 cm = [ 4 / 3 ∏ * 1 * 1 * 1 ] cm ³ = 4 / 3 ∏ cm ³ answer b
Answer: b
Problem: a = { 20 , 1 , - 3 , 6 , - 8 } b = { - 1 , 2 , - 4 , 7 , - 620 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab > 0 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 5 / 12 , d ) 4 / 9 , e ) 1 / 2
Rationale: for the product of 2 numbers to be positive either both of them must be positive or both of them must be negative : p ( positive , positive ) = 3 / 6 * 3 / 6 = 9 / 36 ; p ( negative , negative ) = 2 / 6 * 3 / 6 = 6 / 36 . p = 9 / 36 + 6 / 36 = 15 / 36 = 5 / 12 . answer : c .
Answer: c
Problem: if x is 40 percent greater than 88 , then x =
Options: a ) 68 , b ) 70.4 , c ) 123.2 , d ) 105.6 , e ) 108
Rationale: "x = 88 * 1.4 = 123.2 so the answer is c ."
Answer: c
Problem: the perimeter of an isosceles right triangle is 4 + 4 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 2.82 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 4 + 4 sqrt 2 or , a . ( 2 + sqrt 2 ) = 4 ( 1 + sqrt 2 ) a = 4 . ( 1 + sqrt 2 ) / 2 + sqrt 2 = 4 * 2.414 / 3.414 = then hypotenuse = 2.82 a"
Answer: a
Problem: an 11 - 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 ) 3 / 7
b ) 5 / 8
c ) 3 / 10
d ) 5 / 11
e ) 6 / 11
Rationale: the longer wire will form a square with an area more than 4 if the wire is cut at a point within three meters of either end . the probability of this is 6 / 11 . the answer is e .
Answer: e
Problem: how many different positive integers are factors of 36 ?
Options: a ) 4 , b ) 6 , c ) 7 , d ) 9 , e ) 11
Rationale: "6 × 6 = 3 ^ 2 × 2 ^ 2 so total factors = ( 2 + 1 ) ( 2 + 1 ) = 9 answer : d"
Answer: d
Problem: the list price of an article is rs . 65 . a customer pays rs . 57.33 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 12 % , e ) 2 %
Rationale: "option e explanation : 65 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 57.33 x = 2 %"
Answer: e
Problem: the supplementary of an angle is thrice its complimentary . find the angle .
Options: a ) 60 , b ) 45 , c ) 90 , d ) 180 , e ) 120
Rationale: let angle = x ; by question - - 180 - x = 3 ( 90 - x ) x = 45 answer : b
Answer: b
Problem: 9 log 9 ( 2 ) = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 2 ) = 2 correct answer b
Answer: b
Problem: there are 2 vessels a & b containing 25 liters each of pure milk and pure water respectively . 5 liters of milk from a is taken and poured into b , then 6 liters of mixture from b is taken and poured in a . what is ratio of water a and b respectively .
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 1 : 6 , e ) 1 : 7
Rationale: at first a cotain milk = 25 water = 0 b cotain milk = 00 water = 25 5 litres of milk taken from a and poured in b then a cotain milk = 20 water = 0 b cotain milk = 5 water = 25 6 litres ( 1 lit milk & 5 lit water ) of mixture from b and poured in a . so , finally a cotain milk = 21 water = 5 b cotain milk = 4 water = 20 ratio of water in a & b is 5 : 20 = 1 : 4 answer : b
Answer: b
Problem: tim and é lan are 150 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 30 miles . , b ) 35 miles . , c ) 45 miles . , d ) 90 miles . , e ) 100 miles .
Rationale: "tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice e meet the 2 : 1 ( tim : elan = 100 : 50 ) ratio of maintaining total distance traveled 150 miles socorrect answer e"
Answer: e
Problem: 16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 4 girls will take to construct ?
Options: a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 4 girls = 8 ã — 6 / 4 + 12 = 12 + 4 = 16 girls 9 days to complete the work answer : option e"
Answer: e
Problem: 30 pens and 75 pencils were purchased for 630 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 16
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 630 – 150 ) = 480 ∴ average price of a pen = 480 ⁄ 60 = 16 answer e"
Answer: e
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 1,600 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 5.55 % , b ) 5.65 % , c ) 5.75 % , d ) 5.85 % , e ) 5.95 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 8400 = 5 / 84 which is about 5.95 % the answer is e ."
Answer: e
Problem: find the cost of fencing around a circular field of diameter 34 m at the rate of rs . 2 a meter ?
Options: a ) 215 , b ) 212 , c ) 278 , d ) 279 , e ) 222
Rationale: "2 * 22 / 7 * 17 = 106 106 * 2 = rs . 212 answer : b"
Answer: b
Problem: a man covered a certain distance at some speed . if he had moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . what is the the distance in km ?
Options: a ) 33 , b ) 37 , c ) 40 , d ) 38 , e ) 27
Rationale: "let the distance be x km , the speed in which he moved = v kmph time taken when moving at normal speed - time taken when moving 3 kmph faster = 40 minutes ⇒ xv − xv + 3 = 4060 ⇒ x [ 1 v − 1 v + 3 ] = 23 ⇒ x [ v + 3 − vv ( v + 3 ) ] = 23 ⇒ 2 v ( v + 3 ) = 9 x . . . . . . . . . . . . . . . . ( equation 1 ) time taken when moving 2 kmph slower - time taken when moving at normal speed = 40 minutes ⇒ xv − 2 − xv = 4060 ⇒ x [ 1 v − 2 − 1 v ] = 23 ⇒ x [ v − v + 2 v ( v − 2 ) ] = 23 ⇒ x [ 2 v ( v − 2 ) ] = 23 ⇒ x [ 1 v ( v − 2 ) ] = 13 ⇒ v ( v − 2 ) = 3 x . . . . . . . . . . . . . . . . ( equation 2 ) equation 1 equation 2 ⇒ 2 ( v + 3 ) ( v − 2 ) = 3 ⇒ 2 v + 6 = 3 v − 6 ⇒ v = 12 substituting this value of v in equation 1 ⇒ 2 × 12 × 15 = 9 x = > x = 2 × 12 × 159 = 2 × 4 × 153 = 2 × 4 × 5 = 40 hence distance = 40 km answer : c"
Answer: c
Problem: if x + y = 280 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 240 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 280 x - y = 200 2 x = 80 x = 40 y = 240 answer is b"
Answer: b
Problem: there are 10 students named alphabetically from a to j . what is the probability that a and d do not sit together if all 10 sit around a circular table ?
Options: a ) 2 / 9 , b ) 2 / 5 , c ) 7 / 9 , d ) 4 / 5 , e ) 8 / 9
Rationale: number of students = 10 number of ways 10 students can sit around a circular table = ( 10 - 1 ) ! = 9 ! number of ways a and d sit together ( consider a and d as one entity ) = ( 9 - 1 ) ! = 8 ! * 2 number of ways a and d do not sit together = 9 ! - ( 8 ! * 2 ) probability = ( 9 ! - ( 8 ! * 2 ) ) / 9 ! = 1 - 2 / 9 = 7 / 9 answer : c
Answer: c
Problem: a pipe can empty 2 / 3 rd of a cistern in 10 mins . in 8 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 3 / 7 , c ) 8 / 15 , d ) 3 / 8 , e ) 4 / 7
Rationale: "2 / 3 - - - - 10 ? - - - - - 8 = = > 8 / 15 c"
Answer: c
Problem: if $ 10 be allowed as true discount on a bill of $ 110 due at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is :
Options: a ) $ 18.33 , b ) $ 22.33 , c ) $ 28.33 , d ) $ 26.23 , e ) $ 16.23
Rationale: s . i . on $ ( 110 - 10 ) for a certain time = $ 10 . s . i . on $ 100 for double the time = $ 20 . t . d . on $ 120 = $ ( 120 - 100 ) = $ 20 . t . d . on $ 110 = $ ( 20 / 120 * 100 ) = $ 18.33 answer : a
Answer: a
Problem: if you multiply two integers together and then add 4 , the result is 40 . which of the following could not be the sum of the two numbers ?
Options: a ) 12 , b ) 13 , c ) 15 , d ) 18 , e ) 20
Rationale: let the two integers equal x and y , and then create the following equation and simplify : xy + 4 = 40 xy = 36 so x and y are a pair of integers that equal 36 . try adding all possible combinations of two integers that multiply out to 36 : 1 × 36 = 36 1 + 36 = 37 2 × 18 = 36 2 + 18 = 20 3 × 12 = 36 3 + 12 = 15 4 × 9 = 36 4 + 9 = 13 6 × 6 = 36 6 + 6 = 12 this list of sums includes 12 , 13 , 15 , and 20 , but not 18 . thus , no pair of integers both satisfies the original equation and adds up to 18 correct answer d ) 18
Answer: d
Problem: a train 460 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 87 , c ) 48 , d ) 21 , e ) 14
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 460 + 140 = 600 m required time = 600 * 2 / 25 = 48 sec answer : c"
Answer: c
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what might be the weight of the new person ?
Options: a ) 65 kg , b ) 90 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "a 65 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 64 + 20 ) kg = 65 kg ."
Answer: a
Problem: a shopkeeper loses 15 % , if an article is sold for rs . 187 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 247 , b ) s . 248 , c ) s . 264 , d ) s . 329 , e ) s . 412
Rationale: "given that sp = rs . 187 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 187 ) / 85 = 20 * 6 = rs . 220 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 220 * 120 ) / 100 = rs . 264 answer : c"
Answer: c
Problem: if 9 a - b = 10 b + 65 = - 12 b - 2 a , what is the value of 11 a + 11 b ?
Options: a ) - 11 , b ) - 5 , c ) 0 , d ) 5 , e ) 11
Rationale: "( i ) 9 a - 11 b = 65 ( ii ) 2 a + 22 b = - 65 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ."
Answer: c
Problem: find the average of all numbers between 1 and 76 which are divisible by 5
Options: a ) 40 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 + 70 + 75 ) / 15 = 600 / 15 = 40 answer : option a"
Answer: a
Problem: a cricketer makes a score of 134 runs in the 22 nd inning and thus increases his average by 3.5 . find his average after 22 nd inning .
Options: a ) 40 , b ) 60.5 , c ) 52 , d ) 55 , e ) 36
Rationale: explanation : let the average after 22 nd innings = x then average after 21 th innings = ( x - 3.5 ) therefore 21 ( x - 3.5 ) + 134 = 22 x therefore x = 60.5 answer : b
Answer: b
Problem: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 30 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 percent , c ) 25 % , d ) 28 % , e ) 27 %
Rationale: "total sales = 800 commission = ( 20 / 100 ) * 500 + ( 30 / 100 ) * 300 = 100 + 90 = 190 % commission = ( 190 / 800 ) * 100 = 23.7 ~ 24 % answer is b"
Answer: b
Problem: in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 6 rows in all and a total of 135 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 21 , b ) 20 , c ) 22 , d ) 19 , e ) 24
Rationale: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 + x - 5 = 135 6 x - 15 = 135 6 x = 120 x = 20 answer : b"
Answer: b
Problem: the average marks of a class of 25 students is 50 and that of another class of 40 students is 65 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 59 , e ) 52.9
Rationale: "sum of the marks for the class of 25 students = 25 * 50 = 1250 sum of the marks for the class of 40 students = 40 * 65 = 2600 sum of the marks for the class of 65 students = 1250 + 2600 = 3850 average marks of all the students = 4850 / 65 = 59 . answer : d"
Answer: d
Problem: how many plants will be there in a circular bed whose outer edge measure 34 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 23 , d ) 120 , e ) none of these
Rationale: "circumference of circular bed = 34 cm area of circular bed = ( 34 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 34 ) 2 â  „ 4 ï € ã · 4 = 22.98 = 23 ( approx ) answer c"
Answer: c
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 10 % ?
Options: a ) 550 , b ) 882 , c ) 772 , d ) 652 , e ) 271
Rationale: "cost price = rs . 500 profit = 10 % of 500 = rs . 50 selling price = cost price + profit = 500 + 50 = 550 answer : a"
Answer: a
Problem: stacy and helon are 30 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour faster than helon ' s constant rate of 5 miles / hour . if helon starts her journey 24 minutes after stacy , how far from the original destination has helon walked when the two meet ?
Options: a ) 5 miles , b ) 8 miles , c ) 6 miles , d ) 13 miles , e ) 12 miles
Rationale: original distance between s and h = 30 miles . speed of s = 5 + 1 = 6 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 24 / 60 = t + 2 / 5 hours . now , the total distances traveled by s and h = 20 miles - - - > 6 * ( t + 2 / 5 ) + 5 * t = 30 - - - > t = 138 / 55 hours . thus h has traveled for 138 / 55 hours giving you a total distance for h = 5 * 138 / 55 = 13 miles . d is thus the correct answer . p . s . : based on the wording of the question , you should calculatehow far from theoriginal destination has heather walkedwhen the two meet . ' original destination ' for h does not make any sense . original destination for h was situated at a distance of 20 miles .
Answer: d
Problem: if log 2 = 0.30103 and log 3 = 0.4771 , find the number of digits in ( 648 ) 5
Options: a ) 14.05 , b ) 14.02 , c ) 277 , d ) 288 , e ) 222
Rationale: "log ( 648 ) 5 = 5 log ( 648 ) = 5 log ( 81 × 8 ) = 5 [ log ( 81 ) + log ( 8 ) ] = 5 [ log ( 34 ) + log ( 23 ) ] = 5 [ 4 log ( 3 ) + 3 log ( 2 ) ] = 5 [ 4 × 0.4771 + 3 × 0.30103 ] = 5 ( 1.9084 + 0.90309 ) = 5 × 2.81149 ≈ 14.05 answer : a"
Answer: a
Problem: if the ratio of the areas of two squares is 225 : 256 , then the ratio of their perimeters is :
Options: a ) 15 : 12
b ) 15 : 14
c ) 15 : 16
d ) 15 : 22
e ) none of these
Rationale: explanation : a 2 / b 2 = 225 / 256 = 15 / 16 < = > 4 a / 4 b = 4 ∗ 15 / 4 ∗ 16 = 15 / 16 = 15 : 16 option c
Answer: c
Problem: what least number must be subtracted from 12702 to get number exactly 99 ?
Options: a ) 49 , b ) 30 , c ) 29 , d ) 31 , e ) 32
Rationale: "explanation : divide the given number by 99 and find the remainder . if you subtract the remainder from the given number then it is exactly divisible by 99 . 99 ) 12702 ( 128 99 280 198 822 792 30 required number is 30 . answer is b"
Answer: b
Problem: if x is 20 percent greater than 40 , then x =
Options: a ) 48 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108
Rationale: "x is 20 % greater than 40 means x is 1.2 times 40 ( in other words 40 + 20 / 100 * 40 = 1.2 * 40 ) therefore , x = 1.2 * 40 = 48 answer : a"
Answer: a
Problem: in a theater , the first row has 14 seats and each row has 2 more seats than previous row . if the last row has 56 seats , what is the total number of seats in the theater ?
Options: a ) 770 , b ) 780 , c ) 790 , d ) 800 , e ) 810
Rationale: "the number of seats in the theater is 14 + ( 14 + 2 ) + . . . + ( 14 + 42 ) = 22 ( 14 ) + 2 ( 1 + 2 + . . . + 21 ) = 22 ( 14 ) + 2 ( 21 ) ( 22 ) / 2 = 22 ( 14 + 21 ) = 22 ( 35 ) = 770 the answer is a ."
Answer: a
Problem: a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 60 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 36 , b ) 96 , c ) 100 , d ) 76 , e ) 72
Rationale: "total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 60 vehicles . hence 2 / 3 constitutes 120 speedster convertibls = 120 * 4 / 5 = 96 b"
Answer: b
Problem: a bag of potatoes weighs 12 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 18 lb , c ) 12 lb , d ) 15 lb , e ) 5 lb
Rationale: "sol . 12 ÷ 1 = 12 . answer : c"
Answer: c
Problem: the price of 80 apples is equal to that of 120 oranges . the price of 60 apples and 75 oranges together is rs . 1320 . the total price of 25 apples and 40 oranges is
Options: a ) 620 , b ) 610 , c ) 630 , d ) 625 , e ) 635
Rationale: "let the price of one apple = a and price of one orange = b the price of 80 apples is equal to that of 120 oranges 80 a = 120 b = > 2 a = 3 b ⇒ b = 2 a / 3 - - - - - ( equation 1 ) price of 60 apples and 75 oranges together is rs . 1320 = > 60 a + 75 b = 1320 = > 4 a + 5 b = 88 ⇒ 4 a + 5 ( 2 a ) / 3 = 88 ( ∵ substituted the value of b from equation 1 ) = > 12 a + 10 a = 88 × 3 = > 6 a + 5 a = 44 × 3 = > 11 a = 44 × 3 = > a = 4 × 3 = 12 b = 2 a / 3 = ( 2 × 12 ) / 3 = 8 total price of 25 apples and 40 oranges = 25 a + 40 b = ( 25 × 12 ) + ( 40 × 8 ) = 300 + 320 = 620 answer is a ."
Answer: a
Problem: two vessels a and b contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively . find the ratio in which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ration 8 : 5 ?
Options: a ) 4 : 3 , b ) 3 : 4 , c ) 5 : 6 , d ) 7 : 9 , e ) none
Rationale: let the c . p . of spirit be re . 1 litre . spirit in 1 litre mix . of a = 5 / 7 litre , c . p . of 1 litre mix . in a = re . 5 / 7 spirit in 1 litre mix . of b = 7 / 13 litre , c . p . of 1 litre mix . in b = re . 7 / 13 spirit in 1 litre mix . of c = 8 / 13 litre , mean price = re . 8 / 13 . by the rule of alligation , we have : required ratio = 1 / 13 : 9 / 91 = 7 : 9 . answer d
Answer: d
Problem: a scale 7 ft . 6 inches long is divided into 5 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 18 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 7 * 12 ) + 6 = 90 inches length of each of the 5 parts = 90 / 5 = 18 inches answer : d"
Answer: d
Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of three cubic feet . if a large block has twice the width , twice the depth , and three times the length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 18
b ) 6
c ) 27
d ) 48
e ) 36
Rationale: volume of cube = lbh = 3 new cube l , b , h are increases of 3 l , 2 b , 2 h new volume of cube = 3 l * 2 b * 2 h = 12 lbh = 12 * 3 = 36 answer : e
Answer: e