regisss/math_qa huggingface dataset:
Problem: find the ones digit of 73 ^ 355
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: the units digit of 73 ^ 355 will be the same as the units digit of 3 ^ 355 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 355 = 352 + 3 = ( multiple of 4 ) + 2 , then the units digit of 3 ^ 355 will be the third number in the pattern thus 7 . answer : d .
Answer: d
Problem: how long will it take a train travelling at 98 kmph to pass an electric pole if the train is 140 m long
Options: a ) 6.15 , b ) 5.15 , c ) 3.15 , d ) 1.15 , e ) 7.15
Rationale: "sol . speed = [ 98 x 5 / 18 ] m / sec = 27.2 m / sec . time taken = ( 140 / 27.2 ) sec = 5.15 sec . answer b"
Answer: b
Problem: a train can travel 50 % faster than a car . both start from point a at the same time and reach point b 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . the speed of the car is :
Options: a ) 120 kmph , b ) 150 kmph , c ) 50 kmph , d ) 80 kmph , e ) 75 kmph
Rationale: "let speed of the car be x kmph . then , speed of the train = 150 / 100 x = 3 / 2 x kmph . 75 / x - 75 / ( 3 / 2 ) x = 125 / 10 x 60 75 / x - 50 / x = 5 / 24 x = 25 x 24 / 5 = 120 kmph . answer : a"
Answer: a
Problem: from below option 22 is divisible by which one ?
Options: a ) a ) 3 , b ) b ) 4 , c ) c ) 11 , d ) d ) 9 , e ) e ) 7
Rationale: "22 / 11 = 2 c"
Answer: c
Problem: by approximately what percent is x greater than 1 / 2 if ( 1 / 2 ) ( x ) = 1 ?
Options: a ) 732 % , b ) 560 % , c ) 641 % , d ) 370 % , e ) 300 %
Rationale: "what percent is x greater than 1 / 2 if ( 1 / 2 ) ( x ) = 1 ? = > x = 2 % change = [ ( 2 - 1 / 2 ) / ( 1 / 2 ) ] * 100 = ( 4 - 1 ) * 100 = 300 % approx ans , e"
Answer: e
Problem: set x consists of all two - digit primes and set y consists of all positive multiples of 6 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 91
Rationale: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 6 , 12 , 18 , . . . . . . . . . . . . . . . , 84 , 90 , 96 } combining two sets , say set z set z = { 6 , 11 , 12 , 13 , 17 , 18 , . . . . . . . . . . . . . . . . . . . , 83 , 84 , 89 , 90 , 96,97 } range = max value - min value range ( z ) = 97 - 6 = 91 oa e is the answer ."
Answer: e
Problem: if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 23 , 30 , 22 , 26 , 19 , 33 and 35 ?
Options: a ) 33 , b ) 28 , c ) 22.5 , d ) 24 , e ) 23
Rationale: "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 23 , 30 , 22 , 26 , 19 , 33 and 35 19 , 22 , 23 , 26 , 30 , 33 , 35 , 42 . . . numbers less than median are 19 , 22 , 23 , 26 . . the median of these numbers = center of 22 and 23 = 22.5 c"
Answer: c
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 800 * ( 25 / 100 ) = 200 - - - - 5 ? - - - - 1 = > rs . 40"
Answer: a
Problem: 37 . if the cost price of 15 tables be equal to the selling price of 20 tables , the loss per cent is ?
Options: a ) 20 % , b ) 30 % , c ) 25 % , d ) 37.5 % , e ) 38 %
Rationale: let c . p . of each table = re . 1 c . p . of 20 tables = rs . 20 s . p . of 20 table = c . p . of 15 tables = rs . 15 loss = ( 5 / 20 ) x 100 % = 25 % answer : c
Answer: c
Problem: the number 46 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 10 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 46 : 1 , 4 , 9 , 16 , 25 , 36 . now , 46 should be the sum of 3 of those 8 numbers . also to simplify a little bit trial and error , we can notice that as 46 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 46 equals to 1 + 9 + 36 = 1 ^ 2 + 3 ^ 2 + 6 ^ 2 = 46 - - > 1 + 3 + 6 = 10 . answer : d ."
Answer: d
Problem: in a certain circle there are 9 points . what is the number of the triangles connecting 4 points of the 9 points ?
Options: a ) 80
b ) 96
c ) 108
d ) 126
e ) 132
Rationale: imo : d here we have to select 4 points out of 9 points . order is not important so the answer will be 9 c 4 = 126 answer d
Answer: d
Problem: find the amount on rs . 5000 in 2 years , the rate of interest being 5 % per first year and 6 % for the second year ?
Options: a ) 3377 , b ) 2678 , c ) 5565 , d ) 1976 , e ) 1671
Rationale: "5000 * 105 / 100 * 106 / 100 = > 5565 answer : c"
Answer: c
Problem: how many trailing zeroes does 49 ! + 50 ! have ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 22
Rationale: "49 ! + 50 ! = 51 * 49 ! no of trailing 0 ' s = no of 5 * 2 no of 2 ' s = 49 / 2 + 49 / 4 + 49 / 8 + 49 / 16 + 49 / 32 = d no of 5 ' s = 49 / 5 + 49 / 25 = 10 = p now since p < d no of trailing 0 ' s = 10 answer : b"
Answer: b
Problem: a club wants to mix 30 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 30 * 8 + 5 * w ) / ( 30 + w ) = > 180 + 6 w = 240 + 5 w = > w = 60 answer d"
Answer: d
Problem: the sum of the ages of 5 children born at the intervals of 3 years each is 70 years . what is the age of the youngest child ?
Options: a ) 2 years , b ) 4 years , c ) 6 years , d ) 8 years , e ) 10 years
Rationale: "let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 70 5 x = 40 = > x = 8 . age of youngest child = x = 8 years . answer : d"
Answer: d
Problem: rs . 1070 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) rs . 190 , b ) rs . 260 , c ) rs . 493 , d ) rs . 393 , e ) rs . 593
Rationale: "a + b + c = 1070 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1070 = rs . 493 answer : c"
Answer: c
Problem: nancy obtained 66 , 75 , 52 , 68 and 89 marks ( out of 100 ) in american literature , history , home economics , physical education and art . calculate her average marks ?
Options: a ) 50 , b ) 80 , c ) 70 , d ) 60 , e ) 71
Rationale: explanation : average = ( 66 + 75 + 52 + 68 + 89 ) / 5 = 70 . answer : c ) 70
Answer: c
Problem: the difference between the local value and the face value of 7 in the numerical 32675149 is
Options: a ) 75142 , b ) 64851 , c ) 5149 , d ) 69993 , e ) none of them
Rationale: "= ( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 answer is d"
Answer: d
Problem: the average of numbers 0.64206 , 0.64207 , 0.64208 and 0.64209 is ?
Options: a ) 0.64202 , b ) 0.64204 , c ) 0.642022 , d ) 0.642075 , e ) none
Rationale: "answer average = ( 0.64206 + 0.64207 + 0.64208 + 0.64209 ) / 4 = 2.5683 / 4 = 0.642075 correct option : d"
Answer: d
Problem: a textile manufacturing firm employees 80 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 80 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 4375 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 79 / 80 ) â ˆ ’ 150000 ã — ( 79 / 80 ) â ˆ ’ 75000 . = > rs 2 , 70,625 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 70,625 = > rs . 4,375 answer : d"
Answer: d
Problem: a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 12 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 12 = 1 km . the time it takes the hiker to complete this distance is 1 / 4 hours = 15 minutes the cyclist needs to wait 15 - 5 = 10 minutes the answer is a ."
Answer: a
Problem: a milk man has 30 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 25 % , c ) 33.33 % , d ) 35 % , e ) none of these
Rationale: explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 30 liters of milk . therefore , profit percentage = 35 % . answer : d
Answer: d
Problem: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 180 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 900 , e ) 840
Rationale: "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 180 geese survived the first year : 1 / 5 * ( total ) = 180 - - > ( total ) = 900 . answer : d ."
Answer: d
Problem: 20 litres of mixture of acid and water contain 10 % water . how much water should be added so that percentage of water becomes 20 % in this mixture ?
Options: a ) 2 l , b ) 3 l , c ) 2.5 l , d ) 4 l , e ) 5 l
Rationale: total mixture = 20 ltr water contain = 10 % of 20 ltr = > 2 ltr water it means 18 ltr is acid in that mixture we have to make 20 % water so . . 20 % of 20 = 4 ltr water must be there in the new mixture we have already 2 ltr water so we have to add 2 ltr more answer : a
Answer: a
Problem: what will be the remainder when 8 - 3 + 3 ^ 5 + 2 ^ 10 is divided by 4 ?
Options: a ) 12 , b ) 3 , c ) 16 , d ) 0 , e ) 9
Rationale: "the multiplication ( e . g . 2 ^ 10 ) is done first and then the sum ( e . g . 15 + 20 ) and subtraction ( e . g . 8 - 3 ) , and after all this expression it should be divided by 4 and the answer is 0 , option d ."
Answer: d
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 64 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 5 , b ) 8 : 3 , c ) 8 : 4 , d ) 4 : 8 , e ) 4 : 1
Rationale: let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 64 : √ 9 = 8 : 3 answer : b
Answer: b
Problem: a trader bought a car at 15 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 119 , b ) 110 , c ) 112 , d ) 113 , e ) 115
Rationale: "original price = 100 cp = 85 s = 85 * ( 140 / 100 ) = 119 100 - 119 = 19 % answer : a"
Answer: a
Problem: the ratio between the present ages of a and b is 6 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 5 : 4 , b ) 3 : 0 , c ) 5 : 1 , d ) 3 : 2 , e ) 3 : 7
Rationale: "let the present ages of a and b be 6 x and 3 x years respectively . then , ( 6 x - 4 ) / ( 3 x + 4 ) = 1 / 1 3 x = 8 = > x = 2.67 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 20 : 4 = 5 : 1 . answer : c"
Answer: c
Problem: if the height of a cone is increased by 100 % then its volume is increased by ?
Options: a ) 200 % , b ) 300 % , c ) 100 % , d ) 500 % , e ) 350 %
Rationale: "height of = > 100 % so increased by 100 % answer c"
Answer: c
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 225 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) 1000 , b ) 1500 , c ) 2778 , d ) 2788 , e ) 2991
Rationale: "90 % 105 % - - - - - - - - 15 % - - - - 225 100 % - - - - ? = > rs . 1500 answer : b"
Answer: b
Problem: in what time will a train 60 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.8 sec , c ) 7.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 60 / 40 = 1.5 sec . answer : e"
Answer: e
Problem: how much is 50 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 0 , b ) 67 , c ) 88 , d ) 12 , e ) 66
Rationale: "( 50 / 100 ) * 40 – ( 4 / 5 ) * 25 = 0 answer : a"
Answer: a
Problem: a certain telescope increases the visual range at a particular location from 80 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 87.5 %
Rationale: "original visual range = 80 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 80 ) / 80 * 100 % = 7 / 8 * 100 % = 87.5 % answer e"
Answer: e
Problem: 34 . the side surface of a cylinder is rolled with a rectangle . if the height of a cylinder is 16 feet and the perimeter of the circular base . is 12 feet , what is the diagonal of the rectangle ?
Options: a ) 16
b ) 20
c ) 18
d ) 22
e ) 21
Rationale: think of an aluminum can can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the hypothenuse , 20 . ( correct answer b )
Answer: b
Problem: if ( x + yi ) / i = ( 7 + 9 i ) , where x and y are real , what is the value of ( x + yi ) ( x - yi ) ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: ( x + yi ) / i = ( 7 + 9 i ) ( x + yi ) = i ( 7 + 9 i ) = - 9 + 7 i ( x + yi ) ( x - yi ) = ( - 9 + 7 i ) ( - 9 - 7 i ) = 81 + 49 = 130 correct answer is c 0130
Answer: c
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 240 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 21.00 sec , e ) 72.0 sec
Rationale: "d = 110 + 240 = 350 m s = 60 * 5 / 18 = 50 / 3 t = 350 * 3 / 50 = 21.00 sec answer : d"
Answer: d
Problem: convert 250 inches into centimeter ?
Options: a ) 635 cm , b ) 620 cm , c ) 650 cm , d ) 610 cm , e ) 654 cm
Rationale: "1 inch = 2.54 cm 250 inches = 250 * 2.54 = 635 cm answer is a"
Answer: a
Problem: it takes 40 identical printing presses 12 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: "40 printing presses can do 1 / 12 of the job each hour . 30 printing presses can do 3 / 4 * 1 / 12 = 1 / 16 of the job each hour . the answer is c ."
Answer: c
Problem: a certain company reported that the revenue on sales increased 60 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 13 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 160 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 160 ) / 160 = 20 / 160 = 13 % answer : e ."
Answer: e
Problem: if the price of a book is first decreased by 25 % and then increased by 20 % , then the net change in the price will be :
Options: a ) 10 , b ) 388 , c ) 37 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . new final price = 120 % of ( 75 % of rs . 100 ) = rs . ( 120 / 100 * 75 / 100 * 100 ) = rs . 90 . decrease = 10 % answer : a ) 10"
Answer: a
Problem: p runs 20 % faster than q so p gives q a 300 meter head start . if the race ends in a tie , how far ( in meters ) did p run in the race ?
Options: a ) 1500 , b ) 1600 , c ) 1700 , d ) 1800 , e ) 1900
Rationale: "let d be the race distance that p ran . let t be the time it took to complete the race . let v be q ' s speed . t = d / 1.2 v = ( d - 300 ) / v d = 1.2 d - 360 0.2 d = 360 d = 1800 meters . the answer is d ."
Answer: d
Problem: if a certain number is divided by 11 , the quotient , dividend , and divisor , added together , will amount to 71 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 55
Rationale: "let x = the number sought . then x / 11 + x + 11 = 71 and x = 55 . e"
Answer: e
Problem: the population of a town increases 25 % and 30 % respectively in two consecutive years . after the growth the present population of the town is 1950 . then what is the population of the town 2 years ago ?
Options: a ) a ) 800 , b ) b ) 900 , c ) c ) 1000 , d ) d ) 1100 , e ) e ) 1200
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1950 * 100 / 125 * 100 / 130 = 1200 answer : option e"
Answer: e
Problem: the number 0.127 is how much greater than 1 / 8 ?
Options: a ) 1 / 100 , b ) 1 / 1500 , c ) 1 / 2 , d ) 1 / 500 , e ) 1 / 600
Rationale: "explanation : 0.127 expressed as a fraction = 127 / 1000 1 / 8 can also be expressed as ( 1 x 125 ) / ( 8 x 125 ) = 125 / 1000 the difference is 2 / 1000 , which is 1 / 500 answer is d"
Answer: d
Problem: a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 80 percent greater than the wholesale price . if the retailer decreases the retail price by 25 percent this will have the same effect as increasing the wholesale price by what percent ?
Options: a ) 26 , b ) 37.5 , c ) 35 , d ) 44 , e ) 50
Rationale: "answer : c = 35 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 80 % increase makes retail price = 180 . now 25 % decrease - > ( 1 - 25 / 100 ) * 180 = 135 . now compared to the wholesale price of 100 , 35 % increase is what will have the same effect as increasing the wholesale price ."
Answer: c
Problem: a cistern which could be filled in 4 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 55 hrs , d ) 20 / 3 hrs , e ) 11 hrs
Rationale: "1 / 4 - 1 / x = 1 / 10 = > 20 / 3 hrs answer : d"
Answer: d
Problem: let p be a prime number . if n = 7 p , how many divisors does n have ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: two . n = 7 * p , and both 7 and p are prime . so the answer is b .
Answer: b
Problem: in a factory there are 3 types of machine m 1 , m 2 and m which produces 25 % , 35 % and 40 % of the total products respectively . m 1 , m 2 and m 3 produces 2 % , 4 % and 5 % defective products , respectively . what is the percentage of non - defective products ?
Options: a ) 89 % , b ) 97.1 % , c ) 96.1 % , d ) 86.1 % , e ) none of these
Rationale: solution : non - defective products , { [ ( 25 * 0.98 ) + ( 35 * 0.96 ) + ( 40 * 0.95 ) ] / 100 } * 100 = 96.1 % . answer : option c
Answer: c
Problem: if a = - 1 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 + a ^ 6 ) ?
Options: a ) - 14 , b ) - 4 , c ) - 1 , d ) 4 , e ) 14
Rationale: if a = - 1 , then putting values in equation = - [ ( - 1 ) ^ 2 + ( - 1 ) ^ 3 + ( - 1 ^ 4 ) + ( - 1 ^ 5 ) + ( - 1 ^ 6 ) ] = - [ 1 - 1 + 1 - 1 + 1 ] = - 1 answer = c = - 1
Answer: c
Problem: 6 animals of a circus has to be placed inside in 6 cages one in each cage . if 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal .
Options: a ) a . 240 , b ) b . 808250 , c ) c . 502450 , d ) d . 784200 , e ) e . 302400
Rationale: ways for cages that are too small = 5 * 4 * 3 * 2 = 120 since we have 2 cages and 2 animal left therefore ways for 2 cages = 2 ! total ways = 120 * 2 ! = 604800 answer a
Answer: a
Problem: a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 30 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 350 m , c ) 260 m , d ) 270 m , e ) none of these
Rationale: "explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 30 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 30 ] = 20 = > x + 250 = 600 = > x = 350 . answer : b"
Answer: b
Problem: in a class of 20 students , 3 students did not borrow any books from the library , 9 students each borrowed 1 book , 4 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 9 * 1 + 4 * 2 = 17 books . the 4 students who borrowed at least three books borrowed 40 - 17 = 23 books . if 3 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 23 - 9 = 14 books . the answer is b ."
Answer: b
Problem: the speed at which a man can row a boat in still water is 6 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 80 meters ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "the speed of the boat downstream = 6 + 3 = 9 km / hr 9 km / hr * 5 / 18 = 2.5 m / s the time taken to cover 80 meters = 80 / 2.5 = 32 seconds . the answer is b ."
Answer: b
Problem: a prison of 10,000 inmates has enough food to feed them all for 50 days . after 10 days some of the inmates leave and the food is now enough for the same period of 50 days as before . how many of them left ?
Options: a ) 3,000 , b ) 2,200 , c ) 2,000 , d ) 1,000 , e ) 200
Rationale: 10,000 - - - 50 10,000 - - - 40 x - - - 50 x * 50 = 10,000 * 40 x = 8,000 10,000 - - - - - - - - 2,000 answer = c
Answer: c
Problem: a retailer buys a radio for rs 225 . his overhead expenses are rs 15 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 10 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) none of these
Rationale: "explanation : cost price = ( 225 + 15 ) = 240 sell price = 300 gain = ( 60 / 240 ) * 100 = 25 % . answer : c"
Answer: c
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 52.5 miles ahead of joe ?
Options: a ) 15 , b ) 240 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 52.5 miles . teena can cover 7.5 miles in 30 mins teena will cover 52.5 miles in 210 mins so answer 30 + 210 = 240 mins . ( answer b )"
Answer: b
Problem: on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction r of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is r = 2 / 14 = 1 / 7 . answer : e
Answer: e
Problem: fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 5 kg of fresh grapes ?
Options: a ) 2 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 10 kg , e ) 0.625
Rationale: "the weight of non - water in 5 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 5 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 0.625 answer : e ."
Answer: e
Problem: steve traveled the first 2 hours of his journey at 50 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 68 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "average speed = total distance / total time = ( 50 * 2 + 80 * 3 ) / ( 2 + 3 ) = 68 ans : a"
Answer: a
Problem: in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 5 % , c ) 16 % , d ) 20 % , e ) 25 %
Rationale: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 25 % of democrats ( 40 * 0.25 = 10 ) voted for candidate x , means that out of total of 100 voters ; 58 ( 48 + 10 ) voters voted for candidate x and 42 voted for candidate y . thus we can infer that candidate x is expected to win the election by 16 ( 58 - 42 ) votes . therefore candidate x is expected to win the election by ( 16 / 100 ) votes which is equivalent to 16 % . i think the answer is c ."
Answer: c
Problem: the simple interest on a certain sum of money at the rate of 5 % p . a . for 8 years is rs . 840 . at what rate of interest the same amount of interest can be received on the same sum after 5 years ?
Options: a ) 6 % , b ) 8 % , c ) 9 % , d ) 10 % , e ) none
Rationale: "solution s . i . = rs . 840 , r = 5 % , t = 8 years . principal = rs . ( 800 x 840 / 5 x 8 ) = rs . 2100 . now , p = rs . 2100 , s . i . = rs . 840 , t = 5 years . ∴ rate = ( 100 x 840 / 2100 x 5 ) = 8 % . answer b"
Answer: b
Problem: what is the rate percent when the simple interest on rs . 1200 amount to rs . 400 in 4 years ?
Options: a ) 8.33 % , b ) 6 % , c ) 2 % , d ) 95 % , e ) 1 %
Rationale: "interest for 4 yrs = 400 interest for 1 yr = 100 interest rate = 100 / 1200 x 100 = 8.33 % answer : a"
Answer: a
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is ?
Options: a ) 24 kg , b ) 62 kg , c ) 34 kg , d ) 31 kg , e ) 37 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 * 3 ) = 135 - - - ( i ) a + b = ( 40 * 2 ) = 80 - - - ( ii ) b + c = ( 43 * 2 ) = 86 - - - ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 - - - ( iv ) subtracting ( i ) from ( iv ) , we get : b = 31 b ' s weight = 31 kg . answer : d"
Answer: d
Problem: what is the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 83 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "to find : the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 87 let ' s reduce the clutter and simplify the product ( 7 ^ 83 ) ( 3 ^ 82 ) ( 1 ^ 87 ) 7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4 th power so 7 ^ 5 has the same last digit as 7 ^ 1 , 7 ^ 9 , 7 ^ 13 thus , 7 ^ 83 has the same last digit as 7 ^ 3 , 7 ^ 7 , 7 ^ 11 i . e . 3 3 has a cyclicity of 4 : exactly the same routine as above thus , 3 ^ 82 has the same last digit as 3 ^ 2 , 3 ^ 6 , 3 ^ 10 i . e . 9 any power of 1 will result in 1 as the last digit so , product of our last digits = 3 x 9 x 1 = 27 . . . . last digit is 5 correct option : b"
Answer: b
Problem: 400 students took a mock exam in delhi , 60 % of the boys and 80 % of the girls cleared the cut off in the examination . if the total percentage of students qualifying is 65 % , how many girls appeared in the examination ?
Options: a ) 50 , b ) 100 , c ) 120 , d ) 140 , e ) 180
Rationale: 60 % * x + 80 % * ( 400 - x ) = 65 % * 400 ans = 100 answer : b
Answer: b
Problem: what is the greater of the two numbers whose product is 2688 , given that the sum of the two numbers exceeds their difference by 64 ?
Options: a ) a ) 84 , b ) b ) 104 , c ) c ) 110 , d ) d ) 72 , e ) of these
Rationale: "let the greater and the smaller number be g and s respectively . gs = 2560 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2688 / s = 84 . answer : a"
Answer: a
Problem: the proportion of copper and zinc in the brass is 3 : 7 . how much zinc will there be in 100 kg of brass ?
Options: a ) 70 , b ) 50 , c ) 40 , d ) 270 , e ) 170
Rationale: "7 / 10 * 100 = 70 answer : a"
Answer: a
Problem: a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days q will the work get over ?
Options: a ) q = 60 , b ) q = 70 , c ) q = 75 , d ) 80 , e ) 100
Rationale: we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )
Answer: c
Problem: find the value of c from ( 8 ) ^ 3 x 9 ^ 3 ã · 679 = c .
Options: a ) 249.7 , b ) 529.7 , c ) 549.7 , d ) 594.7 , e ) 119.7
Rationale: given exp . = ( 8 ) ^ 3 x 9 ^ 3 ã · 679 = c = 512 x 729 ã · 679 = 549.7 c
Answer: c
Problem: a man has $ 10,000 to invest . he invests $ 4000 at 5 % and $ 3500 at 4 % . in order to have a yearly income of $ 500 , he must invest the remainder at
Options: a ) 6 % , b ) 6.1 % , c ) 6.2 % , d ) 6.3 % , e ) 6.4 %
Rationale: income from $ 4000 at 5 % in one year = $ 4000 of 5 % . = $ 4000 × 5 / 100 . = $ 4000 × 0.05 . = $ 200 . income from $ 3500 at 4 % in one year = $ 3500 of 4 % . = $ 3500 × 4 / 100 . = $ 3500 × 0.04 . = $ 140 . total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340 . remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340 . = $ 160 . total invested amount = $ 4000 + $ 3500 = $ 7500 . remaining invest amount = $ 10000 - $ 7500 = $ 2500 . we know that , interest = principal × rate × time interest = $ 160 , principal = $ 2500 , rate = r [ we need to find the value of r ] , time = 1 year . 160 = 2500 × r × 1 . 160 = 2500 r 160 / 2500 = 2500 r / 2500 [ divide both sides by 2500 ] 0.064 = r r = 0.064 change it to a percent by moving the decimal to the right two places r = 6.4 % therefore , he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year . the answer is ( e )
Answer: e
Problem: a train speeds past a pole in 11 seconds and a platform 120 m long in 22 seconds . its length is ?
Options: a ) 128 , b ) 177 , c ) 199 , d ) 120 , e ) 150
Rationale: let the length of the train be x meters and its speed be y m / sec . they , x / y = 11 = > y = x / 11 x + 120 / 22 = x / 11 x = 120 m . answer : d
Answer: d
Problem: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 180 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 31 , b ) 33 , c ) 55 , d ) 77 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 180 = > . 1 x + 3 / 4 x = 180 = > x = 211 211 - 180 = pure gala = 31 . a"
Answer: a
Problem: the banker â € ™ s gain on a sum due 3 years hence at 12 % per annum is rs . 90 . the banker â € ™ s discount is
Options: a ) rs . 340 , b ) rs . 840 , c ) rs . 1020 , d ) rs . 760 , e ) none
Rationale: "solution t . d = ( b . g x 100 / r x t ) = rs . ( 90 x 100 / 12 x 3 ) = rs . 250 . b . d = rs ( 250 + 90 ) = rs . 340 . answer a"
Answer: a
Problem: in the quadratic equation x 2 - bx + 20 = 0 , if the product of two roots is 20 , what is the sum of the two roots ?
Options: a ) 20 , b ) 12 , c ) 16 , d ) 14 , e ) 18
Rationale: explanation : the sum of the roots of the quadratic equation ax 2 + ax + c = 0 are ( - b / a ) and the product of the roots are ( c / a ) . thus , in the equation x 2 - ax + 20 = 0 , where a = 1 , b = - a and c = 20 . we get , product of the roots = 20 sum of the roots = - ( - 12 ) / 1 = 12 answer : b
Answer: b
Problem: a carpenter worked alone for 1 day on a job that would take him 7 more days to finish . he and another carpenter completed the job in 4 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 16 , b ) 7 , c ) 9 , d ) 14 , e ) 24
Rationale: "a carpenter worked only 1 day on something that takes him 7 more days . means ; carpenter finishes his work in 8 days . let his buddy finish the same task in x days . respective rates per day : 1 / 8 and 1 / x to complete 1 work : first guy worked for 5 days @ rate = 1 / 8 per day . second one worked for 4 days @ rate = 1 / x per day expression : days * rate = work 5 * 1 / 8 + 4 * 1 / x = 1 5 x + 32 = 8 x 2 x = 32 x = 16 days . ans : a"
Answer: a
Problem: in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 55 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 29 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 55 % means total women in company 45 % ( assume total people in company 100 % ) no of men employees attended picnic = 55 x ( 20 / 100 ) = 11 no of women employees attend picnic = 45 x ( 40 / 100 ) = 18 total percentage of employees attend the picnic = 11 + 18 = 29 % answer : a"
Answer: a
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 7 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 18 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "you know that fox jeans costs $ 15 , and pony jeans costs $ 18 , you also know that 3 pairs of fox jeans and 2 pairs of pony jeans were purchased . so 3 ( 15 ) = 45 - fox 2 ( 18 ) = 36 - pony the total discount discount is $ 3 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 7 or 45 * 18 - 45 * x + 36 * x = 7 * 100 or 9 x = - 7 * 100 + 45 * 18 x = 110 / 9 = 12.2 % e"
Answer: e
Problem: how many of the positive factors of 42 are not factors of 56 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 42 - 1 , 2,3 , 6,7 , 14,42 factors of 56 - 1,2 , 4,7 , 8,14 , 28,56 comparing both , we have three factors of 42 which are not factors of 56 - 3 , 6,42 . the answer is 3 . pls check your options again - d $ e are same . answer : c"
Answer: c
Problem: if taxi fares were $ 10.00 for the first 1 / 5 mile and $ 1.00 for each 1 / 5 mile there after , then the taxi fare for a 10 - mile ride was
Options: a ) $ 55.10 , b ) $ 59.20 , c ) $ 59.40 , d ) $ 59.00 , e ) $ 55.00
Rationale: "in 10 miles , initial 1 / 5 mile charge is $ 10 rest of the distance = 10 - ( 1 / 5 ) = 49 / 5 rest of the distance charge = 49 ( 1.00 ) = $ 49.00 ( as the charge is 1.00 for every 1 / 5 mile ) = > total charge for 4 miles = 10 + 49.00 = 59.00 answer is d"
Answer: d
Problem: two cubes of tire sides ratio 2 : 3 . find its cube volumes ratio ?
Options: a ) 2 : 27
b ) 3 : 27
c ) 1 : 27
d ) 8 : 27
e ) 5 : 27
Rationale: a ( power 3 ) : b ( power 3 ) = 2 ( power 3 ) : 3 ( power 3 ) = 8 : 27 answer is d .
Answer: d
Problem: the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 7000 , brokerage being 1 / 4 % , is :
Options: a ) 96.97 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 7000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 7000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 97.22 . = market value of rs . 100 stock = rs . 97.22 - re . 0.25 . = market value of rs . 100 stock = rs . 96.97 answer : a"
Answer: a
Problem: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 3600 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 450 , c ) s . 600 , d ) s . 800 , e ) s . 850
Rationale: c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 3600 ) = rs . 450 answer = b
Answer: b
Problem: in town x , 60 percent of the population are employed , and 15 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 75 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "total employed people 60 % , out of which 15 are employed males , hence 45 % are employed females . ( employed females ) / ( total employed people ) = 45 / 60 = 3 / 4 = 75 % answer : b ."
Answer: b
Problem: according to a recent student poll , 5 / 6 out of 30 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?
Options: a ) 1 / 14 , b ) 4 / 49 , c ) 2 / 7 , d ) 28 / 29 , e ) 13 / 14
Rationale: 25 students are interested , 5 are not interested prob = 1 - 5 c 2 / 30 c 2 = 1 - ( 5 * 4 / ( 30 * 29 ) ) = 1 - 20 / 580 = 1 - 1 / 29 = 28 / 29 answer : d
Answer: d
Problem: for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 80 ?
Options: a ) 24 , b ) 26 , c ) 20 , d ) 22 , e ) 18
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 80 4 n < 73 n < 18 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 18 ) combining the two - 1.5 < n < 18.25 n = 1 to 18 ( 18 integers ) and n = - 1 and 0 so 20 integers . c is the answer"
Answer: c
Problem: three cubes of metal whose edges are 5 , 12 and 15 cm respectively , are melted and one new cube is made . find the edge of the new cube ?
Options: a ) 28 , b ) 77 , c ) 17.3 , d ) 18 , e ) 99
Rationale: "53 + 123 + 153 = a 3 = > a = 17.3 answer : c"
Answer: c
Problem: a rectangular pig farm has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 1250 square feet , what is the total length of the fence , in feet ?
Options: a ) 25
b ) 50
c ) 100
d ) 150
e ) 200
Rationale: two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 1250 ie x ^ 2 = 625 ie x = 25 l = 50 w = 25 total length of fence = 2 * 25 + 50 = 100 my answer is c
Answer: d
Problem: the ratio of pens to pencils is 5 to 6 . there are 6 more pencils than pens . how many pencils are there ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48
Rationale: "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 6 x = 6 the number of pencils is 36 . the answer is b ."
Answer: b
Problem: there is a clock which shows false timing ie it shows 10 minutes less for each 1 hour . . . . if the clock shows 12 noon now how many minutes will be lost when it shows 3 pm ?
Options: a ) 16 minutes , b ) 26 minutes , c ) 36 minutes , d ) 46 minutes , e ) 56 minutes
Rationale: for 1 hour , 10 minutes is slower , then for 06 miuntes - 1 minutes is slower 30 minutes - 5 minutes actual time false time 12 12 01 pm 12.50 pm ( 10 minutes slower ) 02 pm 01.40 pm ( 12.50 + 60 min - 10 minutes slower ) 03 pm 02.30 pm ( 01.40 + 60 min - 10 minutes slower ) 03.36 pm 03.00 pm ( 02.30 + 36 min - 6 minutes slower ) so , 36 minutes will be lost when it is showing 3.00 pm . and the actual time is 3.36 pm answer : c
Answer: c
Problem: in a box of 7 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 2 , b ) 1 / 5 , c ) 2 / 3 , d ) 2 / 7 , e ) 1 / 7
Rationale: "first , there are 5 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 7 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 5 c 3 / 7 c 3 = 10 / 35 = 2 / 7 answer is d"
Answer: d
Problem: the mean of 50 observations was 36 . it was found later that an observation 90 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 37.3 , b ) 36.1 , c ) 36.5 , d ) 36.9 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 90 - 23 ) = 1867 . correct mean = 1825 / 50 = 37.3 answer : a"
Answer: a
Problem: how many kilograms of pure water is to be added to 100 kilograms of a 30 % saline solution to make it a 10 % saline solution .
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: let x be the weights , in kilograms , of pure water to be added . let y be the weight , in kilograms , of the 10 % solution . hence x + 100 = y x = 200 kilograms . answer b
Answer: b
Problem: there is a escalator and 2 persons move down it . a takes 50 steps and b takes 75 steps while the escalator is moving down . given that the time taken by a to take 1 step is equal to time taken by b to take 3 steps . find the no . of steps in the escalator while it is staionary ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: if a takes 1 step in one second , then b takes 3 steps in one second . if a takes t 1 seconds to take 50 steps , then b takes 150 steps in t 1 seconds . for b , to take 150 steps he requires t 1 seconds , then to take 75 steps he requires t 1 / 2 seconds . now use relative velocity l - v * t 1 = 50 ( for first person ) l - v * t 1 / 2 = 75 ( for second person ) s ( escalator w . r . t ground ) - s ( person w . r . t escalator ) = s 1 ( person w . r . t ground ) s , s , s 1 are the steps now put the v * t 1 from 1 into the second equation and u get l - ( l - 50 ) / 2 = 75 l + 50 = 150 l = 100 answer : e
Answer: e
Problem: at what price must an article costing rs . 57 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 69.5 , c ) 62.3 , d ) 62.1 , e ) 75
Rationale: "cp = 57 sp = 57 * ( 125 / 100 ) = 71.25 mp * ( 95 / 100 ) = 71.25 mp = 75 answer : e"
Answer: e
Problem: if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.20 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 2.80
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.2 ) = $ 2.8 ( as the charge is 0.2 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 2.8 = 3.8 answer is c ."
Answer: c
Problem: if 3 ^ x * 4 ^ y = 59,049 and x – y = 10 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 59,049 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 10 and y = 0 , then x = 10 . the answer is a ."
Answer: a
Problem: a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 18 seconds . what is the length of the train in meters ?
Options: a ) 180 meters , b ) 1111 meters , c ) 1777 meters , d ) 1822 meters , e ) none of these
Rationale: "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 18 seconds distance = speed * time 36000 * 18 / 3600 = 180 meters . a is the answer ."
Answer: a
Problem: from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 11 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 11 x = 45 - - > 10 / 9 * x = 45 - - > x = 45 * 9 / 10 = 1500 / 37 = ~ 41 . answer : d ."
Answer: d
Problem: when you multiply a number by 4 and then subtract 3 , the result is the same as if you first subtracted 7 from the same number and then multiplied by 9 . what is the number ?
Options: a ) a ) 23 , b ) b ) 13 , c ) c ) 19 , d ) d ) 12 , e ) e ) 10
Rationale: let x equal the number and then change the words into an equation and solve for x : 4 x – 3 = 9 ( x – 7 ) 4 x – 3 = 9 x – 63 60 = 5 x 12 = x correct answer d ) 12
Answer: d
Problem: a man can row his boat with the stream at 25 km / h and against the stream in 13 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 2 kmph , c ) 6 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 25 us = 13 s = ? s = ( 25 - 13 ) / 2 = 6 kmph answer : c"
Answer: c
Problem: an alloy of zinc and copper contains the metals in the ratio 5 : 3 . the quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is :
Options: a ) 2 , b ) 9 , c ) 8 , d ) 7 , e ) 4
Rationale: explanation : in sixteen kg of alloy 10 kg of zinc and 6 kg copper is present to make the ratio 3 : 1 we must add 8 kg of zinc to make it 18 kg of zinc and 6 kg copper so answer is 8 . answer : c
Answer: c
Problem: what is the cp of rs 100 stock at 5 discount , with 1 / 5 % brokerage ?
Options: a ) 96.9 , b ) 96.3 , c ) 95.2 , d ) 96.7 , e ) 96.21
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 5 + 1 / 5 95.2 thus the cp is rs 95.2 . answer : c"
Answer: c