regisss/math_qa huggingface dataset:
Problem: find the area of a right - angled triangle whose base is 12 cm and hypotenuse is 13 cm .
Options: a ) 15
b ) 30
c ) 18
d ) 12
e ) 25
Rationale: sol . height of the triangle = [ ( 13 ) 2 - ( 12 ) 2 ] ( 1 / 2 ) cm = ( 25 ) ( 1 / 2 ) cm = 5 cm . its area = ( 1 / 2 ) * base * height = ( ( 1 / 2 ) * 12 * 5 ) cm ^ 2 = 30 cm ^ 2 . ans : b
Answer: b
Problem: a motorist travels to a place 150 km away at an average speed of 50 km / hr and returns at 30 km / hr . his average speed for the whole journey in km / hr is ?
Options: a ) 37.9 , b ) 37.53 , c ) 37.5 , d ) 37.1 , e ) 37.4
Rationale: explanation : average speed = ( 2 xy ) / ( x + y ) km / hr = ( 2 * 50 * 30 ) / ( 50 + 30 ) km / hr . 37.5 km / hr . answer : c
Answer: c
Problem: 4685 * 999
Options: a ) 4680250 , b ) 4685850 , c ) 4680315 , d ) 4685975 , e ) none of these
Rationale: "explanation : 4685 * ( 1000 - 1 ) = 4685000 - 4685 = 4680315 option c"
Answer: c
Problem: 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 5 like all . how many people like apple ?
Options: a ) 48 , b ) 46 , c ) 54 , d ) 58 , e ) 62
Rationale: "orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 5 40 + 10 + 5 - 7 = 48 like apple answer : a"
Answer: a
Problem: a textile manufacturing firm employees 56 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 56 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 ) 6250 , c ) 10000 , d ) 5000 , 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 — ( 55 / 56 ) â ˆ ’ 150000 ã — ( 55 / 56 ) â ˆ ’ 75000 . = > rs 2 , 68,750 decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 68,750 = > rs . 6,250 answer : b"
Answer: b
Problem: a factory produces 5505 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 4436 toys , b ) 5487 toys , c ) 1101 toys , d ) 2354 toys , e ) 1375 toys
Rationale: to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 5505 / 5 = 1101 toys correct answer c
Answer: c
Problem: 8 men , working 8 hours a day can complete a work in 24 days . how many hours a day must 12 men work to complete the same work in 16 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the number of hours required to complete the work is 8 * 8 * 24 = 1536 12 × 16 × ( x ) = 1536 x = 8 the answer is c ."
Answer: c
Problem: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 9 , 1 ) , ( 1 , 1 ) , ( 1 , - 8 ) and ( - 9 , - 8 ) ?
Options: a ) 72 , b ) 180 , c ) 70 , d ) 90 , e ) 140
Rationale: "length of side 1 = 9 + 1 = 10 length of side 2 = 8 + 1 = 9 area of rectangle = 10 * 9 = 90 d is the answer"
Answer: d
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 1 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 14 / 19 , e ) 1 / 2
Rationale: "# of basic stereos was 1 / 3 of total and # of deluxe stereos was 2 / 3 of total , let ' s assume total = 15 , then basic = 5 and deluxe = 10 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 5 * 1 = 5 and total time for deluxe would be 10 * 7 / 5 = 14 - - > total time for both of them would be 5 + 14 = 19 - - > deluxe / total = 14 / 19 . answer : d ."
Answer: d
Problem: a train is 460 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 76 seconds , b ) 18 seconds , c ) 40 seconds , d ) 48 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 460 + 140 = 600 meter time = distance / speed = 600 * ( 2 / 25 ) = 48 seconds answer : d"
Answer: d
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 6 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 135 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 6 ) * 270 = 45 gallons total paint used = 135 gallons . option b"
Answer: b
Problem: a train 100 m long crosses a platform 180 m long in 14 sec ; find the speed of the train ?
Options: a ) 72 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 59 kmph
Rationale: "d = 100 + 180 = 280 t = 14 s = 280 / 14 * 18 / 5 = 72 kmph answer : a"
Answer: a
Problem: a meal cost $ 48.75 adn there was no tax . if the tip was more than 5 pc but less than 20 pc of the price , then the total amount paid should be :
Options: a ) 60 - 65 , b ) 55 - 58 , c ) 51 - 59 , d ) 39 - 41 , e ) 38 - 40
Rationale: "5 % ( 48.75 ) = 2.4375 20 % ( 48.75 ) = 9.75 total amount could have been 48.75 + 2.4375 and 48.75 + 9.75 = > could have been between 51.1875 and 58.5 = > approximately between 51 and 59 answer is c ."
Answer: c
Problem: on a map , 1 inch represents 28 miles . how many c inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "c inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c"
Answer: c
Problem: a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many apples f did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .
Rationale: "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons f = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c"
Answer: c
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 1232 cm is ?
Options: a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11
Rationale: "2 * 22 / 7 * 14 * x = 1232 = > x = 14 answer : c"
Answer: c
Problem: what is the volume of an tetrahedron with edge length of 1 ?
Options: a ) 3.11545466
b ) 0.76678113
c ) 0.11785113
d ) 2.11785113
e ) 0.11786667
Rationale: the answer is sqr ( 2 ) / 12 = 0.11785113 the following can be derived using the pythagorean theorem : the height of a face is 3.5 / 2 . the area of any face is 3.5 / 4 . the distance from any corner to the center of a joining face is 1 / 3.5 . the height of the tetrahedron is ( 2 / 3 ) . 5 the area is 1 / 3 * base * height = ( 1 / 3 ) * 3.5 / 4 * ( 2 / 3 ) . 5 = 21 / 2 / 12 . the above cube has sides of length 1 / sqr ( 2 ) . the area formed by the diagonals along four of the faces as shown in the diagram is a tetrahedrom . left over are four pyramids . the base of each pyramid is half of the side of the cube and the height is the height of the cube . thus the area of each pyramid is : 1 / 2 * ( 1 / sqr ( 2 ) ) 2 * 1 / sqr ( 2 ) * 1 / 3 = ( 12 * sqr ( 2 ) ) - 1 the total area of the cube is ( 1 / sqr ( 2 ) ) 3 = ( 2 * sqr ( 2 ) ) - 1 the area of the tetrahedrom is thus ( 2 * sqr ( 2 ) ) - 1 - 4 * ( 12 * sqr ( 2 ) ) - 1 = 3 / ( 6 * sqr ( 2 ) ) - 2 / ( 6 * sqr ( 2 ) ) = 1 / ( 6 * sqr ( 2 ) ) = sqr ( 2 ) / 12 correct answer c
Answer: c
Problem: an exam consists of 2 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 70 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16
Rationale: "if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 1 / 16 . a"
Answer: a
Problem: the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 28 years . find the average age of the women ?
Options: a ) 87 , b ) 98 , c ) 32 , d ) 28 , e ) 37
Rationale: "20 + 28 + 8 * 2 = 64 / 2 = 32 answer : c"
Answer: c
Problem: a girl was riding her scooter . her father wanted to calculate her speed . he knew that the street was 600 meters from end to end . he saw his daughter make the roundtrip 6 times . it took her 20 minutes to complete those 6 trips . how fast was the girl riding her scooter in kilometers per hour ?
Options: a ) 2 , b ) 2.4 , c ) 1.2 , d ) 2.1 , e ) 2.7
Rationale: the distance of the street was 600 meters . the made the roundtrip 6 times , which would be 2 trips for each roundtrip . multiply 12 times 600 to get the total distance . 600 * 12 = 7200 meters of 7.2 km . the question asked for the speed in km / hour and 20 minutes is one third of an hour . multiply 7200 by 1 / 3 to get approximately 2400 meters . correct answer is b
Answer: b
Problem: the ratio of two quantities is 2 : 3 . if each of the quantities is increased by 6 , what is the ratio of the new quantities ?
Options: a ) 2 : 3 , b ) 6 : 7 , c ) 8 : 9 , d ) 8 : 3 , e ) it can not be determined from the information given
Rationale: "let quantities are 2 x and 3 x ratio of quantities after each is increased by 6 = ( 2 x + 6 ) / ( 3 x + 6 ) for x = 1 , ( 2 x + 6 ) / ( 3 x + 6 ) = 8 / 9 for x = 2 , ( 2 x + 6 ) / ( 3 x + 6 ) = 10 / 12 the value of final expression is dependent on the value of x which ca n ' t be determined as per given information . hence , the answer can not be determined answer : option e"
Answer: e
Problem: a rower whose speed is 2.5 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 0.5 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 2.2 , b ) 2.3 , c ) 2.4 , d ) 2.5 , e ) 2.6
Rationale: time upstream = d / 2 time downstream = d / 3 total time = d / 2 + d / 3 = 5 d / 6 average speed = 2 d / ( 5 d / 6 ) = 2.4 km / hr the answer is c .
Answer: c
Problem: in what ratio should a variety of wheat costing rs . 3 per kg be mixed with another variety of wheat costing rs . 6.25 per kg to obtain a mixture costing rs . 4.50 per kg ?
Options: a ) 8 : 6 , b ) 7 : 6 , c ) 5 : 6 , d ) 7 : 5 , e ) 6 : 7
Rationale: let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 6.25 - 4.50 ) / ( 4.50 - 3 ) = 7 / 6 answer : b
Answer: b
Problem: in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 5,3 ) , ( 8,3 ) , ( 4,5 ) , ( 7,5 ) ?
Options: a ) 21 . , b ) 28 . , c ) 35 . , d ) 49 . , e ) 6 .
Rationale: "delta x will give us the dimension of one side of the parallelogram = 8 - 5 = 3 unit delta y will give us the dimension of the other side of parallelogram = 5 - 3 = 2 unit area of parallelogram = 3 * 2 = 6 answer is e"
Answer: e
Problem: the captain of a cricket team of 11 members is 27 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: let the average age of the whole team be x years . 11 x - ( 27 + 30 ) = 9 ( x - 1 ) 11 x - 9 x = 48 2 x = 48 x = 24 . the average age of the team is 24 years . the answer is d .
Answer: d
Problem: angelina walked 180 meters from her home to the grocery at a constant speed . she then walked 240 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 180 / x . . the speed to gym = 2 x . . so time taken = 240 / 2 x = 120 / x . . its given 180 / x - 120 / x = 40 . . 60 / x = 40 = > 40 x = 60 = > x = 60 / 40 x = 1.5 m / secs . . so grocery to gym = 2 * 1.5 = 3 m / s . . . answer : b"
Answer: b
Problem: i have 150 pieces of cake . there are 50 friends in my house . i would like to give each friend the same amount of cake , how much should i give to each friend ?
Options: a ) 12 , b ) 7 , c ) 9 , d ) 15 , e ) 3
Rationale: 150 / 50 = 3 the answer is e .
Answer: e
Problem: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 4 days more ?
Options: a ) 3022 , b ) 3040 , c ) 3099 , d ) 3088 , e ) 3066
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 4 x * 4 = 760 * 20 x = 3800 760 - - - - - - - 3040 answer : b"
Answer: b
Problem: sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1260 , what is the gain percent ?
Options: a ) 3 % , b ) 5 % , c ) 7 % , d ) 9 % , e ) 11 %
Rationale: "selling price / total cost = 1260 / 1200 = 1.05 the gain percent is 5 % . the answer is b ."
Answer: b
Problem: find the amount on rs . 8000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ?
Options: a ) 5568 , b ) 6369 , c ) 8736 , d ) 5635 , e ) 6734
Rationale: "8000 * 104 / 100 * 105 / 100 = > 8736 answer : c"
Answer: c
Problem: of the 1000 inhabitants of a town , 60 % are males of whom 20 % are literate . if , of all the inhabitants , 25 % are literate , then what percent of the females of the town are literate ?
Options: a ) 22.5 , b ) 27.5 , c ) 32.5 , d ) 37.5 , e ) none
Rationale: sol . number of males = 60 % of 1000 = 600 . number of females = ( 1000 - 600 ) = 400 . number of literates = 25 % of 1000 = 250 . number of literate males = 20 % of 600 = 120 . number of literate females = ( 250 - 120 ) = 130 . ∴ required percentage = ( 130 / 400 x 100 ) % = 32.5 % answer c
Answer: c
Problem: how much water must be added to 68 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 17 litres , c ) 15 litres , d ) 18 litres , e ) none of these
Rationale: "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 68 litres of milk = ( 1 ⁄ 4 × 68 ) litres = 17 litres . answer b"
Answer: b
Problem: i bought two books ; for rs . 600 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 197 , b ) 280 , c ) 189 , d ) 278 , e ) 350
Rationale: "x * ( 85 / 100 ) = ( 600 - x ) 119 / 100 x = 350 answer : e"
Answer: e
Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 , 8 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 2 . answer : c ."
Answer: c
Problem: the largest four digit number which is a multiple of 8 , 10,12 and 15 is :
Options: a ) 9960 , b ) 9950 , c ) 9940 , d ) 9930 , e ) 9920
Rationale: "lcm = 120 9999 / 120 = 83 83 * 120 = 9960 answer : a"
Answer: a
Problem: in how many ways can the integer 84 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2
Rationale: "84 = ( 2 ^ 2 ) * 3 * 7 since 84 is not a perfect square , no of ways = 4 answer d"
Answer: d
Problem: find the value of y from ( 12 ) ^ 3 x 6 ^ 2 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 144
Rationale: "144 e"
Answer: e
Problem: a man buys an article for $ 20 . and sells it for $ 35 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 75 % , e ) 30 %
Rationale: "c . p . = $ 20 s . p . = $ 35 gain = $ 15 gain % = 15 / 20 * 100 = 75 % answer is d"
Answer: d
Problem: a ball dropped from h height and moves 80 % of height each time . total distance covered is
Options: a ) 4 h , b ) 5 h , c ) 7 h , d ) 9 h , e ) 8 h
Rationale: first time distance is h second time 80 h / 100 = 4 h / 5 similarly third time 80 % of 4 h / 5 = h ( 4 ^ 2 ) / ( 5 ^ 2 ) and so on . . . this will lead to infinite terms of geometric progression i . e h + 2 * 4 h / 5 + 2 * 16 h / 25 . . . . . . . . . . . . sum = h + 2 * 4 h / ( 5 ( 1 - 4 / 5 ) ) = 9 h answer : d
Answer: d
Problem: calculate 73196 ÷ ? = 631
Options: a ) 101 , b ) 116 , c ) 119 , d ) 116 , e ) 32
Rationale: "answer let 62976 / x = 631 then x = 62976 / 631 = 116 option : d"
Answer: d
Problem: two trains of equal length , running with the speeds of 60 and 20 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 12.5 , b ) 8.01 , c ) 7.5 , d ) 26 , e ) 22
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 20 = 80 * 5 / 18 t = 2500 / 9 * 18 / 400 = 12.5 sec . answer : a"
Answer: a
Problem: on the number line , the number p is twice as many units from - 2 as - 2 is from 7 . if p is less than – 2 , what is the value of p ?
Options: a ) – 20 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: "distance between - 2 and 7 = 9 since number p is twice as many units from - 2 as - 2 is from 7 , therefore p can be - 20 since , p is less than - 2 , the value of p = - 20 answer a"
Answer: a
Problem: find value for x from below equation ? x + 1 = 4
Options: a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = 4 - 1 2 . simplify both sides : x = 3 d"
Answer: d
Problem: find large number from below question the difference of two numbers is 1325 . on dividing the larger number by the smaller , we get 5 as quotient and the 5 as remainder
Options: a ) 1650 , b ) 1324 , c ) 1245 , d ) 1300 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1325 ) . x + 1325 = 5 x + 5 4 x = 1320 x = 330 large number = 330 + 1320 = 1650 answer : a"
Answer: a
Problem: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 4 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Rationale: "u / i = 4 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 20 : 10 : 2 i . e . u : b = 20 : 2 answer : option d"
Answer: d
Problem: if 11 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 55 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 11 * 10 / 2 = 55 answer : a"
Answer: a
Problem: 0.0005215 / 0.000305 x 6.2 = ?
Options: a ) 10.6 , b ) 11.3 , c ) 12.7 , d ) 13.4 , e ) 14.5
Rationale: "explanation : ? = 0.0005215 / 0.000305 x 6.2 = 10.6 answer : option a"
Answer: a
Problem: the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 25 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 27 % , e ) 79 %
Rationale: "the original output increases by 10 % and then 25 % . total % change = a + b + ab / 100 total % change = 10 + 25 + 10 * 25 / 100 = 37.5 % now , you want to change it to 0 , so , 0 = 37.5 + x + 37.5 x / 100 x = - 37.5 ( 100 ) / 137.5 = 27 % approximately answer is d"
Answer: d
Problem: a and b started a business investing rs . 24,000 and rs 18,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 4 : 3 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 4 , e ) 18 : 4
Rationale: "a : b = 24000 : 18000 = 8 : 6 = 4 : 3 answer : a"
Answer: a
Problem: find 283 / 1983 × 100
Options: a ) 14.29 , b ) 14.21 , c ) 14.22 , d ) 14.27 , e ) 14.23
Rationale: "never start finding common factors . adjust the denominator to 2000 . so we are introducing an error of 17 which is 171983 = 1117171983 = 1117 th of the denominator . 283002000 = 14.15283002000 = 14.15 but this answer is slightly less than actual answer . now 14 . 1511714.15117 = 0.12 approximately . adding 0.12 to 14.25 gives 14.27 . option b is correct ."
Answer: b
Problem: three unbiased coins are tossed . what is the probability of getting at least 2 tails ?
Options: a ) 0.75 , b ) 0.5 , c ) 0.25 , d ) 0.2 , e ) 0.3
Rationale: "explanation : s = { hhh , hht , hth , htt , thh , tht , tth , ttt } e = { htt , tht , tth , ttt } n ( s ) = 8 n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 0.5 answer is b"
Answer: b
Problem: compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 342 grams of compound x ?
Options: a ) 54 , b ) 162 , c ) 250 , d ) 270 , e ) 280
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 342 gms of x have 342 * 10 / 12 = 280 gms of b and 342 - 280 = 62 gms of a . cross check : - a / b = 62 / 280 = 2 / 10 ( as given ) ans e"
Answer: e
Problem: a certain article of clothing was discounted during a special sale to 4 / 5 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 33.33 % , c ) 40 % , d ) 16.66 % , e ) 12.5 %
Rationale: "say the original retail price of the item was $ 200 . the price after the first sale = 4 / 5 * $ 200 = $ 160 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 160 - 100 ) / 150 = 1 / 3 = 40 % . answer : c ."
Answer: c
Problem: income and expenditure of a person are in the ratio 8 : 7 . if the income of the person is rs . 40000 , then find his savings ?
Options: a ) 5000 , b ) 6000 , c ) 7000 , d ) 8000 , e ) 9000
Rationale: "let the income and the expenditure of the person be rs . 8 x and rs . 7 x respectively . income , 8 x = 40000 = > x = 5000 savings = income - expenditure = 8 x - 7 x = x so , savings = rs . 5000 . answer : a"
Answer: a
Problem: workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.50 lacs . how many workers were they ?
Options: a ) 220 , b ) 230 , c ) 500 , d ) 560 , e ) 1000
Rationale: "n * 50 = ( 350000 - 300000 ) = 50000 n = 50000 / 50 = 1000 e"
Answer: e
Problem: how many positive integers less than 60 have a reminder 01 when divided by 4 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "1 also gives the remainder of 1 when divided by 4 . so , there are total of 15 numbers . answer : c ."
Answer: c
Problem: a boat goes 100 km downstream in 10 hours , and 200 km upstream in 25 hours . the speed of the stream is ?
Options: a ) 1 , b ) 22 1 / 7 , c ) 2 , d ) 22 1 / 2 , e ) 3
Rationale: "100 - - - 10 ds = 10 ? - - - - 1 200 - - - - 30 us = 8 ? - - - - - 1 s = ( 10 - 8 ) / 2 = 1 kmph . answer : a"
Answer: a
Problem: if 25 % of x is 30 less than 20 % of 1000 , then x is ?
Options: a ) 188 , b ) 216 , c ) 156 , d ) 680 , e ) 121
Rationale: "25 % of x = x / 4 ; 20 % of 1000 = 20 / 100 * 1000 = 200 given that , x / 4 = 200 - 30 = > x / 4 = 170 = > x = 680 . answer : d"
Answer: d
Problem: mr . bhaskar is on tour and he has rs . 360 for his expenses . if he exceeds his tour by 4 days , he must cut down his daily expenses by rs . 3 . for how many days is mr . bhaskar on tour ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: if his tour is for x days and he is spending rs y per day , then xy = 360 x = 360 / y or y = 360 / x ( x + 4 ) * ( y - 3 ) = 360 or xy + 4 y - 3 x - 12 = 360 or 4 y - 3 x - 12 = 0 4 * 360 / x - 3 x - 12 = 0 solving it , we get x = 20 answer : b
Answer: b
Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability z that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability z = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Problem: a boat having a length 5 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 5 x 3 x 0.01 ) m 3 = 0.15 m 3 . mass of man = volume of water displaced × density of water = ( 0.15 × 1000 ) kg = 150 kg . answer e"
Answer: e
Problem: a batsman in his 15 th inning makes a score of 75 and their by increasing his average by 3 . what is his average after the 15 th inning ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "14 x + 75 = 15 ( x + 3 ) x = 30 + 3 = 33 answer : c"
Answer: c
Problem: a man purchased 3 blankets @ rs . 100 each , 1 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 1050 , b ) 2770 , c ) 1550 , d ) 5102 , e ) 5000
Rationale: "10 * 150 = 1500 3 * 100 + 1 * 150 = 450 1500 – 450 = 1050 answer : a"
Answer: a
Problem: five bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8,10 seconds respectively . in 60 minutes , how many times do they toll together ?
Options: a ) 41 , b ) 10 , c ) 31 , d ) 16 , e ) 17
Rationale: l . c . m of 2 , 4,6 , 8,10 is 240 . i . e after each 2 min they will toll together . so in 60 min they will toll 30 times . as they have initially tolled once , the answer will be 30 + 1 = 31 . answer : c
Answer: c
Problem: a cube of side 4 meter length is cut into small cubes of side 25 cm each . how many such small cubes can be obtained ?
Options: a ) 4069 , b ) 6048 , c ) 1000 , d ) 4096 , e ) 4060
Rationale: "along one edge , the number of small cubes that can be cut = 400 / 25 = 16 along each edge 16 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 16 * 16 * 16 = 4096 answer : d"
Answer: d
Problem: on a certain date , pat invested $ 6,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24,000 , in how many years total will the total value of the investment plus interest increase to $ 48,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Problem: if | y + 7 | = 12 , what is the sum of all the possible values of y ?
Options: a ) - 14 , b ) - 12 , c ) - 8 , d ) 8 , e ) 12
Rationale: there will be two cases y + 7 = 12 or y + 7 = - 12 = > y = 5 or y = - 19 sum of both the values will be - 19 + 5 = - 14 answer : a
Answer: a
Problem: the tax on a commodity is diminished by 15 % and its consumption increased by 10 % . the effect on revenue is ?
Options: a ) 8.5 , b ) 6.5 , c ) 5.5 , d ) 5.6 , e ) 4.4
Rationale: "100 * 100 = 10000 85 * 110 = 9350 - - - - - - - - - - - 10000 - - - - - - - - - - - 650 100 - - - - - - - - - - - ? = > 6.5 % decrease answer : b"
Answer: b
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 25 . what is the value of x ?
Options: a ) 25 , b ) 50 , c ) 75 , d ) 100 , e ) 125
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 25 ( y / 100 ) * x = 25 ( x / 400 ) * x = 25 x ^ 2 = 25 * 400 x = 100 the answer is d ."
Answer: d
Problem: cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 78.2 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 5.75 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80
Rationale: "0.85 * { original price } = $ 78.2 - - > { original price } = $ 92 . { final price } = $ 78.2 * 1.25 = $ 97.75 . the difference = $ 97.75 - $ 92 = $ 5.75 answer : b ."
Answer: b
Problem: evaluate 20 % of 450 + 45 % of 200
Options: a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 180
Rationale: "explanation : = ( 20 / 100 ) * 450 + ( 45 / 100 ) * 200 = 180 option e"
Answer: e
Problem: which greatest possible length can be used to measure exactly 12 meter 34 cm , 8 meter 98 cm and 6 meter 65 cm
Options: a ) 1 cm , b ) 2 cm , c ) 24 cm , d ) 55 cm , e ) 50 cm
Rationale: explanation : convert first all terms into cm . i . e . 1234 cm , 898 cm , 665 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 1 . option a
Answer: a
Problem: working together , printer a and printer b would finish the task in 20 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 4 pages a minute more than printer a ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 340
Rationale: "20 * a + 20 * b = x pages in 20 mins printer a will print = 20 / 60 * x pages = 1 / 3 * x pages thus in 20 mins printer printer b will print x - 1 / 3 * x = 2 / 3 * x pages also it is given that printer b prints 4 more pages per min that printer a . in 20 mins printer b will print 80 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 80 = > x = 240 pages answer : c"
Answer: c
Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 20,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 . the answer is c ."
Answer: c
Problem: if 20 liters of chemical x are added to 80 liters of a mixture that is 30 % chemical x and 70 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 32 % , b ) 35 % , c ) 38 % , d ) 41 % , e ) 44 %
Rationale: "the amount of chemical x in the solution is 20 + 0.3 ( 80 ) = 44 liters . 44 liters / 100 liters = 44 % the answer is e ."
Answer: e
Problem: the present population of a town is 60000 . the population increases annually at 10 % . find the population after 3 years .
Options: a ) 86000 , b ) 79860 , c ) 76300 , d ) 82900 , e ) none of these
Rationale: explanation : solution : the required population is 60000 ( 1 + 10 / 100 ) ^ 3 = 60000 * 110 / 100 * 110 / 100 * 110 / 100 = 79860 answer : b
Answer: b
Problem: sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 4 more than 1 / 4 of the fine and peter paid $ 4 less than 1 / 3 of the fine , leaving pay $ 5 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 30 , b ) $ 25 , c ) $ 35 , d ) $ 40 , e ) $ 45
Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 4 ] + [ ( 1 / 3 ) f – 4 ] + [ ( 1 / 2 ) f – 5 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 5 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 60 12 f = 13 f – 60 – f = – 60 f = 60 well , if the fine cost $ 60 , then sam paid the part not covered by joe or peter . half the fine is $ 30 , and sam paid $ 5 less than this : $ 25 . answer = b"
Answer: b
Problem: the total car population in a chennai is 900 out of which 500 are made by honda . out of every 100 honda cars , 90 are red in color , but only 60 % of the total car population is red . find the % of non - honda cars that are red
Options: a ) 20.5 % , b ) 22.5 % , c ) 21.5 % , d ) 10.5 % , e ) 32.5 %
Rationale: "total honda brand red cars = 90 / 100 * 500 = 450 total red cars = 60 / 100 * 900 = 540 no . of non - honda cars = 900 - 500 = 400 no . of non - honda red cars = 540 - 450 = 90 % of non - honda red cars = 90 / 400 * 100 = 22.5 % answer : b"
Answer: b
Problem: find the least number of 5 digits which is exactly divisible by 12 , 15 and 18 ?
Options: a ) 1080 , b ) 10080 , c ) 10025 , d ) 11080 , e ) 12080
Rationale: lcm = 180 180 ) 10000 ( 55 9900 - - - - - - - - - 100 10000 + 180 - 100 = 10080 answer : b
Answer: b
Problem: the length of a rectangle is 3 times its width . if the width of the rectangle is 5 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 89 square inches , e ) 92 square inches
Rationale: "if the width is 5 in and the length is 3 times the width , then the length is 3 * 5 = 15 in the area is given by 5 * 15 = 75 square inches correct answer b"
Answer: b
Problem: a certain sum amount to $ 1400 in 2 yrs and $ 2000 in 5 years on certain fixed simple interest . in how many yrs would the amount be $ 1640 had it been put at the rate of interest compounded annually ?
Options: a ) 4.5 , b ) 3.5 , c ) 3 , d ) 2 , e ) 1.5
Rationale: we can form equations as following : initial amount = p , total amount after interest = t , interest per year = i t = p + i given t 1 = p + 2 i = 1400 t 2 = p + 5 i = 2000 from this we get , p = 1000 i = 200 $ now we know that simple interest is < compound interest ( ci = si only after 1 st year if ci is compounded annually ) consider simple interest - after 1 st yer it is 200 $ , after 2 nd years it is 400 $ and after 3 rd year it is 600 $ . to get a 240 $ compound interest the duration have to be > 1 year and < 2 years . only option fitting : option e .
Answer: e
Problem: the h . c . f . of two numbers is 15 and their l . c . m . is 620 . if one of the numbers is 375 , then the other is :
Options: a ) 36.6 , b ) 42.8 , c ) 28.4 , d ) 11.6 , e ) 24.8
Rationale: "other number = ( 15 x 620 ) / 375 = 24.8 . answer : e"
Answer: e
Problem: from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn .
Options: a ) 4 / 13 , b ) 1 / 52 , c ) 1 / 4 , d ) 1 / 3 , e ) none of these
Rationale: "explanation : total number of cases = 52 total face cards = 16 [ favourable cases ] so probability = 16 / 52 = 4 / 13 option a"
Answer: a
Problem: what is 92 % of 3 / 5 ?
Options: a ) 0.552 , b ) 69.0 , c ) 0.6845 , d ) 0.6859 , e ) 0.69
Rationale: "92 % * ( 3 / 5 ) = 0.92 * 0.6 = 0.552 answer : a"
Answer: a
Problem: if 9 a - b = 10 b + 80 = - 12 b - 2 a , what is the value of 2 a + 22 b ?
Options: a ) - 4 , b ) - 2 , c ) - 80 , d ) 2 , e ) 4
Rationale: "this implies 9 a - b = 10 b + 80 , 9 a - b = - 12 b - 2 a , 10 b + 80 = - 12 b - 2 a manipulating the second equation gives us 10 b + 80 = - 12 b - 2 a = = > 2 a + 22 b = - 80 answer is c"
Answer: c
Problem: a can do a work in 24 days and b can do it in 8 days . in how many days a and b can do the work ?
Options: a ) 20 days , b ) 10 days , c ) 6 days , d ) 8 days , e ) 7 days
Rationale: "explanation : a ' s 1 day ' s work = 1 / 24 b ' s 1 day ' s work = 1 / 8 they work together = 1 / 24 + 1 / 8 = 6 days answer : option c"
Answer: c
Problem: the difference between the ages of two persons is 10 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the elder person is :
Options: a ) 25 years , b ) 35 years , c ) 45 years , d ) 55 years , e ) 75 years
Rationale: "solution let their ages be x year and ( x + 10 ) years respectively . then , ( x + 10 ) - 15 = 2 ( x - 15 ) ⇔ x - 5 = 2 x - 30 ⇔ x = 25 . ∴ present age of the elder person = ( x + 10 ) = 35 years . answer b"
Answer: b
Problem: sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 65 marks . how many sums did sandy get correct ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 65 5 x = 125 x = 25 the answer is d ."
Answer: d
Problem: a person distributed 20 % of his income to his 3 children each . he deposited 25 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ?
Options: a ) a ) 452000 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 400000 , e ) e ) 652000
Rationale: "3 children got = 3 * 20 % = 60 % wife got = 25 % orphan house = 5 % total = 60 + 25 + 5 = 90 % remaining = 100 - 90 = 10 % 10 % = 40000 100 % = 40000 * 100 / 10 = $ 400000 answer is d"
Answer: d
Problem: the average weight of 4 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 71 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 4 × 1.5 = 6 kg so the weight of new person = 65 + 6 = 71 kg answer a"
Answer: a
Problem: convert 0.38 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 17 / 50 , d ) 19 / 50 , e ) none
Rationale: "answer 0.38 = 38 / 100 = 19 / 50 correct option : d"
Answer: d
Problem: on selling 17 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) rs . 20 , b ) rs . 60 . , c ) rs . 40 , d ) rs . 30 , e ) rs . 90
Rationale: ( c . p . of 17 balls ) - ( s . p . of 17 balls ) = ( c . p . of 5 balls ) c . p . of 12 balls = s . p . of 17 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 12 = rs . 60 . answer : b
Answer: b
Problem: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 5 times , what is the probability that it will land on either side all 5 times ?
Options: a ) 1 / 5 , b ) 1 / 10 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 32
Rationale: "must be either 5 heads or 5 tails 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 1 / 32 + 1 / 32 = 1 / 16 answer : d"
Answer: d
Problem: the average of 10 numbers is 210 . the average of first 5 numbers is 40 and the average of last 4 numbers is 200 . what is the middle number ?
Options: a ) a ) 200 , b ) b ) 2000 , c ) c ) 800 , d ) d ) 2100 , e ) e ) 1100
Rationale: the total of ten numbers = 10 x 210 = 2100 the total of first 5 and last 4 numbers is = 5 x 40 + 4 x 200 = 1000 so , the middle number is ( 2100 - 1000 ) = 1100 e
Answer: e
Problem: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 10 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 36.55 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.9 = $ 14 - - > x = $ 15.55 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 15.55 + 21 = $ 36.55 . answer : a ."
Answer: a
Problem: a rectangular swimming pool is 20 feet by 22 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 728 square feet . what is the width of the deck ?
Options: a ) 2
b ) 4
c ) 3
d ) 5
e ) 6
Rationale: let the width = w total area of the pool and deck = ( 2 w + 20 ) ( 2 w + 22 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 24 * 26 has unit digit 8 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 25 * 33 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 26 * 28 has unit digit 4 . . . . . . . . . . . hold d ) 4 feet . . . . . . . . . . . . 28 * 30 has unit digit 0 . . . . . . . . . . . eliminate e ) 5 feet . . . . . . . . . . . . 30 * 32 has unit digit 0 . . . . . . . . . . . eliminate answer : c w = 3
Answer: c
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 240 . their h . c . f is ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 240 x = 4 the numbers are 3 * 4 , 4 * 4 , 5 * 4 hence required h . c . f . = 4 answer is c"
Answer: c
Problem: a cistern is normally filled in 14 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 88 , c ) 40 , d ) 99 , e ) 112
Rationale: "1 / 14 - 1 / x = 1 / 16 x = 112 answer : e"
Answer: e
Problem: the overall age of x and y is 15 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19
Rationale: b 15 ( x + y ) â € “ ( y + z ) = 15 x â € “ z = 15
Answer: b
Problem: sachin is younger than rahul by 5 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 15.5
Rationale: "if rahul age is x , then sachin age is x - 5 , so ( x - 5 ) / x = 7 / 9 = > 9 x - 45 = 7 x = > 2 x = 45 = > x = 22.5 so sachin age is 22.5 - 7 = 15.5 answer : e"
Answer: e
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 42 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 , b ) 27 , c ) 50 , d ) 99 , e ) 12
Rationale: "relative speed = 42 + 30 = 72 km / hr . 72 * 5 / 18 = 20 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 / 20 = 50 sec . answer : c"
Answer: c
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 128 and $ 140 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 640 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1440
Rationale: "$ 128 for 2 years = $ 64 per year . extra $ 12 yearned with the compound interest is the percent yearned on percent . so , $ 12 is yearned on $ 64 , which means that the interest = 5 % . this on the other hand means that half of the savings = 64 * 5 = $ 320 . twice of that = $ 640 . answer : a ."
Answer: a
Problem: every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 2 / 5 of the juniors is equal to 1 / 3 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 3 / 20 , b ) 1 / 3 , c ) 5 / 12 , d ) 12 / 17 , e ) 5 / 11
Rationale: "let total number of juniors = j total number of seniors = s ( 2 / 5 ) j = ( 1 / 3 ) s = > s = 6 / 5 j total number of students = j + s = ( 11 / 5 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 11 / 5 ) j ] = 5 / 11 answer e"
Answer: e
Problem: dominos charges $ 6.25 for a veg pizza of std size that costs a total of $ 2.85 to make . pizza hut charges $ 5.80 for a similar pizza that costs $ 1.80 to make . if dominos sells 2000 pizzas , how many must pizza hut sell to make at least as much in total gross profit as its competitor does ?
Options: a ) 858 , b ) 1875 , c ) 14667 , d ) 63840 , e ) 146667
Rationale: dominos : profit / pizza = 6.25 - 2.85 = 3.75 : no of pizza = 2000 : gross profit = 2000 * 3.75 = 7500 pizza hut : profit / pizza = 4 : gross profit = 7500 : no of cups = 7500 / 4 = 1875 answer b
Answer: b
Problem: a certain company reported that the revenue on sales increased 20 % from 2000 to 2003 , and increased 40 % 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 ) 17 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 120 and and in 2005 140 , so from 2003 to 2005 it increased by ( 140 - 120 ) / 120 = 20 / 120 = 17 % answer : e ."
Answer: e
Problem: the average height of 30 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm . what was the actual average height of the students in the class ?
Options: a ) 174.5 , b ) 173.5 , c ) 172.5 , d ) 171.5 , e ) 170.5
Rationale: "the total height was 15 cm too much . the average height should be reduced by 15 cm / 30 = 0.5 cm the answer is a ."
Answer: a
Problem: how many integers are between 2 and 57 / 7 , inclusive ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12
Rationale: "57 / 7 = 8 . xx we are not concerned about the exact value of 57 / 7 as we just need the integers . the different integers between 2 and 57 / 7 would be 2,3 , 4 , 5 , 6 , 7 , 8 . total number of integers = 7 option b"
Answer: b
Problem: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 130 mangoes .
Options: a ) 360 , b ) 380 , c ) 400 , d ) 406 , e ) 433
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 130 mangoes = 130 * 3.33 = 433 . answer e"
Answer: e