Cheukting/mathqa huggingface dataset:
Question (gain): a sum of money at simple interest amounts to rs . 830 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 698 , c ) 758 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 830 ) = rs . 24 . s . i . for 3 years = rs . ( 24 x 3 ) = rs . 72 . principal = rs . ( 830 - 72 ) = rs . 758 . answer : c"
Answer: c
Question (physics): a person p takes 4 hrs time to complete a job and q takes 6 hrs to complete the same job if they work together how much time will they require to complete the job ?
Options: a ) 1.2 hrs , b ) 1.8 hrs , c ) 2.4 hrs , d ) 3.0 hrs , e ) none of these
Rationale: explanation : p ’ s 1 hr work = 1 / 4 q ’ s 1 hr work = 1 / 6 ( p + q ) ’ s 1 hr work = 1 / 4 + 1 / 6 = 5 / 12 = > time = 12 / 5 = 2.4 hrs answer : option c
Answer: c
Question (gain): a shopkeeper fixes the marked price of an item 35 % above its cost price . the percentage of discount allowed to gain 8 % is
Options: a ) 20 % , b ) 27 % , c ) 31 % , d ) 43 % , e ) none
Rationale: solution let c . p = rs . 100 then , marked price = rs . 135 , s . p = rs . 108 . discount % = ( 27 / 135 × 100 ) % = 20 % answer a
Answer: a
Question (gain): if the cost price of 22 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 37.5 % profit , c ) 37.5 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 22 articles = rs . 22 . selling price of 16 articles = rs . 22 therefore , selling price of 22 articles is : - = > 22 / 16 ã — 22 = > 30.25 . therefore , profit = selling price - cost price . = > 30.25 â ˆ ’ 22 = 8.25 hence , the percentage of profit = profit x 100 / c . p . = > 8.25 / 22 ã — 100 . = > 37.5 % profit . answer : b"
Answer: b
Question (physics): six bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 30 minutes , how many times do they toll together ?
Options: a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) none
Rationale: "l . c . m . of 2 , 4 , 6 , 8 , 10 , 12 is 120 . so , the bells will toll together after every 120 seconds ( 2 minutes ) . in 30 minutes , they will toll together 30 / 2 + 1 = 16 times answer d"
Answer: d
Question (gain): at what rate percent per annum will the simple interest on a sum of money be 4 / 5 of the amount in 10 years ?
Options: a ) 4 % , b ) 7 % , c ) 8 % , d ) 3 % , e ) 1 %
Rationale: "let sum = x . then , s . i . = 4 x / 5 , time = 10 years . rate = ( 100 * 4 x ) / ( x * 5 * 10 ) = 8 % answer : c"
Answer: c
Question (geometry): the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the length of this rectangle .
Options: a ) 40 , b ) 70 , c ) 20 , d ) 80 , e ) 60
Rationale: "l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c"
Answer: c
Question (physics): a man can row at 5 kmph in still water . if the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 1 km , b ) 1.5 km , c ) 5 km , d ) 3.2 km , e ) 2.4 km
Rationale: speed of down stream = 5 + 1 = 6 kmph speed of upstream = 5 - 1 = 4 kmph let the required distance be xkm x / 6 + x / 4 = 1 2 x + 3 x = 12 x = 2.4 km answer is e
Answer: e
Question (gain): a sum fetched a total simple interest of $ 4106.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8927
Rationale: "e 8927 principal = $ 100 x 4106.25 / 9 x 5 = $ 410625 / 45 = $ 8927 ."
Answer: e
Question (geometry): find the perimeter and area of a square of side 13 cm .
Options: a ) 121
b ) 144
c ) 169
d ) 196
e ) 225
Rationale: we know that the perimeter of square = 4 ã — side side = 13 cm therefore , perimeter = 4 ã — 13 cm = 52 cm now , area of the square = ( side ã — side ) sq . units = 13 ã — 13 cm â ² = 169 cm â ² answer : c
Answer: c
Question (general): a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 75 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1733.33 , d ) 1800 , e ) 2025
Rationale: 300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 75 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 75 = 1733.33 c is the answer
Answer: c
Question (gain): the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 45 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 928 , d ) $ 870 , e ) $ 660
Rationale: "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 145 % of $ 640 = $ 928 . c"
Answer: c
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (geometry): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (other): 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
Question (general): 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
Question (other): 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
Question (geometry): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (gain): 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
Question (gain): 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
Question (general): 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
Question (gain): 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
Question (probability): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (general): 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