Cheukting/mathqa huggingface dataset:
Question (gain): jerry went to a shop and bought things worth rs . 30 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19 , b ) 19.7 , c ) 21.3 , d ) 21.5 , e ) 24.7
Rationale: "total cost of the items he purchased = rs . 30 given that out of this rs . 30 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 30 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 30 − 0.3 − x ) = 30 ⇒ ( 30 − 0.3 − x ) = 5 ⇒ x = 30 − 0.3 − 5 = 24.7 e )"
Answer: e
Question (physics): a train 250 m long is running at a speed of 27 km / hr . in what time will it pass a bridge 200 m long ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "speed = 27 * 5 / 18 = 15 / 2 m / sec total distance covered = 250 + 200 = 450 m required time = 450 * 2 / 15 = 60 sec answer : e"
Answer: e
Question (probability): how many different ways can 2 students be seated in a row of 6 desks , so that there is always at least one empty desk between the students ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 20 , e ) 12
Rationale: "10 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 10 x 2 = 20 d"
Answer: d
Question (other): if 75 percent of a class answered the first question on a certain test correctly , 35 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 35 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 110 x = 30 ans : c"
Answer: c
Question (gain): fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 30 kg of fresh grapes ?
Options: a ) 3.75 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 10 kg , e ) none of these
Rationale: "the weight of non - water in 30 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 30 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 3.75 answer : a"
Answer: a
Question (general): what least number must be added to 1056 , so that the sum is completely divisible by 23 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "23 ) 1056 ( 45 92 - - - 136 115 - - - 21 - - - required number = ( 23 - 21 ) = 2 . a )"
Answer: a
Question (general): 4 ! / ( 4 - 3 ) ! = ?
Options: a ) 24 , b ) 34 , c ) 35 , d ) 36 , e ) 39
Rationale: 4 ! / ( 4 - 3 ) ! = 4 ! / 1 ! = 4 * 3 * 2 = 24 . hence , the correct answer is a .
Answer: a
Question (physics): natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 1.5 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 1.065 , b ) 1.125 , c ) 1.225 , d ) 1.375 , e ) 1.425
Rationale: "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 1.5 km / hour x / 3 = 1.5 x = 4.5 km the average speed while climbing = distance / time = 4.5 / 4 = 1.125 km / h the answer is b ."
Answer: b
Question (general): 5358 x 61 = ?
Options: a ) 326838 , b ) 323758 , c ) 323298 , d ) 273258 , e ) 327382
Rationale: "a 5358 x 61 = 5358 x ( 60 + 1 ) = 5358 x 60 + 5358 x 1 = 321480 + 5358 = 326838 ."
Answer: a
Question (general): if n = 4 ^ 11 – 4 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 4 ^ 3 - 4 . now 4 ^ 3 has last digit 4 . , we subtract 4 from 4 = 0 is the answer . option a
Answer: a
Question (general): company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 11 / 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 ) 11 / 21 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 11 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 11 / 5 = 11 - - > total time for both of them would be 10 + 11 = 21 - - > deluxe / total = 11 / 21 . answer : a ."
Answer: a
Question (gain): after decreasing 24 % in the price of an article costs rs . 608 . find the actual cost of an article ?
Options: a ) 128 , b ) 277 , c ) 800 , d ) 2688 , e ) 1991
Rationale: "cp * ( 76 / 100 ) = 608 cp = 8 * 100 = > cp = 800 answer : c"
Answer: c
Question (general): in a zoo there are 30 penguins , 22 zebras , and 8 tigers with some zookeepers . if the total number of heads are 132 less than the number of feet , the number of zookeepers is
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 22
Rationale: explanation : let number of zookeepers be x . then , total number of feet = 2 x 30 + 4 x 22 + 4 x 8 + 2 x = 2 x + 180 . total number of heads = 30 + 22 + 8 + x = 60 + x . therefore ( 2 x + 180 ) - 132 = ( 60 + x ) + or x = 12 . answer : a
Answer: a
Question (general): what is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out ? ( two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal )
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: since no flowers are to be left out , then the number of bouquets must be a factor of both 21 and 91 . for example , we can not have 2 bouquets since we can not divide 91 red tulips into 2 bouquets without one tulip left over . only answer choice which is a factor of 91 is e ( 7 ) . answer : e .
Answer: e
Question (general): what least number must be added to 1049 , so that the sum is completely divisible by 25 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 1
Rationale: if we divide 1049 by 25 remainder is 24 25 - 24 = 1 answer : e
Answer: e
Question (physics): man can row upstream at 25 kmph and downstream at 35 kmph , and then find the speed of the man in still water ?
Options: a ) 12 , b ) 22 , c ) 30 , d ) 88 , e ) 13
Rationale: "us = 25 ds = 35 m = ( 35 + 25 ) / 2 = 30 answer : c"
Answer: c
Question (general): according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 10 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 30 , d ) 67 , e ) 100
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 10 oz can = 300 oz / 10 oz = 30 answer c , 30 cans"
Answer: c
Question (general): when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 213.28 , what is value of j ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 213.28 here 213 is the quotient . given that remainder = 14 so , 213.28 = 213 + 14 / j so , j = 50"
Answer: d
Question (geometry): the diagonals of a rhombus are 30 cm and 12 cm . find its area ?
Options: a ) 176 , b ) 190 , c ) 180 , d ) 278 , e ) 292
Rationale: "1 / 2 * 30 * 12 = 180 answer : c"
Answer: c
Question (gain): if the cost price of 50 articles is equal to the selling price of 30 articles , then the gain or loss percent is ?
Options: a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 67
Rationale: "percentage of profit = 20 / 30 * 100 = 67 % answer : e"
Answer: e
Question (general): a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent w of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , w = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d ."
Answer: d
Question (general): a man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph , find his average speed for the total journey ?
Options: a ) 3.1 kmph , b ) 5 kmph , c ) 6 kmph , d ) 4 kmph , e ) 7 kmph
Rationale: explanation : speed of man = 4.5 kmph speed of stream = 2.5 kmph speed in downstream = 7 kmph speed in upstream = 2 kmph average speed = ( 2 x 7 x 2 ) / 9 = 3.1 kmph . answer : a
Answer: a
Question (general): nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 1.5 screws and 4.5 nails ?
Options: a ) a . 4 , b ) b . 5 / 2 , c ) c . 2 , d ) d . 3 / 2 , e ) e . 20 / 11
Rationale: "let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 1.5 s and 4.5 n = 1.5 s + 4.5 * 1.5 s = 8.25 s . . ratio = 15 s / 8.25 s = 15 / 8.25 = 20 / 11 e"
Answer: e
Question (general): a camera lens filter kit containing 5 filters sells for $ 52.50 . if the filters are purchased individually , 2 of them are priced at $ 6.45 each , 2 at $ 11.05 each , 1 at $ 15.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 3.76 % , b ) 4.76 % , c ) 5.76 % , d ) 6.76 % , e ) 7.76 %
Rationale: "cost of kit = $ 52.50 if filters are purchased individually - $ 6.45 * 2 + $ 11.05 * 2 + $ 15.50 = $ 50.50 amount saved = $ 52.50 - $ 50.50 = $ 2.50 required % age = ( $ 2.50 / $ 52.50 ) * 100 = 4.76 % so , the correct answer is b ."
Answer: b
Question (general): the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 2 students ?
Options: a ) 133 years , b ) 177 years , c ) 119 years , d ) 212 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 2 = 133 years . answer a"
Answer: a
Question (geometry): if the sides of a cube are in the ratio 4 : 3 . what is the ratio of their diagonals ?
Options: a ) 4 : 3 , b ) 4 : 8 , c ) 4 : 1 , d ) 4 : 2 , e ) 4 : 7
Rationale: "a 1 : a 2 = 4 : 3 d 1 : d 2 = 4 : 3 answer : a"
Answer: a
Question (general): if 638521 is to be divisible by 5 , what is the least whole number that should be added to ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 4 , e ) 3
Rationale: "a number is divisible by 5 if the last digit is either 0 or 5 . here , 638521 = 1 ( last digit is neither 0 or 5 ) . the next multiple of 5 i . e to make the last digit 0 or 5 add 4 4 must be added to 638521 to make it divisible by 5 d"
Answer: d
Question (general): the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 37 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 24.67 litres , c ) 11 litres , d ) 24.07 litres , e ) 38.67 litres
Rationale: "262.85 ( 37 ) + 3 , 104.35 x = 1 , 399.45 ( 37 + x ) solve the equation . 262.85 ( 37 ) + 3 , 104.35 x = 1 , 399.45 ( 37 + x ) 9725.45 + 3 , 104.35 x = 51779.65 + 1 , 399.45 x 9725.45 + 1 , 704.9 x = 51779.65 1 , 704.9 x = 42054.2 x ≈ 24.67 answer is b ."
Answer: b
Question (geometry): two equilateral triangle of side 12 cm are placed one on top another , such a 6 pionted star is formed if the six vertices lie on a circle what is the area of the circle not enclosed by the star ?
Options: a ) 21
b ) 88937
c ) 269
d ) 279
e ) 2701
Rationale: answer : a
Answer: a
Question (general): the average age of a class is 15.8 years . the average age of boys in the class is 16.4 years while that of girls is 15.4 years . what is the ratio of boys to girls in the class ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 3 : 5 , d ) 2 : 3 , e ) none of these
Rationale: let x = number of girls y = number of boys sum of girls ages / x = 15.4 sum of boys ages / y = 16.4 the sum of the girls ' ages is 15.4 x , and boys ' sum is 16.4 y ( sum of girls ages + sum of boys ages ) / ( x + y ) = 15.8 ( 15.4 x + 16.4 y ) / ( x + y ) = 15.8 15.4 x + 16.4 y = 15.8 ( x + y ) 15.4 x + 16.4 y = 15.8 x + 15.8 y 0.6 y = 0.4 x 0.6 y / x = 0.4 y / x = 0.4 / 0.6 y / x = 2 / 3 which is the ratio of boys to girls answer : d
Answer: d
Question (general): subtracting 7 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.93 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: "answer let a - 7 % of a = ab . ⇒ ( 93 x a ) / 100 = ab ∴ b = 0.93 correct option : a"
Answer: a
Question (general): a number divided by 84 leaves remainder 57 what is the remainder when same number divided by 12
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "add 84 + 57 = 141 now 141 divided by 12 so we get 9 as reaminder answer : c"
Answer: c
Question (physics): a children ' s gift store sells gift certificates in denominations of $ 3 and $ 5 . the store sold ' m ' $ 3 certificates and ' n ' $ 5 certificates worth $ 93 on a saturday afternoon . if ' m ' and ' n ' are natural numbers , how many different values can ' m ' take ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 31 , e ) 18
Rationale: explanatory answer step 1 : key data 1 . total value of all certificates sold = $ 93 . 2 . certificates sold were in denominations of $ 3 and $ 5 . 3 . both ' m ' and ' n ' are natural numbers . step 2 : approach the value of all certificates sold , 93 is divisible by 3 . so , a maximum of 31 $ 3 certificates and no $ 5 certificates could have been sold . however , the question states that both ' m ' and ' n ' are natural numbers . hence , at least 1 $ 5 certificate should have been sold . let us reduce the number of $ 3 certificates from theoretical maximum count of 31 by say ' x ' and correspondingly increase $ 5 certificates by ' y ' . evidently , 3 x = 5 y because the value of $ 3 certificates reduced should be the same as the value of $ 5 certificates increased . it means that x has to be a multiple of 5 and y has to be a multiple of 3 . or $ 3 certificates reduce in steps of 5 certificates . step 3 : list down possibilities the following combinations are possible 1 . m = 26 , n = 3 2 . m = 21 , n = 6 3 . m = 16 , n = 9 4 . m = 11 , n = 12 5 . m = 6 , n = 15 6 . m = 1 , n = 18 an alternative way to think of the same concept - replacing five $ 3 certificates with three $ 5 certificates leads to no change in the overall value of certficates sold and gives us a new combination each time . we need to see how many such combinations are possible . answer c
Answer: c
Question (gain): how long will a boy take to run round a square field of side 45 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 72 sec , b ) 45 sec , c ) 1 min , d ) 32 sec , e ) 25 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 45 * 4 = 180 m time taken = 180 * 2 / 5 = 72 sec answer is a"
Answer: a
Question (other): what is the greatest positive integer w such that 3 ^ w is a factor of 9 ^ 10 ?
Options: a ) 5 , b ) w = 9 , c ) w = 10 , d ) w = 20 , e ) w = 30
Rationale: "what is the greatest positive integer w such that 3 ^ w is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Question (other): in a group of 100 people , 60 like volleyball , 50 like hockey . how many like both volleyball and hockey ?
Options: a ) 20 , b ) 15 , c ) 10 , d ) 5 , e ) 25
Rationale: "make a venn diagram , and enter your data . let the number of people who like both volleyball and hockey be x 60 - x + x + 50 - x = 100 x = 10 so number who like both volleyball and hockey = 10 answer c"
Answer: c
Question (physics): triathlete dan runs along a 2 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 10 miles per hour and swims at a rate of 8 miles per hour , what is his average rate for the entire trip in miles per minute ?
Options: a ) 1 / 7 , b ) 2 / 15 , c ) 3 / 15 , d ) 1 / 4 , e ) 3 / 8
Rationale: "dan travels 4 miles round trip . running part : ( 2 / 10 = 1 / 5 * 60 = 12 minutes ) swimming part : ( 2 / 8 = 1 / 4 * 60 = 15 minutes ) 4 miles in ( 12 + 15 ) minutes 4 / 27 = 1 / 7 mile per minute answer : 1 / 7 mile per minute a"
Answer: a
Question (physics): a square has a side 5 centimeters shorter than the side of a second square . the area of the larger square is four times the area of the smaller square . find the side of each square
Options: a ) 5
b ) 6
c ) 7
d ) 8
e ) 9
Rationale: let x be the side of the smaller square and y be the side of the larger square . the statement ` ` a square has a side 5 centimeters shorter than the side of a second square ' ' may be formulated by x = y - 5 the area of the smaller square is equal to x 2 = ( y - 5 ) 2 and the area of the larger square is equal to y 2 the statement ` ` the area of the larger square is four times the area of the smaller square ' ' may be formulated by y 2 = 4 ( y - 5 ) 2 write the above equation so that the right side is equal to 0 y 2 - 4 ( y - 5 ) 2 = 0 the left side is made up of the difference of two squares and can be easily factored as follows [ y - 2 ( y - 5 ) ] [ y + 2 ( y - 5 ) ] = 0 solve for y to find y = 10 and y = 10 / 3 . we now use the equation x = y - 5 to find x y = 10 and x = 5 for the second solution y = 10 / 3 , x is negative and can not be accepted as the length of the side of a square must be positive . answer a
Answer: a
Question (physics): a train 360 m long is running at a speed of 48 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 11 sec , c ) 37.5 sec , d ) 19 sec , e ) 10 sec
Rationale: "speed = 48 * 5 / 18 = 40 / 3 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 3 / 40 = 37.5 sec answer : c"
Answer: c
Question (physics): a train covers a distance of 100 km in 1 hour . if its speed is decreased by 30 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 25 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: "speed = 100 / 1 = 100 km / hr new speed = 100 - 30 = 70 km / hr time taken = 100 / 70 = 1 hr 25 min answer is b"
Answer: b
Question (general): the ratio of the present age of sandy to that of molly is 7 : 2 . sixteen years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 66 , b ) 70 , c ) 74 , d ) 78 , e ) 82
Rationale: let the present age of sandy be 7 x years and that of molly be 2 x years . ( 7 x + 16 ) / ( 2 x + 16 ) = 5 / 2 4 x = 48 x = 12 six years ago , sandy ' s age was 7 ( 12 ) - 6 = 78 the answer is d .
Answer: d
Question (general): evaluate : 50 - 12 * 3 * 2 = ?
Options: a ) 62 , b ) 52 , c ) 32 , d ) 12 , e ) 42
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 50 - 12 * 3 * 2 = 50 - 8 = 42 correct answer e"
Answer: e
Question (gain): a grocer has 400 pounds of coffee in stock , 20 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 40 %
Rationale: "1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 140 pounds of decaffeinated out of 500 pounds , that means 140 / 500 * 100 % = 28 % . the correct answer is a ."
Answer: a
Question (geometry): the area of a parallelogram is 1764 sq m and its base is nine times size of the corresponding altitude . then the length of the base is ?
Options: a ) 21 , b ) 9 , c ) 11 , d ) 14 , e ) 7
Rationale: "9 x * x = 1764 = > x = 14 answer : d"
Answer: d
Question (gain): at what rate percent per annum will a sum of money double in 8 years .
Options: a ) 12.5 % , b ) 12.9 % , c ) 18.5 % , d ) 11.5 % , e ) 12.3 %
Rationale: "explanation : let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 8 ) ] % = 12.5 % per annum . answer : a ) 12.5 %"
Answer: a
Question (geometry): paper charge is rs . 60 per kg . how much expenditure would be there to cover a cube of edge 10 m with a paper , if one kg of paper covers 20 sq . m . area ?
Options: a ) rs . 2250
b ) rs . 3600
c ) rs . 2700
d ) rs . 1800
e ) none of these
Rationale: explanation : total surface area of the cube = 6 x ( 10 ) 2 = 600 sq . m 1 kg covers 20 sq . m area , for 600 we need = 600 / 20 = 30 kg paper . expenditure = rate x quantity = rs . 60 x 30 kg = rs . 1800 answer is d
Answer: d
Question (gain): a shopkeeper sells his goods at cost price but uses a weight of 800 gm instead of kilogram weight . what is his profit percentage ?
Options: a ) 25 % , b ) 18 % , c ) 20 % , d ) 40 % , e ) 45 %
Rationale: "100 ( 1000 - 800 ) / 800 = 25 % profit percentage = 25 % answer a"
Answer: a
Question (geometry): how many odd numbers between 10 and 900 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 13 numbers . answer : b ."
Answer: b
Question (general): what is the value of x ^ 2 yz − xyz ^ 2 , if x = 2 , y = 1 , and z = 2 ?
Options: a ) 20 , b ) 24 , c ) 0 , d ) 32 , e ) 48
Rationale: "4 * 1 * 2 - ( 2 * 1 * 4 ) = 8 + 8 = 0 ans : c"
Answer: c
Question (gain): by selling 18 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 35 % ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 12
Rationale: 90 % - - - 18 135 % - - - ? 90 / 135 * 18 = 12 answer : e
Answer: e
Question (physics): how many pieces of 0.35 meteres can be cut from a rod 12.5 meteres long
Options: a ) 30 , b ) 40 , c ) 35 , d ) 60 , e ) 70
Rationale: "explanation : we need so simple divide 42.5 / 0.85 , = ( 1250 / 35 ) = 35 option c"
Answer: c