Cheukting/mathqa huggingface dataset:
Question (physics): the speed of a car increases by 2 kms after every one hour . if the distance travelled in the first one hour was 35 kms , what was the total distance travelled in 12 hours ?
Options: a ) 456 kms , b ) 482 kms , c ) 552 kms , d ) 556 kms , e ) none of these
Rationale: "total distance travelled in 12 hours = ( 35 + 37 + 39 + . . . upto 12 terms ) . this is an a . p . with first term , a = 35 , number of terms , n = 12 , common difference d = 2 required distance = 12 / 2 ( 2 * 35 + ( 12 - 1 ) * 2 ) = 6 ( 70 + 22 ) = 552 km . correct option : c"
Answer: c
Question (general): evaluate : 11110 + 24 * 3 * 10 = ?
Options: a ) 90111 , b ) 52631 , c ) 11190 , d ) 65321 , e ) 11133
Rationale: "according to order of operations , 24 ? 3 ? 10 ( division and multiplication ) is done first from left to right 24 / 2 = 8 * 10 = 80 hence 11110 + 24 * 3 * 10 = 11110 + 80 = 11190 correct answer c"
Answer: c
Question (physics): mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 15 candidates . she plans to have one working interview with 3 of the 15 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 120 , c ) 300 , d ) 360 , e ) 333
Rationale: "360 . answer d"
Answer: d
Question (general): what is the difference between the largest number and the least number written with the digits 6 , 3 , 2 , 5 ?
Options: a ) 6084 , b ) 4176 , c ) 2077 , d ) 2721 , e ) 1812
Rationale: "explanation : 2356 6532 - - - - - - - - - - - - 4176 answer : b"
Answer: b
Question (gain): a money lender lent rs . 1000 at 4 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.2 , b ) 3.75 , c ) 4 , d ) 4.25 , e ) 4.5
Rationale: ( 1000 xtx 4 / 100 ) + ( 1400 xtx 5 / 100 ) = 350 â † ’ t = 3.2 answer a
Answer: a
Question (general): a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 4 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 30 , b ) 34 , c ) 38 , d ) 42 , e ) 46
Rationale: "n = 4 k + 1 = 5 j + 4 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 5 j + 4 . 1 , 5 , 9 = 5 ( 1 ) + 4 the next such number is 9 + 4 * 5 = 29 . 9 + 29 = 38 the answer is c ."
Answer: c
Question (general): in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 7 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 78 , c ) 86 , d ) 92 , e ) 106
Rationale: divisor = ( 6 * 3 ) + 7 = 25 5 * quotient = 25 quotient = 5 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 5 ) + 6 = 106 . e )
Answer: e
Question (physics): a and b together can do a piece of work in 8 days . if a alone can do the same work in 20 days , then b alone can do the same work in ?
Options: a ) 0.075 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.15 days
Rationale: "b = 1 / 8 – 1 / 22 = 0.075 days answer : a"
Answer: a
Question (physics): circular gears l and r start to rotate at the same time at the same rate . gear l makes 20 complete revolutions per minute and gear r makes 60 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 8 more revolutions than gear l ?
Options: a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 14 , e ) e ) 12
Rationale: "gear l - - 20 rotations per 60 seconds - - 2 rotation per 6 seconds . gear r - - 60 rotations per 60 seconds - - 6 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 4 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 4 units . required net difference should be 8 rotations = > 2 ( 6 seconds later ) = = > 12 seconds . answer : e"
Answer: e
Question (general): for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 90 θ 33 ) θ 17 ) - ( 97 θ ( 33 θ 17 ) ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: ( ( 90 θ 33 ) θ 17 ) the remainder of 90 divided by 33 is 24 ; the remainder of 24 divided by 17 is 7 ; ( 97 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 97 divided by 16 is 1 . 7 - 1 = 6 . answer : d .
Answer: d
Question (general): what is the range of all the roots of | x ^ 2 - 3 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 3 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 3 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 3 or x = 1 i guess range is 3 - 1 = 2 c"
Answer: c
Question (general): if 1,000 microns = 1 decimeter , and 1,000 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 1,000 , b ) 100 , c ) 1 , 000,000 , d ) 10 , e ) 10,000
Rationale: "given that 1,000 microns = 1 decimeter = 1,000 , 000,000 angstroms so , 1 micron = 1,000 , 000,000 / 1,000 = 1 , 000,000 answer : c"
Answer: c
Question (general): if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of $ 8400 ?
Options: a ) 14 , b ) 24 , c ) 34 , d ) 12 , e ) 13
Rationale: "required difference = [ 3 1 / 2 % of $ 8400 ] – [ 3 1 / 3 % of $ 8400 ] = [ ( 7 / 20 ) - ( 10 / 3 ) ] % of $ 8400 = 1 / 6 % of $ 8400 = $ [ ( 1 / 6 ) * ( 1 / 100 ) * 8400 ] = $ 14 . answer a ."
Answer: a
Question (physics): the sum of three consecutive numbers is 63 . the greatest among these three number is :
Options: a ) 26 , b ) 28 , c ) 29 , d ) 22 , e ) 31
Rationale: "let the numbers be x , x + 1 and x + 2 then , x + ( x + 1 ) + ( x + 2 ) = 63 3 x = 60 x = 20 greatest number , ( x + 2 ) = 22 . answer : d"
Answer: d
Question (gain): machine p and machine q are each used to manufacture 770 sprockets . it takes machine p 10 hours longer to produce 770 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 770 / x = 770 / 1.1 x + 10 1.1 ( 770 ) = 770 + 11 x 11 x = 77 x = 7 the answer is c ."
Answer: c
Question (gain): the c . p of 20 books is equal to the s . p of 30 books . find his gain % or loss % ?
Options: a ) 63.33 % , b ) 34.33 % , c ) 33.33 % , d ) 31.33 % , e ) 36.33 %
Rationale: explanation : 20 cp = 30 sp 30 - - - 10 cp loss 100 - - - ? = > 33.33 % loss answer : c
Answer: c
Question (gain): weights of two friends ram and shyam are in the ratio 3 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 18 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
Rationale: "solution : given ratio of ram and shayam ' s weight = 3 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 3 / 5 or , x = 18 % . answer : option a"
Answer: a
Question (gain): in the manufacture of a certain product , 7 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.28 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "percent of defective produced = 7 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 7 / 100 ) * 100 % = ( 28 / 10000 ) * 100 % = ( 28 / 100 ) % = . 28 % answer 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 7 students ?
Options: a ) 14 years , b ) 17 years , c ) 19 years , d ) 38 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 7 = 38 years . answer d"
Answer: d
Question (gain): a trader bought a car at 30 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 18 % , b ) 26 % , c ) 12 % , d ) 32 % , e ) 15 %
Rationale: "original price = 100 cp = 70 s = 70 * ( 180 / 100 ) = 126 100 - 126 = 26 % answer : b"
Answer: b
Question (physics): a boy goes to his school from his house at a speed of 3 km / hr and return at a speed of 2 km / hr . if he takes 5 hours in going and coming , the distance between his house and school is ?
Options: a ) 5 km , b ) 6 km , c ) 10 km , d ) 12 km , e ) 8 km
Rationale: average speed = 2 * 3 * 2 / 3 + 2 = 12 / 5 km / hr distance traveled = 12 / 5 * 5 = 12 km distance between house and school = 12 / 2 = 6 km answer is b
Answer: b
Question (physics): how many seconds will a 600 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 700 , b ) 288 , c ) 500 , d ) 277 , e ) 121
Rationale: let length of tunnel is x meter distance = 600 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 600 + x = ( 65 / 3 ) * 60 600 + x = 20 * 65 = 1300 x = 1300 - 600 = 700 meters answer : a
Answer: a
Question (physics): a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , which a and b together can do it in 2 hours . how long will c alone take to do it ?
Options: a ) 12 hours , b ) 10 hours , c ) 6 hours , d ) 8 hours , e ) 4 hours
Rationale: a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 3 ; ( a + b ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 3 ) = 7 / 12 c ' s 1 hour work = ( 7 / 12 - 1 / 2 ) = 1 / 12 c alone will take 12 hours to do the work . answer : a
Answer: a
Question (gain): a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 60 percent of books that were loaned out are returned and there are 65 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 25 , c ) 35 , d ) 40 , e ) 55
Rationale: "total = 75 books . 60 % of books that were loaned out are returned - - > 100 % - 60 % = 40 % of books that were loaned out are not returned . now , there are 68 books , thus 75 - 65 = 10 books are not returned . { loaned out } * 0.4 = 10 - - > { loaned out } = 25 . answer : b ."
Answer: b
Question (general): cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost q is what percent of the original cost ?
Options: a ) q = 200 , b ) q = 600 , c ) q = 800 , d ) q = 1600 , e ) q = 50
Rationale: "original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
Answer: d
Question (general): albert is 2 times mary ’ s age and 4 times as old as betty . mary is 12 years younger than albert . how old is betty ?
Options: a ) 6 , b ) 12 , c ) 10 , d ) 15 , e ) 18
Rationale: "a = 2 m = m + 12 m = 12 a = 24 a = 4 b , and so b = 6 the answer is a ."
Answer: a
Question (general): what is the next number : 2 , 10 , 82 , __
Options: a ) 630 , b ) 730 , c ) 830 , d ) 848 , e ) 900
Rationale: "3 ^ 0 + 1 = 2 3 ^ 2 + 1 = 10 3 ^ 4 + 1 = 82 3 ^ 6 + 1 = 730 the answer is b ."
Answer: b
Question (general): the wages earned by robin is 40 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 23 % , b ) 18.75 % , c ) 28.57 % , d ) 50 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 140 and $ 160 respectively . charles earns $ 40 more than robin who earns $ 140 . therefore , charles ' wage is 40 / 140 * 100 = 28.57 % . the correct choice is ( c )"
Answer: c
Question (general): marts income is 50 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) b ) 120 % , c ) c ) 96 % , d ) d ) 90 % , e ) e ) 64 %
Rationale: m = ( 150 / 100 ) t t = ( 60 / 100 ) j = > m = ( 90 / 100 ) j answer d .
Answer: d
Question (general): what least number should be subtracted from 13601 such that the remainder is divisible by 87 ?
Options: a ) 27 , b ) 29 , c ) 28 , d ) 30 , e ) 31
Rationale: "13601 ÷ 87 = 156 , remainder = 29 hence 29 is the least number which can be subtracted from 13601 such that the remainder is divisible by 87 answer is b"
Answer: b
Question (geometry): if the complement of a certain angle is 7 times the measure of that certain angle , then what is the measure of that certain angle ?
Options: a ) 45 ° , b ) 30 ° , c ) 22.5 ° , d ) 18 ° , e ) 11.25 °
Rationale: thecomplementof angle a is the angle which , when added to angle a , gives 90 degrees . the two acute angles of a right triangle are complements , for example . the original angle is x , so the complement is 7 x , and together , these add up to 90 degrees . x + 7 x = 90 8 x = 90 x = 11.25 ° answer = ( e )
Answer: e
Question (general): if the average ( arithmetic mean ) of x and y is 80 , and z – x = 100 , what is the average of y and z ?
Options: a ) 140 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: "x + y / 2 = 80 = > x + y = 160 x = z - 100 . . . sub this value z - 100 + y = 160 = > z + y = 260 = > z + y / 2 = 130 answer : e"
Answer: e
Question (geometry): the area of a triangle is with base 2 m and height 5 m ?
Options: a ) 11 , b ) 10 , c ) 787 , d ) 122 , e ) 5
Rationale: "1 / 2 * 2 * 5 = 5 m 2 answer : e"
Answer: e
Question (other): the ratio of 2 numbers is 2 : 8 and their h . c . f . is 40 . their l . c . m . is ?
Options: a ) 400 , b ) 120 , c ) 80 , d ) 320 , e ) 40
Rationale: "let the numbers be 2 x and 8 x their h . c . f . = 40 so the numbers are 2 * 40 , 8 * 40 = 80 , 320 l . c . m . = 320 answer is d"
Answer: d
Question (general): if n divided by 3 has a remainder of 2 , what is the remainder when 2 times n is divided by 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 0
Rationale: "as per question = > n = 3 p + 2 for some integer p hence 2 n = > 6 q + 4 = > remainder = > 1 for some integer q hence a"
Answer: a
Question (gain): ramu bought an old car for rs . 38000 . he spent rs . 12000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 17 % , b ) 19 % , c ) 18 % , d ) 14 % , e ) 29.8 %
Rationale: "total cp = rs . 38000 + rs . 12000 = rs . 50000 and sp = rs . 64900 profit ( % ) = ( 64900 - 50000 ) / 50000 * 100 = 29.8 % answer : e"
Answer: e
Question (physics): two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 90 kmph and 70 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 19 sec , c ) 12 sec , d ) 10 sec , e ) 11.25 sec
Rationale: "explanation : d = 250 m + 250 m = 500 m rs = 90 + 70 = 160 * 5 / 18 = 400 / 9 t = 500 * 9 / 400 = 11.25 sec answer : option e"
Answer: e
Question (geometry): the mass of 1 cubic meter of a substance is 200 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 0.8 , b ) 1.25 , c ) 8.0 , d ) 12.5 , e ) 5.0
Rationale: "density is mass divided by volume . so density of the given substance will be mass / volume = 200 kg / 1 m ^ 3 = 800 kg / m ^ 3 or 1 g / 5 cm ^ 3 = 0.2 g / cm ^ 3 . next , ask yourself if 200,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 800,000 = 10 / 2 = 5 cubic centimeters . answer is e"
Answer: e
Question (gain): alfred buys an old scooter for $ 4700 and spends $ 800 on its repairs . if he sells the scooter for $ 6400 , his gain percent is ?
Options: a ) 5.45 % , b ) 16.36 % , c ) 7 % , d ) 8.12 % , e ) 10 %
Rationale: "c . p . = 4700 + 800 = $ 5500 s . p . = $ 6400 gain = 6400 - 5500 = $ 900 gain % = 900 / 5500 * 100 = 16.36 % answer is b"
Answer: b
Question (general): 3251 + 587 + 369 - ? = 3007
Options: a ) 1250 , b ) 1300 , c ) 1375 , d ) 1200 , e ) none of them
Rationale: let 4207 - x = 3007 then x = 4207 - 3007 = 1200 answer is d
Answer: d
Question (general): the manufacturer ’ s suggested retail price ( msrp ) of a certain item is $ 60 . store a sells the item for 20 percent more than the msrp . the regular price of the item at store b is 30 percent more than the msrp , but the item is currently on sale for 10 percent less than the regular price . if sales tax is 5 percent of the purchase price at both stores , what is the result when the total cost of the item at store b is subtracted from the total cost of the item at store a ?
Options: a ) $ 0 , b ) $ 0.63 , c ) $ 1.80 , d ) $ 1.89 , e ) $ 2.10
Rationale: msrp = 60 price at store a = 60 ∗ 120100 = 72 = 60 ∗ 120100 = 72 price at store b = 60 ∗ 130100 ∗ 90100 = 70.2 = 60 ∗ 130100 ∗ 90100 = 70.2 difference = 72.0 - 70.2 = 1.8 sales tax applicable = 5 % on both = 1.8 + 0.09 = 1.89 answer = d
Answer: d
Question (gain): in business , a and c invested amounts in the ratio 3 : 2 , whereas the ratio between amounts invested by a and b was 3 : 4 , if rs 30,000 was their profit , how much amount did b receive .
Options: a ) 1235 , b ) 62896 , c ) 6666 , d ) 8974 , e ) 5626
Rationale: "explanation : a : b = 3 : 4 = 3 : 4 = > a : c = 3 : 2 = 3 : 2 = > a : b : c = 3 : 4 : 2 c share = ( 2 / 9 ) * 30000 = 6666 option c"
Answer: c
Question (gain): if the selling price of 100 articles is equal to the cost price of 63 articles , then the loss or gain percent is :
Options: a ) 39 % , b ) 36 % , c ) 35 % , d ) 40 % , e ) 37 %
Rationale: "let c . p . of each article be re . 1 . then , c . p . of 100 articles = rs . 100 ; s . p . of 100 articles = rs . 63 . loss % = 37 / 100 * 100 = 37 % answer : e"
Answer: e
Question (general): rs . 1775 is divided amongst a , b , c so that 5 times a ' s share , 3 times b ' s share and 7 times c ' s share are all equal . find c ' s share ?
Options: a ) 177 , b ) 150 , c ) 817 , d ) 716 , e ) 375
Rationale: a + b + c = 590 5 a = 3 b = 7 c = x a : b : c = 1 / 5 : 1 / 3 : 1 / 7 = 21 : 35 : 15 15 / 71 * 1775 = rs . 375 answer : e
Answer: e
Question (general): n ^ ( n / 2 ) = 2 is true when n = 2 in the same way what is the value of n if n ^ ( n / 2 ) = 4 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "n ^ ( n / 2 ) = 4 apply log n / 2 logn = log 4 nlogn = 2 log 4 = log 4 ^ 2 = log 16 logn = log 16 now apply antilog n = 16 / n now n = 4 . answer : c"
Answer: c
Question (gain): a team won 50 percent of its first 60 games in a particular season , and 80 percent of its remaining games . if the team won a total of 60 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 180 , b ) 120 , c ) 90 , d ) 85 , e ) 30
Rationale: "won 50 % of the first 60 games means it won 30 games . let the number of remaining games played be x . hence the number of remaining games won is 0.8 x . so the equation for winning can be written as : 30 + 0.8 x = 0.6 ( 60 + x ) x = 30 total games played = 60 + 30 = 90 option c ."
Answer: c
Question (general): if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 23 , find the value of ab .
Options: a ) 5 , b ) 8 , c ) 7 , d ) 10 , e ) 3
Rationale: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 23 - 9 = 14 ab = 7 . answer is c ."
Answer: c
Question (gain): a person buys an article at $ 380 . at what price should he sell the article so as to make a profit of 25 % ?
Options: a ) 445 , b ) 449 , c ) 475 , d ) 740 , e ) 460
Rationale: "c 475 cost price = $ 380 profit = 25 % of 380 = $ 95 selling price = cost price + profit = 380 + 95 = 475"
Answer: c
Question (gain): in certain code ' twice ' is written as ' 34 $ 5 δ ' and ' wears ' is written as ' 4 δ 29 % ' . how is ' seat ' written in that code ?
Options: a ) 22 , b ) 23 , c ) 697 , d ) 66 p , e ) 82
Rationale: answer : option b
Answer: b
Question (gain): the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 12.5 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 11.36 % , e ) 10.8 %
Rationale: "12.5 = 1.1 * x x = 11.36 % answer d )"
Answer: d
Question (physics): two pipes a and b can fill a cistern in 10 and 15 minutes respectively . both fill pipes are opened together , but at the end of 3 minutes , ‘ b ’ is turned off . how much time will the cistern take to fill ?
Options: a ) 6 min , b ) 8 min , c ) 10 min , d ) 12 min , e ) none of these
Rationale: in one min , ( a + b ) fill the cistern = 1 ⁄ 10 + 1 ⁄ 15 = 1 ⁄ 6 th in 3 min , ( a + b ) fill the cistern = 3 ⁄ 6 = 1 ⁄ 2 th remaining part = 1 - 1 ⁄ 2 = 1 ⁄ 2 ∵ 1 ⁄ 10 th part filled by a in one min . ∴ 1 ⁄ 2 nd part filled by a in 10 × 1 ⁄ 2 = 5 min . ∴ total time = 3 + 5 = 8 min . answer b
Answer: b
Question (physics): a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 8 km ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 8 / 2 = 4 hours . the answer is d ."
Answer: d
Question (gain): find the simple interest on rs . 945 for 5 months at 4 paisa per month ?
Options: a ) s . 325 , b ) s . 500 , c ) s . 200 , d ) s . 189 , e ) s . 211
Rationale: "explanation : i = ( 945 * 5 * 4 ) / 100 = 189 answer : option d"
Answer: d
Question (general): find a sum for first 8 prime numbers ?
Options: a ) 22 , b ) 28 , c ) 59 , d ) 77 , e ) 84
Rationale: required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 ) = 77 note : 1 is not a prime number option d
Answer: d
Question (general): a jogger running at 9 km / hr along side a railway track is 290 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 67 sec , b ) 89 sec , c ) 36 sec , d ) 87 sec , e ) 41 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 290 + 120 = 410 m . time taken = 410 / 10 = 41 sec . answer : e"
Answer: e
Question (general): if you write down all the numbers from 1 to 100 , then how many times do you write 1 ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 20 , d ) d ) 21 , e ) e ) 22
Rationale: "explanation : explanation : clearly , from 1 to 100 , there are ten numbers with 1 as the unit ' s digit - 1 , 11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91 ; and ten numbers with 1 as the ten ' s digit - 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 100 so , required number = 10 + 11 = 21 . answer : d"
Answer: d