Cheukting/mathqa huggingface dataset:
Question (general): if you multiply all the numbers on your mobile phone except 0 , what is the answer ?
Options: a ) 256485 , b ) 362880 , c ) 125425 , d ) 0 , e ) 125826
Rationale: "we have to multiply 1 to 9 to find the answer . therefore 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 = 362880 answer is b"
Answer: b
Question (general): a straight line in the xy - plane has slope 4 . on this line the x - coordinate of the point is 50 and y - coordinate is 300 then what is the y intercept of the plane ?
Options: a ) 150 , b ) 110 , c ) 100 , d ) 200 , e ) 50
Rationale: eq of line = y = mx + c m = 4 x = 50 y = 50 * 4 + c , substitute y by 300 as given in question . 300 = 200 + c , c = 100 correct option is c
Answer: c
Question (general): what two - digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5 ?
Options: a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 13 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 13 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 99 thus the answer is b
Answer: b
Question (geometry): the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area q of that hemisphere ?
Options: a ) 6 / π , b ) 9 / π , c ) 6 , d ) 9 , e ) 12
Rationale: "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
Answer: d
Question (gain): a and b invests rs . 10000 each , a investing for 8 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 25000 , find their shares ?
Options: a ) 22277 , b ) 26782 , c ) 22882 , d ) 15000 , e ) 28761
Rationale: "the ratio of their profits a : b = 8 : 12 = 2 : 3 share of a in the total profit = 2 / 5 * 25000 = rs . 10000 share of a in the total profit = 3 / 5 * 25000 = rs . 15000 answer : d"
Answer: d
Question (physics): a river 3 m deep and 36 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 , b ) 2678 , c ) 3600 , d ) 3400 , e ) 2500
Rationale: "( 2000 * 3 * 36 ) / 60 = 3600 m 3 answer : c"
Answer: c
Question (physics): a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 20 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 1111 meters , c ) 1777 meters , d ) 200 meters , e ) none of these
Rationale: "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 20 seconds distance = speed * time 36000 * 20 / 3600 = 200 meters . d is the answer ."
Answer: d
Question (physics): how many seconds will a 900 m 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 ) 23 sec , b ) 30 sec , c ) 49 sec , d ) 54 sec , e ) 59 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 900 * 3 / 50 = 54 sec . answer : d"
Answer: d
Question (physics): two airplanes take off from one airfield at noon . one flies due east at 201 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ?
Options: a ) 166 , b ) 332 , c ) 400 , d ) 402 , e ) 566
Rationale: "d in two hours : the plane flying east will be 402 miles away from airport . the other plane will be 566 miles away from airport . 566 / 402 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 402 miles apart . d"
Answer: d
Question (general): what is the sum of all the multiples of 10 between 0 and 120 ?
Options: a ) 500 , b ) 620 , c ) 450 , d ) 340 , e ) 780
Rationale: "the multiples of 10 between 0 and 120 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , 100 , 110 and 120 . if these are all added together , the result is 780 . final answer : e"
Answer: e
Question (general): if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 11,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 100,500 , e ) 100,000
Rationale: answer equals c in 48 years . i thought by 50 th year it would reach 95,500 . options should have been separated more widely for clarity .
Answer: c
Question (general): the ratio 4 : 20 expressed as percent equals to
Options: a ) 20 % , b ) 25 % , c ) 55 % , d ) 65 % , e ) none of above
Rationale: explanation : actually it means 4 is what percent of 20 , which can be calculated as , ( 4 / 20 ) * 100 = 4 * 5 = 20 answer : option a
Answer: a
Question (general): jack takes a loan of $ 120000 with 12 % annual interest : the interest is paid once , at the end of the year . jill takes a loan of $ 120000 with 12 % annual interest , compounding monthly at the end of each month . at the end of one full year , compared to jack ' s loan interest , approximately how much more does jill have to repay ?
Options: a ) zero , b ) $ 81.90 , c ) $ 8190.03 , d ) $ 819.00 , e ) $ 8.19
Rationale: jack ' s interest = $ 120,000 * 0.12 = $ 14400 or $ 1,200 each month . jills ’ s interest , 12 % / 12 = 1 % each month : for the 1 st month = $ 120,000 * 0.01 = $ 1,200 ; for the 2 nd month = $ 1,200 + 1 % of 1,200 = $ 1,212 , so we would have interest earned on interest ( very small amount ) ; for the 3 rd month = $ 1,212 + 1 % of 1,212 = ~ $ 1,224 ; for the 4 th month = $ 1,224 + 1 % of 1,224 = ~ $ 1,236 ; . . . for the 12 th month = $ 1,320 + 1 % of 1,320 = ~ $ 1,332 . the difference between jack ' s interest and jill ’ s interest = ~ ( 12 + 24 + . . . + 132 ) = $ 792 . answer : d .
Answer: d
Question (general): the area of one square is x ^ 2 + 8 x + 16 and the area of another square is 4 x ^ 2 − 12 x + 9 . if the sum of the perimeters of both squares is 32 , what is the value of x ?
Options: a ) 0 , b ) 2 , c ) 2.5 , d ) 7 / 3 , e ) 10
Rationale: "spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 4 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 5 l 2 = 2 x - 3 p 1 = 4 ( x + 4 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 32 4 ( x + 4 ) + 4 ( 2 x - 3 ) = 32 . . . . . . . . . . . . . . > x = 7 / 3 answer : d"
Answer: d
Question (general): evaluate 45 / . 05
Options: a ) 700 , b ) 900 , c ) 705 , d ) none of these , e ) 506
Rationale: "explanation : 45 / . 05 = 4500 / 5 = 900 option b"
Answer: b
Question (general): how many 3 - digit even numbers are possible such that if one of the digits is 5 , the next / succeeding digit to it should be 1 ?
Options: a ) 5 , b ) 305 , c ) 365 , d ) 405 , e ) 495
Rationale: 510 , 512 , 514 , 516 , and 518 , so total 5 . hence option a .
Answer: a
Question (physics): brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 150 meters . they next meet after sally has run 200 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500
Rationale: nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 100 meters , thus second time she runs 2 * 150 = 300 meters . since second time ( when they run full circumference ) brenda runs 300 meters and sally runs 200 meters , thus the circumference is 300 + 200 = 500 meters . answer : e .
Answer: e
Question (physics): a metal company ' s old machine makes bolts at a constant rate of 100 bolts per hour . the company ' s new machine makes bolts at a constant rate of 150 bolts per hour . if both machines start at the same time and continue making bolts simultaneously , how many minutes will it take the two machines to make a total of 400 bolts ?
Options: a ) 36 , b ) 72 , c ) 96 , d ) 144 , e ) 180
Rationale: "old machine 100 bolts in 60 mins so , 5 / 3 bolts in 1 min new machine 150 bolts in 60 mins so , 5 / 2 bolts in 1 min together , 5 / 3 + 5 / 2 = 25 / 6 bolts in 1 min so , for 400 bolts 400 * 6 / 25 = 96 mins ans c"
Answer: c
Question (general): gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 40 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 110
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 40 . thus , 3434 ( 90 + x ) = 40 + x or 270 + 3 x = 160 + 4 x or x = 110 answer : e"
Answer: e
Question (physics): amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.6 km ?
Options: a ) 600 m , b ) 300 m , c ) 400 m , d ) 700 m , e ) 500 m
Rationale: "a 600 m distance covered by amar = 18 / 4.8 ( 1.6 km ) = 3 / 8 ( 1600 ) = 600 m"
Answer: a
Question (physics): a train passes a station platform in 50 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 615 m , b ) 240 m , c ) 168 m , d ) 300 m , e ) 691 m
Rationale: speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 50 = 15 = > x = 300 m answer : d
Answer: d
Question (general): the lowest number which should be added to 8247 so that the sum is exactly divisible by 5 , 6 , 7 , 8 and 9 is :
Options: a ) 1833 , b ) 1853 , c ) 1733 , d ) 1233 , e ) 1832
Rationale: "l . c . m . of 5 , 6 , 7 , 8 and 9 = 2520 . on dividing 8247 by 2520 , the remainder is 687 . number to be added = ( 2520 - 687 ) = 1833 . answer : option ' a '"
Answer: a
Question (physics): two spherical balls lie on the ground touching . if one of the balls has a radius of 3 cm , and the point of contact is 5 cm above the ground , what is the radius of the other ball ?
Options: a ) 3 cm , b ) 9 cm , c ) 12 cm , d ) 15 cm , e ) none of the these
Rationale: "similar triangle properties . . 2 / r + 3 = 3 / r - 3 giving r = 15 . answer : d"
Answer: d
Question (general): in a class there are a total of 8 rows of desks and each desk can seat one student . there are 10 desks in the first row . in each subsequent row there are 2 more desks than in the previous row . find the maximum number of students seated in the class ?
Options: a ) 112 , b ) 144 , c ) 136 , d ) 132 , e ) 118
Rationale: the 8 rows form an arithmetic progression with first term 10 and last 24 . avg is 17 . so 17 * 8 = 136 answer is c .
Answer: c
Question (geometry): what is the smallest positive integer nn such that 6,480 ∗ n √ 6,480 ∗ n is a perfect cube ?
Options: a ) 5 , b ) 5 ^ 2 , c ) 30 , d ) 30 ^ 2 , e ) 30 ^ 4
Rationale: "sol : let ' s factorize 6480 and we get 6480 = 3 ^ 4 * 2 ^ 4 * 5 now we need to see for what minimum value of n √ n * 6480 = a ^ 3 where a is an integer so from 6480 we already have 2 ^ 4 * 3 ^ 4 * 5 * n √ n = ( 2 ^ 2 ) ^ 3 * ( 3 ^ 2 ) ^ 3 * ( 5 ) ^ 3 why cause a is an integer which will need to be have the same factors which are in lhs solving for n √ n = ( 2 ^ 6 * 3 ^ 6 * 5 ^ 3 ) / 2 ^ 4 * 3 ^ 4 * 5 and we get n √ n = 2 ^ 2 * 3 ^ 2 * 5 ^ 2 or n = 2 ^ 4 * 3 ^ 4 * 5 ^ 4 or 30 ^ 4 ans is e"
Answer: e
Question (gain): a candidate who gets 20 % of the marks fails by 40 marks . but another candidate who gets 30 % marks gets 20 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 200 marks , c ) 280 marks , d ) 160 marks , e ) 827 marks
Rationale: "20 % - - - - - - - - - - - - 40 30 % - - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - - - - - - 60 20 % - - - - - - - - - - - - - - 120 120 + 40 = 160 marks answer : d"
Answer: d
Question (physics): 10 women can complete a work in 8 days and 10 children take 12 days to complete the work . how many days will 6 women and 3 children together take to complete the work ?
Options: a ) 7 , b ) 10 , c ) 8 , d ) 9 , e ) 11
Rationale: "explanation : 1 women ’ s 1 day ’ s work = 1 / 8 / 10 = 1 / 80 1 child ’ s 1 day ’ s work = 1 / 12 / 10 = 1 / 120 6 women ’ s 1 day ’ s work = 1 / 80 × 6 = 3 / 40 3 children ’ s 1 day ’ s work = 1 / 120 × 3 = 1 / 40 6 women ’ s + 3 children ’ s 1 day ’ s work = 3 / 40 + 1 / 40 = 1 / 10 therefore , they will finish the whole work in 10 days . answer : option b"
Answer: b
Question (general): solve for x and check : - 200 x = 1600
Options: a ) 2000 , b ) 2573 , c ) 1600 , d ) 2950 , e ) none of these
Rationale: "solution : dividing each side by - 200 , we obtain ( - 200 x / - 200 ) = ( 1600 / - 200 ) therefore : x = - 8 check : - 200 x = 1600 ( - 200 * - 8 ) = 1600 1600 = 1600 answer : c"
Answer: c
Question (physics): if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 140 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 17.5 hours , d ) 12 hours , e ) 8 hours
Rationale: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 140 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 140 units is ' 7 times ' 20 , we need ' 7 times ' more time . ( 2.5 hours ) ( 7 times ) = 17.5 hours final answer : [ reveal ] spoiler : c"
Answer: c
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 1 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 10 % , e ) 10.8 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.10 i ( last year ) = 1.1 i ( last year ) 1 = 1.1 x i ( last year ) i ( last year ) = 1 / 1.1 = 10 / 11 = 0.90909 . . . or i ( last year ) = 0.91 % answer : c"
Answer: c
Question (general): there are 450 birds at a small zoo . the number of birds is 5 times the number of all the other animals combined . how many more birds are there than non bird animals at the zoo ?
Options: a ) 400 , b ) 360 , c ) 270 , d ) 180 , e ) 90
Rationale: total birds = 450 = 5 * other animals ( x ) or x = 90 . so , difference in birds and x = 450 - 90 = 360 . answer is b .
Answer: b
Question (physics): a man can row downstream at 20 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 15,2 , b ) 15 , 4 , c ) 15 , 8 , d ) 15 , 5 , e ) 15,7
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 20 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 30 = > x = 15 , y = 5 . answer : d"
Answer: d
Question (physics): an seller earns an income of re 1 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 20 th day of business , he earns an income of :
Options: a ) 29 , b ) 57 , c ) 35 , d ) 20 , e ) 30
Rationale: "2 nd day he earns = 3 ( 2 – 1 ) 3 rd day he earns = 3 ( 3 – 1 ) on 20 th day he earns 3 ( 20 - 1 ) = 57 rupees answer : b"
Answer: b
Question (general): if 16 ^ y = 4 ^ 16 , what is y ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 16
Rationale: "16 ^ y = 4 ^ 2 y = 4 ^ 16 2 y = 16 y = 8 the answer is c ."
Answer: c
Question (general): the sum of the ages of 4 children born at the intervals of 3 years each is 38 years . what is the age of the youngest child ?
Options: a ) 2 years , b ) 3 years , c ) 4 years , d ) 5 years , e ) 6 years
Rationale: "let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) = 38 4 x = 20 = > x = 5 . age of youngest child = x = 5 years . answer : d"
Answer: d
Question (gain): if the selling price of 8 articles is same as the cost price of 10 articles . find the gain or loss percentage ?
Options: a ) 25 % , b ) 45 % , c ) 35 % , d ) 65 % , e ) 55 %
Rationale: "let the c . p of each article be re 1 . then , s . p of 8 articles = c . p of 10 articles = rs . 10 now , c . p of 8 articles = rs . 8 , s . p of 8 articles = rs 10 gain = rs ( 10 - 8 ) = rs 2 . gain % = ( 2 / 8 × 100 ) % = 25 % answer : a"
Answer: a
Question (general): a cricket player whose bowling average was 24.85 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.85 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 85 , d ) 96 , e ) 108
Rationale: "average = total runs / total wickets total runs after last match = 24.85 w + 52 total wickets after last match = w + 5 ( 24.85 w + 52 ) / ( w + 5 ) = 24.85 - 0.85 = 24 w = 80 so total wickets aftr last match = w + 5 = 85 answer : c"
Answer: c
Question (general): what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 3
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 , e ) none of these
Rationale: "explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 3 = 1.66 so biggest is 5 / 3 and smallest is 2 / 3 their difference is 5 / 3 - 2 / 3 = 3 / 3 = 1 option d"
Answer: d
Question (general): 10 ^ 222 ÷ 10 ^ 220 = ?
Options: a ) 10 , b ) 1000 , c ) 100 , d ) 10000 , e ) 100000
Rationale: 10 ^ 222 ÷ 10 ^ 220 = 10 ^ ( 222 - 220 ) = 10 ^ 2 = 100 answer is c
Answer: c
Question (general): a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is
Options: a ) 285 , b ) 337 , c ) 878 , d ) 227 , e ) 291
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 . answer : a"
Answer: a
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 50 kg , c ) 70 kg , d ) 80 kg , e ) 60 kg
Rationale: "explanation : total increase in weight = 8 ã — 2.5 = 20 if x is the weight of the new person , total increase in weight = x â ˆ ’ 50 = > 20 = x - 50 = > x = 20 + 50 = 70 answer : option c"
Answer: c
Question (general): the average of 10 numbers is calculated as 15 . it is discovered later on that while calculating the average one number , namely 36 was wrongly read as 26 . the correct average is :
Options: a ) 12.4 , b ) 14 , c ) 16 , d ) 18.6 , e ) none of these
Rationale: explanation : sum of numbers = ( 10 × × 15 - 26 + 36 ) = 160 correct average = 160 / 10 = 16 correct option : c
Answer: c
Question (general): if z is not equal to zero , and z = 6 zs − 9 s 2 − − − − − − − − √ z = 6 zs − 9 s 2 , then z equals :
Options: a ) s , b ) 3 s , c ) 4 s , d ) - 3 s , e ) - 4 s
Rationale: squaring on both the sides gives z ^ 2 = 6 zs - 9 s ^ 2 = z ^ 2 - 6 zs + 9 s ^ 2 = z ( z - 3 s ) - 3 s ( z - 3 s ) = ( z - 3 s ) ( z - 3 s ) = z = 3 s answer = b
Answer: b
Question (general): sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 115 . if the ratio of his marks in english and maths is 5 : 1 , find his marks in science ?
Options: a ) 18 , b ) 77 , c ) 25 , d ) 55 , e ) 31
Rationale: "s : e = 1 : 3 e : m = 5 : 1 - - - - - - - - - - - - s : e : m = 5 : 15 : 3 5 / 23 * 115 = 25 answer : c"
Answer: c
Question (physics): two boats are heading towards each other at constant speeds of 5 miles / hr and 23 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 7 / 12 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 5
Rationale: "the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 5 + 23 = 25 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 28 * 1 / 60 = 7 / 15 miles apart . answer : b ."
Answer: b
Question (general): when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum e of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . e = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616 . b"
Answer: b
Question (general): there are cats got together and decided to kill the mice of 999936 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 991,1001 , c ) 991,1009 , d ) 992,1008 , e ) 931,1009
Rationale: "999936 can be written as 1000000 â € “ 64 = 10002 â € “ 82 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 8 ) * ( 1000 - 8 ) = ( 1008 ) * ( 992 ) given that number of cats is less than number if mice . so number of cats is 992 and number of mice were 1008 answer d"
Answer: d
Question (physics): a man can row 7 â ½ kmph in still water . if in a river running at 1.5 km / hr an hour , it takes him 50 minutes to row to a place and back , how far off is the place ?
Options: a ) 4 km , b ) 2 km , c ) 5 km , d ) 3 km , e ) 1 km
Rationale: speed downstream = ( 7.5 + 1.5 ) km / hr = 9 km / hr ; speed upstream = ( 7.5 - 1.5 ) kmph = 6 kmph . let the required distance be x km . then , x / 9 + x / 6 = 50 / 60 . 2 x + 3 x = ( 5 / 6 * 18 ) 5 x = 15 x = 3 . hence , the required distance is 3 km . answer d
Answer: d
Question (gain): a chemical supply company has 60 liters of a 30 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: 60 liters of a 30 % hno 3 solution means hno 3 = 18 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 18 + x = 50 % of ( 60 + x ) or x = 24 . hence , d
Answer: d
Question (general): what is the sum of all digits for the number 10 ^ 28 - 44 ?
Options: a ) 233 , b ) 245 , c ) 257 , d ) 270 , e ) 285
Rationale: "10 ^ 28 is a 29 - digit number : 1 followed by 28 zeros . 10 ^ 28 - 44 is a 28 - digit number : 26 9 ' s and 56 at the end . the sum of the digits is 26 * 9 + 5 + 6 = 245 . the answer is b ."
Answer: b