Cheukting/mathqa huggingface dataset:
Question (physics): a boat m leaves shore a and at the same time boat b leaves shore b . they move across the river . they met at 500 yards away from a and after that they met 300 yards away from shore b without halting at shores . find the distance between the shore a & b
Options: a ) 1000 yards , b ) 1200 yards , c ) 1400 yards , d ) 1600 yards , e ) 1800 yards
Rationale: if x is the distance , a is speed of a and b is speed of b , then ; 500 / a = ( x - 500 ) / b and ( x + 300 ) / a = ( 2 x - 300 ) / b , solving it , we get x = 1200 yards answer : b
Answer: b
Question (general): a pineapple costs rs 7 each and a watermelon costs rs . 5 each . if i spend rs 38 on total what is the number of pineapple i purchased ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 2 , e ) 3
Rationale: explanation : the equation for this problem can be made as : 5 x + 7 y = 38 where x is the number of watermelons and y is the number of pineapples . now test for 2 , 3 and 4 : for y = 2 5 x + 14 = 38 x is not an integer for y = 3 5 x = 17 x not an integer for y = 4 x = 2 so 4 pineapples and 2 watermelons can be bought by 38 rs . answer : d
Answer: d
Question (other): the sub - duplicate ratio of 25 : 16 is
Options: a ) 4 : 3 , b ) 1 : 2 , c ) 1 : 3 , d ) 5 : 4 , e ) 2 : 3
Rationale: "root ( 25 ) : root ( 16 ) = 5 : 4 answer : d"
Answer: d
Question (general): in δ pqs above , if pq = 7 and ps = 8 , then
Options: a ) 9 / 4 , b ) 12 / 5 , c ) 56 / 9 , d ) 15 / 4 , e ) 20 / 3
Rationale: "there are two ways to calculate area of pqs . area remains same , so both are equal . 7 * 8 / 2 = pr * 9 / 2 pr = 56 / 9 c"
Answer: c
Question (physics): ajay can ride 50 km in 1 hour . in how many hours he can ride 1250 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 1250 km in = 1250 / 50 * 1 = 25 hours answer is d"
Answer: d
Question (physics): a boat covers a certain distance downstream in 1 hour , while it comes back in 11 â  „ 2 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ?
Options: a ) 31 kmph , b ) 16 kmph , c ) 19 kmph , d ) 15 kmph , e ) 14 kmph
Rationale: "let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x â ˆ ’ 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 11 â  „ 2 hour . i . e . , distance travelled downstream in 1 hour = distance travelled upstream in 11 â  „ 2 hour since distance = speed ã — time , we have ( x + 3 ) ã — 1 = ( x - 3 ) 3 / 2 2 ( x + 3 ) = 3 ( x - 3 ) 2 x + 6 = 3 x - 9 x = 6 + 9 = 15 kmph answer : d"
Answer: d
Question (general): in a division , a student took 87 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 58
Rationale: x / 87 = 24 . x = 24 * 87 . so correct answer would be , ( 24 * 87 ) / 36 = 58 . answer : e
Answer: e
Question (general): what is the sum of all digits for the number 10 ^ 26 - 51 ?
Options: a ) 199 , b ) 209 , c ) 219 , d ) 229 , e ) 239
Rationale: "10 ^ 26 is a 27 - digit number : 1 followed by 26 zeros . 10 ^ 26 - 51 is a 26 - digit number : 24 9 ' s and 49 at the end . the sum of the digits is 24 * 9 + 4 + 9 = 229 . the answer is d ."
Answer: d
Question (geometry): what is the measure of the angle w made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90
Rationale: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c"
Answer: c
Question (gain): what is the compound interest paid on a sum of rs . 6000 for the period of 2 years at 10 % per annum .
Options: a ) 1260 , b ) 1320 , c ) 1200 , d ) 1250 , e ) none of these
Rationale: solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 6000 = 6000 * ( 21 / 100 ) = 1260 answer a
Answer: a
Question (general): a fair 2 sided coin is flipped 8 times . what is the probability that tails will be the result at least twice , but not more than 8 times ?
Options: a ) 5 / 8 , b ) 3 / 4 , c ) 7 / 8 , d ) 157 / 64 , e ) 143 / 128
Rationale: "at least twice , but not more than 8 timesmeans exactly 2 times , 3 times , 4 times , 5 times , 6 times , 7 times , 8 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 8 c 2 / 2 ^ 8 + 8 c 3 / 2 ^ 8 + 8 c 4 / 2 ^ 8 + 8 c 5 / 2 ^ 8 + 8 c 6 / 2 ^ 8 + 8 c 7 / 2 ^ 8 = 143 / 128 option : e"
Answer: e
Question (gain): the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 54 . what is the rate of interest per annum ?
Options: a ) 8 , b ) 2 , c ) 9 , d ) 4 , e ) 6
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 54 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 54 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 54 r 2 = ( 54 * 2 ) / 3 = 36 = > r = 6 rate = 6 % answer : option e"
Answer: e
Question (other): find the compound ratio of ( 1 : 2 ) , ( 2 : 3 ) and ( 3 : 4 ) is
Options: a ) 1 : 2 , b ) 3 : 5 , c ) 5 : 7 , d ) 1 : 4 , e ) 2 : 1
Rationale: "required ratio = 1 / 2 * 2 / 3 * 3 / 4 = 1 / 4 = 1 : 4 answer is d"
Answer: d
Question (general): if 1 is added to the denominator of fraction , the fraction becomes 1 / 2 . if 1 is added to the numerator , the fraction becomes 1 . the fraction is
Options: a ) 4 / 7 , b ) 5 / 9 , c ) 2 / 3 , d ) 10 / 11 , e ) none of these
Rationale: explanation : let the required fraction be a / b . then ⇒ a / b + 1 = 1 / 2 ⇒ 2 a – b = 1 - - - - ( 1 ) ⇒ a + 1 / b = 1 ⇒ a – b = – 1 ⇒ a – b = – 1 - - - - - - - ( 2 ) solving ( 1 ) & ( 2 ) we get a = 2 , b = 3 fraction = a / b = 2 / 3 correct option : c
Answer: c
Question (other): if the ratio of two number is 2 : 3 and lcm of the number is 120 then what is the number .
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "product of two no = lcm * hcf 2 x * 3 x = 120 * x x = 20 answer : b"
Answer: b
Question (general): find out the c . i on rs . 4000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 244.83 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01
Rationale: "a = 4000 ( 51 / 50 ) 3 = 4244.832 4000 - - - - - - - - - - - 244.83 answer : a"
Answer: a
Question (gain): bert and rebecca were looking at the price of a condominium . the price of the condominium was 40 % more than bert had in savings , and separately , the same price was also 75 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
Options: a ) 1 : 4 , b ) 4 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 5 : 4
Rationale: suppose bert had 100 so price becomes 140 , this 140 = 1.75 times r ' s saving . . so r ' s saving becomes 80 so required ratio is 100 : 80 = 5 : 4 answer : e
Answer: e
Question (physics): walking at 5 / 6 of her normal speed , a worker is 12 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "let v be her normal speed and let t be her normal time . d = ( 5 / 6 ) v * ( t + 12 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 5 / 6 ) v * ( t + 12 ) t / 6 = 10 t = 60 the answer is e ."
Answer: e
Question (physics): if 12 lions can kill 12 deers in 12 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 12 minute , c ) 120 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 12 ( lions ) * 12 ( min ) / 12 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 12 answer : b"
Answer: b
Question (physics): a man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
Rationale: let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 18 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 18 , d = 18 b - 18 c ; every 6 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 6 , d = 6 b + 6 c ; d = 18 b - 18 c = 6 b + 6 c , - - > b = 2 c , - - > d = 18 b - 9 b = 9 b . interval = \ frac { d } { b } = \ frac { 9 b } { b } = 9 answer : d ( 9 minutes ) .
Answer: d
Question (other): x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 27000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 20 : 9 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 3
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 27000 × 9 = 45 × 12 : 27 × 9 = 15 × 12 : 9 × 9 = 20 : 9 answer is a"
Answer: a
Question (physics): the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 20 , b ) 55 / 4 , c ) 25 , d ) 14 , e ) 13
Rationale: "after passing the hiker the cyclist travels for 5 minutes at a rate of 15 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 4 miles . in those 5 mins the hiker travels a distance of 1 / 3 miles . so the hiker still has to cover 11 / 12 miles to meet the waiting cyclist . the hiker will need 55 / 4 mins to cover the remaining 11 / 12 miles . so the answer is b ."
Answer: b
Question (general): if x + y = 10 , x - y = 18 , for integers of x and y , x = ?
Options: a ) 14 , b ) 15 , c ) 25 , d ) 13 , e ) 42
Rationale: x + y = 10 x - y = 18 2 x = 28 x = 14 answer is a
Answer: a
Question (probability): wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 2 / 3 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
Options: a ) 4 / 15 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22
Rationale: "p ( 1 and not 2 ) = 2 / 3 * ( 1 - 3 / 5 ) = 4 / 15 . answer : a ."
Answer: a
Question (general): find the least number must be subtracted from 964807 so that remaining no . is divisible by 8 ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "on dividing 964807 by 15 we get the remainder 7 , so 7 should be subtracted a"
Answer: a
Question (physics): if 8 people take an hour to complete a piece of work , then how long should 16 people will take to complete the same piece of work ?
Options: a ) 15 min , b ) 30 min , c ) 26 min , d ) 28 min , e ) 18 min
Rationale: if 8 people take an hour to complete a piece of work , then 16 people will take 8 * 60 / 16 = 30 mins to complete the same piece of work . answer : b
Answer: b
Question (geometry): find the area of a parallelogram with base 25 cm and height 15 cm ?
Options: a ) 295 cm 2 , b ) 385 cm 2 , c ) 275 cm 2 , d ) 375 cm 2 , e ) 285 cm 2
Rationale: "area of a parallelogram = base * height = 25 * 15 = 375 cm 2 answer : d"
Answer: d
Question (general): when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 6 ] * [ 4 ] = ?
Options: a ) [ 12 ] , b ) [ 44 ] , c ) [ 45 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 6 ] * [ 4 ] = ( 6 / 2 + 1 ) ( 4 / 2 + 1 ) = [ 12 ] . ans - a"
Answer: a
Question (gain): in a certain company , a third of the workers do not have a retirement plan . 60 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 180 , d ) 120 , e ) 210
Rationale: "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,4 * 1 / 3 * x 120 = 12 / 30 x x = 300 300 - 120 = 180 answer c"
Answer: c
Question (general): a bus started its journey from mumbai and reached pune in 65 min with its average speed of 60 km / hr . if the average speed of the bus is increased by 5 km / hr , how much time will it take to cover the same distance ?
Options: a ) 2 hrs , b ) 3 hrs , c ) 1 hrs , d ) 1 1 / 2 hrs , e ) 2 1 / 2 hrs
Rationale: sol . distance between ramgarh and devgarh = ( 60 * 65 ) / 60 = 60 average speed of the bus is increased by 5 km / hr then the speed of the bus = 60 km / hr required time = 60 / 60 = 1 hr c
Answer: c
Question (general): the mean of 50 observations is 200 . but later he found that there is decrements of 47 from each observations . what is the the updated mean is ?
Options: a ) 165 , b ) 185 , c ) 153 , d ) 198 , e ) 199
Rationale: "153 answer is c"
Answer: c
Question (other): a bag contains 4 red , 6 blue and 3 green balls . if 3 balls are picked at random , what is the probability that both are blue ?
Options: a ) 11 / 144 , b ) 12 / 455 , c ) 10 / 143 , d ) 11 / 125 , e ) 14 / 368
Rationale: "p ( both are red ) , = 6 c 3 / 13 c 3 = 10 / 143 c"
Answer: c
Question (gain): what is 120 % of 13 / 24 of 360 ?
Options: a ) 52 , b ) 117 , c ) 234 , d ) 312 , e ) 576
Rationale: "120 % * 13 / 24 * 360 = 1.2 * 13 * 15 = 234 the answer is c ."
Answer: c
Question (general): if a farmer sells 10 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 15 more chickens , he will run out of feed 3 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 12 , b ) 24 , c ) 48 , d ) 35 , e ) 60
Rationale: "say farmer has n chicken and he is good for d days . : - we have 3 equations given in question : - ( n - 10 ) * d + 4 = ( n + 15 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 15 d - 3 n = 45 4 n - 10 d = 40 = > n = 35 ans d it is !"
Answer: d
Question (general): how many 1 / 2 s are there in 37 1 / 2 ?
Options: a ) 75 , b ) 150 , c ) 300 , d ) 600 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 2 ) = ( 75 / 2 x 2 / 1 ) = 75 answer : a"
Answer: a
Question (general): a , b , c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 175 , then how much amount should c pay as his share of rent ?
Options: a ) 23 , b ) 45 , c ) 15 , d ) 28 , e ) 18
Rationale: a : b : c = 10 * 7 : 12 * 5 : 15 * 3 = 2 * 7 : 12 * 1 : 3 * 3 = 14 : 12 : 9 amount that c should pay = 175 * ( 9 / 35 ) = 5 * 9 = 45 answer is b
Answer: b
Question (general): in a box of 12 pens , a total of 6 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 1 / 6 , b ) 5 / 22 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4
Rationale: "method - 1 there are 9 fine pieces of pen and 6 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 6 / 12 ) i . e . probability of second pen not being defective = ( 5 / 11 ) [ 11 pen remaining with 5 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 6 / 12 ) * ( 5 / 11 ) = 5 / 22 answer : option b"
Answer: b
Question (gain): a part of certain sum of money is invested at 6 % per annum and the rest at 15 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 6 , b ) 4 : 9 , c ) 4 : 3 , d ) 5 : 2 , e ) 4 : 2
Rationale: "15 : 6 = 5 : 2 answer : d"
Answer: d
Question (general): if a randomly selected non - negative single digit integer is added to { 2 , 3 , 5 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6
Rationale: we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 5 ) / 2 = 4 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c .
Answer: c
Question (gain): on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 630 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 8 % , b ) 10 % , c ) 12 % , d ) 14 % , e ) 16 %
Rationale: "difference in c . i . and s . i for 2 years = $ 630 - $ 600 = $ 30 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 30 rate = ( 100 * 30 ) / ( 300 ) = 10 % the answer is b ."
Answer: b
Question (geometry): there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle .
Options: a ) 165 ∏ cm , b ) 65 ∏ cm , c ) 12 ∏ cm , d ) 14 ∏ cm , e ) 16 ∏ cm
Rationale: "let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . answer : c"
Answer: c
Question (physics): y and z walk around a circular track . they start at 5 a . m from the same point in the opposite directions . y and z walk at a speed of 3 rounds per hour and 4 rounds per hour respectively . how many times shall they cross each other before 7 a . m
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: explanation : relative speed = ( 3 + 4 ) = 9 rounds per hour so , they cross each other 9 times in an hour hence , they cross 18 times before 7 a . m answer : option e
Answer: e
Question (probability): a box contains 10 black , 5 red and 4 green marbles . 3 marbles are drawn from the box at random . what is the probability that all the three marbles are of the same color ?
Options: a ) 143 / 969 , b ) 134 / 969 , c ) 120 / 969 , d ) 19 / 969 , e ) 120 / 134
Rationale: "explanation : total marbles in a box = 10 black + 5 red + 4 green marbles = 19 marbles 3 marbles are drawn from 19 marbles at random . therefore , n ( s ) = 19 c 3 = 969 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 10 c 3 + 5 c 3 + 4 c 3 = 120 + 10 + 4 = 134 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 134 / 969 answer : b"
Answer: b
Question (gain): a towel , when bleached , lost 20 % of its length and 10 % of its breadth . what is the percentage decrease in area ?
Options: a ) 26 , b ) 28 , c ) 24 , d ) 20 , e ) 22
Rationale: "formula for percentage change in area is : = ( − x − y + ( xy ) / 100 ) % = ( − 20 − 10 + ( 20 × 10 ) / 100 ) % = − 28 % i . e . , area is decreased by 28 % answer is b ."
Answer: b
Question (gain): two numbers are respectively 35 % and 50 % more than a third number . the percentage that is first of the second is ?
Options: a ) 90 % , b ) 47 % , c ) 38 % , d ) 52 % , e ) 83 %
Rationale: "i ii iii 135 150 100 150 - - - - - - - - - - 135 100 - - - - - - - - - - - ? = > 90 % answer : a"
Answer: a
Question (gain): a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 272 less than the sum lent . what was the sum lent ?
Options: a ) 400 , b ) 278 , c ) 289 , d ) 500 , e ) 821
Rationale: "p - 272 = ( p * 4 * 8 ) / 100 p = 400 answer : a"
Answer: a
Question (other): a marketing firm determined that , of 200 households surveyed , 80 used neither brand r nor brand b soap , 60 used only brand r soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45
Rationale: solution for soap r and soap b ( d ) 40
Answer: d
Question (physics): the length of the bridge , which a train 150 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 388 , b ) 267 , c ) 225 , d ) 288 , e ) 261
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 150 + x ) / 30 = 25 / 2 = = > 2 ( 150 + x ) = 750 = = > x = 225 m . answer : c"
Answer: c
Question (general): if x and y are numbers such that ( x + 4 ) ( y - 4 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 0 , b ) 9 , c ) 12 , d ) 16 , e ) 18
Rationale: "from ( x + 4 ) ( y - 4 ) = 0 it follows that either x = - 4 or y = 4 . thus either x ^ 2 = 16 or y ^ 2 = 16 . now , if x ^ 2 = 16 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 16 + 0 = 16 . similarly if y ^ 2 = 16 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 16 = 16 . answer : d ."
Answer: d
Question (general): in the set of positive integers from 1 to 90 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 320 , d ) 405 , e ) 450
Rationale: "reduce 1 - 90 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 - - 85 are valid multiples . add them - - > 405 d"
Answer: d
Question (physics): 1000 men have provisions for 18 days . if 400 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.8 , c ) 12.6 , d ) 12.2 , e ) 12.1
Rationale: 1000 * 18 = 1400 * x x = 12.8 answer : b
Answer: b
Question (general): if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2014 ) = ?
Options: a ) 2015 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2014 ) = 2015 ans : a"
Answer: a
Question (physics): a , b and c can do a piece of work in 30 days , 30 days and 40 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 30 + 1 / 30 + 1 / 40 = 1 / 11 work done by a and b together in the last 4 days = 4 * ( 1 / 30 + 1 / 30 ) = 4 / 15 remaining work = 11 / 15 the number of days required for this initial work = 8 days . the total number of days required = 4 + 8 = 12 days . answer : a"
Answer: a
Question (gain): a man buys an article for $ 100 . and sells it for $ 110 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 110 gain = $ 10 gain % = 10 / 100 * 100 = 10 % answer is a"
Answer: a
Question (gain): a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) rs . 650 , b ) rs . 690 , c ) rs . 698 , d ) rs . 700 , e ) rs . 740
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 815 - 117 ) = rs . 698 . answer : option c"
Answer: c