regisss/math_qa huggingface dataset:
Problem: the speed at which a man can row a boat in still water is 20 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ?
Options: a ) 16 seconds , b ) 76 seconds , c ) 26 seconds , d ) 9.4 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 20 + 3 = 23 kmph = 23 * 5 / 18 = 115 / 18 m / s hence time taken to cover 60 m = 60 * 18 / 115 = 9.4 seconds . answer : d"
Answer: d
Problem: a 16 % stock yielding 14 % is quoted at :
Options: a ) s . 83.33 , b ) s . 110 , c ) s . 114 , d ) s . 120 , e ) s . 140
Rationale: "income of rs 14 on investment of rs 100 income of rs 16 on investment of ? = ( 16 * 100 ) / 14 = 114 answer : c"
Answer: c
Problem: in filling a lot with sand , that is 40 m * 20 m * 2 m the volumes of the sand filled will be ?
Options: a ) 1200 cu . m
b ) 2200 cu . m
c ) 4800 cu . m
d ) 1600 cu . m
e ) 4000 cu . m
Rationale: 40 * 20 * 2 = 1600 answer : d
Answer: d
Problem: the value of ( ( x – y ) ³ + ( y - z ) ³ + ( z – x ) ³ ) / ( 15 ( x – y ) ( y – z ) ( z – x ) ) is equal to :
Options: a ) 0 , b ) 1 / 12 , c ) 1 , d ) 1 / 5 , e ) 1 / 3
Rationale: since ( x – y ) + ( y – z ) + ( z – x ) = 0 , so ( x – y ) ³ + ( y – z ) ³ + ( z – x ) ³ = 3 ( x – y ) ( y – z ) ( z – x ) . ( 3 ( x – y ) ( y – z ) ( z – x ) ) / ( 15 ( x – y ) ( y – z ) ( z – x ) ) = 1 / 5 . answer : d
Answer: d
Problem: a is the product of each integer from 1 to 50 , inclusive and b = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of a ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 50 = 50 ! no . of trailing zeros in 50 ! = 50 / 5 + 50 / 5 ^ 2 = 10 + 2 = 12 100 ^ k = 10 ^ 2 k → k = 12 / 2 = 6 a
Answer: a
Problem: reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 432 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 3.6 , b ) 6 , c ) 18 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 432 12 r 2 = 432 r 2 = 36 r = 6 . answer : b"
Answer: b
Problem: if n is the greatest positive integer for which 4 ^ n is a factor of 10 ! , then n = ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: 10 ! = 3628800 e . 4 ^ 10 = 1048576 ( 3628800 / 1048576 ) - this is not a factor of 10 ! d . 4 ^ 8 = 65536 ( 3628800 / 65536 ) - this is not a factor of 10 ! c . 4 ^ 6 = 4096 ( 3628800 / 4096 ) - this is not a factor of 10 ! b . 4 ^ 4 = 256 ( 3628800 / 256 ) - this is a factor of 10 ! b is answer
Answer: b
Problem: an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 1400 sculptures are not on display , how many pieces of art does the gallery have ?
Options: a ) 360 , b ) 3150 , c ) 540 , d ) 640 , e ) 720
Rationale: "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1400 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1400 - - > { not on display } = 2100 . according to ( i ) 2 / 3 * { total } = 2100 - - > { total } = 3150 . answer : b ."
Answer: b
Problem: the grade point average of one third of the classroom is 60 ; the grade point average of the rest is 66 . what is the grade point average of the whole class ?
Options: a ) 55 , b ) 56 , c ) 64 , d ) 65 , e ) 66
Rationale: "let n = total students in class total points for 1 / 3 class = 60 n / 3 = 20 n total points for 2 / 3 class = 66 * 2 n / 3 = 44 n total points for whole class = 20 n + 44 n = 64 n 64 n total class points / n total students = 64 grade point average for total class answer : c"
Answer: c
Problem: if the digits 33 in the decimal 0.00033 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00033 ) ?
Options: a ) 0.33 , b ) 33 , c ) 0.033 , d ) 0.0033 , e ) 3.3 e - 05
Rationale: 99 * 0.33 = 32.67 approx . 33 answer : b
Answer: b
Problem: sum of two numbers is 10 . two times of the first exceeds by 5 from the 3 times of the other . then the numbers will be ?
Options: a ) a ) 7 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: explanation : x + y = 10 2 x – 3 y = 5 x = 7 y = 3 a )
Answer: a
Problem: two whole numbers whose sum is 72 can not be in the ratio
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 4 : 5 , d ) 5 : 7 , e ) none
Rationale: "sol . the sum of the ratio terms must divide 72 . so , the ratio can not be 3 : 4 . answer a"
Answer: a
Problem: a group of men decided to do a work in 20 days , but 2 of them became absent . if the rest of the group did the work in 22 days , find the original number of men ?
Options: a ) 15 , b ) 22 , c ) 27 , d ) 29 , e ) 18
Rationale: "original number of men = 2 * 22 / ( 22 - 20 ) = 22 answer is b"
Answer: b
Problem: a train 280 m long is running at 70 kmph . in how much time will it pass a platform 210 m long ?
Options: a ) 1.5 seconds , b ) 9.56 seconds , c ) 28.56 seconds , d ) 30.56 seconds , e ) 3.5 seconds
Rationale: distance travelled = 280 + 210 m = 490 m speed = 70 * 5 / 8 = 205 / 4 m time = 490 * 4 / 205 = 9.56 seconds answer : b .
Answer: b
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 25 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 6 , b ) 1 , c ) 5 , d ) 4 , e ) 7
Rationale: "100 * ( 20 / 100 ) = 20 - - - 25 ? - - - 1 = > rs . 0.8 100 - - - 80 ? - - - 0.8 = > rs . 1 answer : b"
Answer: b
Problem: in how many no . between 10 and 30 exactly two of the digits is 3 ?
Options: a ) 1 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: it ' s simple can be solved by elimination of answer choices . option b and c are too large , not possible . even de are large to have correct choice . ans : a
Answer: a
Problem: ( 208 % of 1265 ) ÷ 6 = ?
Options: a ) a ) 125 , b ) b ) 439 , c ) c ) 225 , d ) d ) 375 , e ) e ) 524
Rationale: "explanation : ? = ( 208 x 1265 / 100 ) ÷ 6 = 263120 / 600 = 439 answer : option b"
Answer: b
Problem: by selling an article at rs . 120 , a profit of 25 % is made . find its cost price ?
Options: a ) s . 96 , b ) s . 45 , c ) s . 120 , d ) s . 180 , e ) s . 189
Rationale: "sp = 120 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 120 * [ 100 / ( 100 + 25 ) ] = 120 * [ 100 / 125 ] = rs . 96 answer : a"
Answer: a
Problem: the average score of a cricketer in 2 matches is 40 and in other 3 matches is 10 . then find the average score in all the 5 matches ?
Options: a ) 25 , b ) 22 , c ) 30 , d ) 35 , e ) 42
Rationale: "average in 5 matches = ( 2 * 40 + 3 * 10 ) / 2 + 3 = 80 + 30 / 5 = 110 / 5 = 22 answer is b"
Answer: b
Problem: which number need to add to 8679921 to get a number exactly divisible by 330 ?
Options: a ) 69 , b ) 62 , c ) 61 , d ) 63 , e ) 64
Rationale: 8679921 / 330 = 26302 and reminder = 261 . 330 - 261 = 69 so , the next number divisible by 339 is 69 places in front of 8679921 which means 69 + 8679921 = 8679990 69 should be added to 8679921 a
Answer: a
Problem: at a certain college , 60 percent of the total number of students are freshmen . if 40 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 20 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?
Options: a ) 4 % , b ) 8 % , c ) 4.2 % , d ) 4.8 % , e ) 5 %
Rationale: "let ' s say there is a total of 100 students at this college . 60 percent of the total number of students are freshmen . # of freshmen = 60 % of 100 = 60 40 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 40 % of 60 = 24 . . . and , of these , 20 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 20 % of 24 = 4.8 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 4.8 / 100 = 4.8 % answer : d"
Answer: d
Problem: what annual installment will discharge a debt of rs . 1008 due in 3 years at 12 % simple interest ?
Options: a ) 300 , b ) 345 , c ) 325 , d ) 335 , e ) none of them
Rationale: "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1008 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1008 ï ƒ › ( 28 x + 31 x + 25 x ) = ( 1008 * 25 ) x = ( 1008 * 25 ) / 84 = rs . 300 . therefore , each installment = rs . 300 . answer is a ."
Answer: a
Problem: what is the smallest integer k for which 64 ^ k > 4 ^ 16 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "64 ^ k > 4 ^ 16 4 ^ ( 3 k ) > 4 ^ 16 3 k > 16 k = 6 the answer is c ."
Answer: c
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 1000 m long ?
Options: a ) 220 sec , b ) 190 sec , c ) 167 sec , d ) 197 sec , e ) 179 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2200 m t = d / s t = 2200 / 10 t = 220 sec answer : a"
Answer: a
Problem: if t = 5 / 9 * ( k - 32 ) , and if t = 50 , then what is the value of k ?
Options: a ) 116 , b ) 119 , c ) 122 , d ) 125 , e ) 128
Rationale: "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 50 ) / 5 + 32 = 122 the answer is c ."
Answer: c
Problem: let q represent a set of 7 distinct prime numbers . if the sum of the numbers in q is even and x is a member of q , then what is the least possible value that x can be ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7
Rationale: q = p 1 + p 2 + p 3 + p 4 + p 5 + p 6 + p 7 = even ( and all primes are distinct ) if the least prime is 2 then we have sum of q = even . ans . c . 3
Answer: c
Problem: how many digits are in the number 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 4 ?
Options: a ) 22 , b ) 20 , c ) 19 , d ) 18 , e ) 17
Rationale: whenever you are asked to find the number of digits , try to bring the number in multiples of 10 . this way , we can wasily calculate the umber of 0 ' s through the powers of 10 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 4 = ( 5 ^ 2 * 2 ) ^ 8 * 2 ^ 9 * 11 ^ 2 * 10 ^ 4 = 5 ^ 16 * 2 ^ 17 * 11 ^ 2 * 10 ^ 4 = 2 * 11 ^ 2 * 10 ^ 16 * 10 ^ 4 = 242 * 10 ^ 16 x 10 ^ 4 hence we would have 16 trailing 0 ' s and the three digits from 242 total digits = 3 + 20 = 23 correct option : d
Answer: d
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 432 per week . how much does she earn in dollars per hour ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 11 , e ) 12
Rationale: "explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 432 . hourly wage = 432 / 36 = 12 answer : e"
Answer: e
Problem: x , y , and z are consecutive numbers and x > y > z . also , 2 x + 3 y + 3 z = 5 y + 11 . what is the value of z ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if x , y , and z are consecutive numbers and x > y > z , then y = z + 1 and x = z + 2 . 2 x + 3 y + 3 z = 5 y + 11 2 z + 4 + 3 z + 3 + 3 z = 5 z + 5 + 11 3 z = 9 z = 3 the answer is b ."
Answer: b
Problem: a and b are two circles . the radius of a is 5 times as large as the radius of b . what is the ratio between the areas of the circles ?
Options: a ) 1 : 8 .
b ) 1 : 2 .
c ) 1 : 4 .
d ) 1 : 25 .
e ) 1 : 6 .
Rationale: given : the radius of a is 5 times as large as the radius of b . = > r ( a ) = 5 r ( b ) . the radius are in ratio of 1 : 5 thus the area will be in the ratio of square of radius . 1 : 25 . hence d .
Answer: d
Problem: [ ( 3.242 x 10 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 0.03242 , d ) 473.88 , e ) none of these
Rationale: "answer multiplying 3.242 x 10 = 3.242 now divide 3.242 by 100 so , 3.242 ÷ 100 = 0.03242 ∴ shift the decimal two places to the left as 100 correct option : c"
Answer: c
Problem: pipe a can fill a pool in 12 hours at a constant rate . if pipe a does the job for 8 hours and pipe b does the rest of the job , which works at 1 / 3 constant rate of pipe a . how long will it take for pipe b alone to do the rest of the job ?
Options: a ) 12 hrs , b ) 6 hrs , c ) 8 hrs , d ) 10 hrs , e ) 24 hrs
Rationale: pipe a will do 8 / 12 in 8 hrs , so a does 2 / 3 of the work . . therefore , b will do the remaining 1 / 3 rd work alone . . as the speed of b is 1 / 3 rate of a , b will do the 1 / 3 rd work in same time that a takes to complete full job . . . ans 12 a
Answer: a
Problem: rs . 1210 were divided among a , b , c so that a : b = 5 : 4 and b : c = 9 : 10 . then , c gets :
Options: a ) rs . 340 , b ) rs . 400 , c ) rs . 450 , d ) rs . 475 , e ) none
Rationale: "solution a : b = 5 : 4 , b : c = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 90 = 4 : 40 / 9 ∴ a : b : c = 5 : 4 : 40 / 9 = 45 : 36 : 40 . sum of ratio terms = ( 45 + 36 + 40 ) = 121 ∴ c ’ s share = rs . ( 1210 x 40 / 121 ) = rs . 400 . answer b"
Answer: b
Problem: two sacks together contained 40 kilograms of sugar . if after 1 kilogram of sugar was taken from the first sack and poured into the second the weight of the sugar in the first sack became 60 % the weight of the sugar in the second , what was the original difference in the weights of the sacks ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: say the weight of the second sack after change is x kilograms , then the weight of the first sack after change would be 0.6 x . since the total weight of sugar in both sacks remained the same then x + 0.6 x = 40 , which gives x = 25 . now , if the weight of the second sack after change is 25 kilograms then initially it was 25 − 1 = 24 kilograms and the initial weight of the first sack was 40 − 24 = 16 kilograms , so the difference was 24 − 16 = 8 kilograms . answer : c
Answer: c
Problem: find a positive number , which when increased by 8 is equal to 128 times reciprocal of the number .
Options: a ) 5 , b ) 6 , c ) 8 , d ) 7 , e ) 9
Rationale: explanation : let the number be x . then , x + 8 = 128 x ( 1 / x ) = > x < sup > 2 < / sup > + 8 x - 128 = 0 = > ( x + 16 ) ( x - 8 ) = 0 = > x = 8 answer : option c
Answer: c
Problem: find the value of x : 2 a ^ 2 - 7 a + 10 = 14
Options: a ) 7 , b ) 5 , c ) 6 , d ) 4 , e ) 2
Rationale: "using the elimination method substitute options for x and find the correct option . answer : d"
Answer: d
Problem: sheela deposits rs . 3400 in bank savings account . if this is 15 % of her monthly income . what is her monthly income in ?
Options: a ) 22666 , b ) 20000 , c ) 25000 , d ) 22235 , e ) none of these
Rationale: "explanation : 15 % of income = rs . 3400 100 % of income = 3400 x 100 / 15 = rs . 22666 answer : a"
Answer: a
Problem: when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of r ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . r * 23 + 39 = 25 * ( r + 1 ) r = 7 ans . ( a )"
Answer: a
Problem: a number when multiplied by 3 is odd and divisible by 9 . this number when multiplied by 4 is 108 . what is the original number ?
Options: a ) 10 , b ) 18 , c ) 13 , d ) 21 , e ) 27
Rationale: working backward , 108 divided by 4 is 27 . this number fits the rules of three and nine , where the digits add up to a sum divisible by nine . answer is e .
Answer: e
Problem: if there is one larger cube with surface area 600 and no . of smaller cubes with surface area 24 . then how many small cubes are required to make a larger cube with surface area of 600 ?
Options: a ) 5
b ) 125
c ) 4
d ) 100
e ) 24
Rationale: the ratio between larger and smaller is 6 a 12 : 6 a 22 = 600 : 24 a 12 : a 22 = 100 : 4 a 1 : a 2 = 10 : 2 then length of cube is 10 and 2 so make a cube with length 10 , we have to 5 small cubes each in length , breadth and height . so total 125 cubes are required . then the answer is b
Answer: b
Problem: in the coordinate plane , line a has a slope of - 1 and an x - intercept of 1 . line b has a slope of 5 and a y - intercept of - 5 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the equation of line a is y = - x + 1 the equation of line b is y = 5 x - 5 5 x - 5 = - x + 1 x = 1 y = 0 the point of intersection is ( 1,0 ) and then a + b = 1 . the answer is b ."
Answer: b
Problem: the interest on a certain deposit at 4.5 % p . a . is rs . 405 in one year . how much will the additional interest in one year be on the same deposit at 5 % p . a . ?
Options: a ) rs . 50 , b ) rs . 45 , c ) rs . 40.5 , d ) rs . 48.5 , e ) rs . 49.5
Rationale: s . i . = rs . 405 r = 4.5 % t = 1 year principal = ( 100 * 405 ) / ( 4.5 * 1 ) = rs . 9000 s . i at 5 % interest = ( 9000 * 5 * 1 ) / 100 = rs . 450 difference in interest = 450 – 405 = rs . 45 answer : b
Answer: b
Problem: a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 16 cm . what is the length of the wire ?
Options: a ) 45 cm , b ) 18 cm , c ) 90 cm , d ) 180 cm , e ) none of these
Rationale: volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 16 ) 2 * h = ( 4 / 3 ) π ( 12 ) 3 = > h = 9 cm answer : e
Answer: e
Problem: approximately how many cubic feet of water are needed to fill a circular swimming pool that is 100 feet across and 4 feet deep ?
Options: a ) 15000 , b ) 30000 , c ) 50000 , d ) 70000 , e ) 90000
Rationale: "answer should be b . v = \ pir ^ 2 h = \ pi * 50 ^ 2 * 4 = approximately 30000"
Answer: b
Problem: in a box of 12 pens , a total of 4 are defective . if a customer buys 3 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 1 / 6 , b ) 2 / 55 , c ) 14 / 55 , d ) 12 / 55 , e ) 3 / 4
Rationale: "method - 1 there are 9 fine pieces of pen and 4 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 8 / 12 ) i . e . probability of second pen not being defective = ( 7 / 11 ) i . e . probability of third pen not being defective = ( 6 / 10 ) probability of both pen being non - defective = ( 8 / 12 ) * ( 7 / 11 ) * ( 6 / 10 ) = 14 / 55 answer : option c"
Answer: c
Problem: two friends plan to walk along a 33 - km trail , starting at opposite ends of the trail at the same time . if friend p ' s rate is 20 % faster than friend q ' s , how many kilometers will friend p have walked when they pass each other ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "if q complete x kilometers , then p completes 1.2 x kilometers . x + 1.2 x = 33 2.2 x = 33 x = 15 then p will have have walked 1.2 * 15 = 18 km . the answer is d ."
Answer: d
Problem: the number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is
Options: a ) 720 , b ) 180 , c ) 75 , d ) 65 , e ) none of these
Rationale: "explanation : the hour hand moves from pointing to 12 to pointing to half way between 2 and 3 . the angle covered between each hour marking on the clock is 360 / 12 = 30 . since the hand has covered 2.5 of these divisions the angle moved through is 75 . answer : c"
Answer: c
Problem: a train running at the speed of 90 km / hr crosses a pole in 15 seconds . what is the length of the train ?
Options: a ) 325 , b ) 350 , c ) 375 , d ) 400 , e ) 425
Rationale: "speed = ( 90 x ( 5 / 18 ) m / sec = ( 25 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 25 ) x 15 ) m = 375 m c"
Answer: c
Problem: two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 60 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ?
Options: a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 2 hours , e ) 2 hours 10 minutes
Rationale: "both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 60 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 60 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 60 + 60 ) = 120 minutes on the road . d . 2 hours"
Answer: d
Problem: four numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number .
Options: a ) 480 , b ) 239 , c ) 270 , d ) 282 , e ) 112
Rationale: answer : a
Answer: a
Problem: five machines , each working at the same constant rate , together can complete a certain job in 20 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 10 days ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 5 , e ) 10
Rationale: rate of one machine = 1 job / ( 20 * 5 ) days let x = number of machines needed to complete the job in 10 days 1 / ( 5 * 20 ) * 10 * x = 1 job x = 10 10 - 5 = 5 answer : d
Answer: d
Problem: find ( 7 x + 4 y ) / ( x - 2 y ) if x / 2 y = 5 / 2 ?
Options: a ) 13 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: "x / 2 y = 3 / 2 = > x = 10 y / 2 = 5 y = > ( 7 x + 4 y ) / ( x - 2 y ) = ( ( 7 * ( 5 y ) ) + 4 y ) / ( 5 y - 2 y ) = > 39 y / 3 y = 13 answer : a"
Answer: a
Problem: there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 11,000 after 3 years at the same rate ?
Options: a ) 3641 , b ) 2572 , c ) 4542 , d ) 2343 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 11000 . t = 3 years and r = 10 % p . a . c . i . = rs . 11000 x 1 + 10 3 - 1 100 = rs . 11000 x 331 1000 = 3641 . a"
Answer: a
Problem: a train travels from albany to syracuse , a distance of 120 miles , at the average rate of 40 miles per hour . the train then travels back to albany from syracuse . the total travelling time of the train is 5 hours and 24 minutes . what was the average rate of speed of the train on the return trip to albany ?
Options: a ) 45 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "40 * t = 120 therefore t = 120 / 40 = 3 on return speed * ( 5.4 - 3 ) = 120 therefore t = 120 / 2.4 = 50 e"
Answer: e
Problem: the ratio between the present ages of a and b is 4 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 3 : 4 , b ) 3 : 0 , c ) 3 : 1 , d ) 3 : 2 , e ) 9 : 5
Rationale: let the present ages of a and b be 4 x and 3 x years respectively . then , ( 4 x - 4 ) / ( 3 x + 4 ) = 1 / 1 1 x = 8 = > x = 8 required ratio = ( 4 x + 4 ) : ( 3 x - 4 ) = 36 : 20 = 9 : 5 . answer : e
Answer: e
Problem: find value of x ( 11 ^ 2 + 12 ^ 2 + 13 ^ 2 + . . . + 20 ^ 2 ) = x
Options: a ) 1200 , b ) 1340 , c ) 1234 , d ) 1203 , e ) 2485
Rationale: ( 11 ^ 2 + 12 ^ 2 + 13 ^ 2 + . . . + 20 ^ 2 ) = ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 20 ^ 2 ) - ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 10 ^ 2 ) 6 = 20 x 21 x 41 - 10 x 11 x 21 6 6 = ( 2870 - 385 ) = 2485 e
Answer: e
Problem: in a mixture 60 litres , the ratio of milk and water 2 : 1 . if the this ratio is to be 1 : 2 , then the quanity of water to be further added is
Options: a ) 20 liters , b ) 30 liters , c ) 50 liters , d ) 60 liters , e ) none of these
Rationale: "explanation : quantity of milk = 60 * ( 2 / 3 ) = 40 liters quantity of water = 60 - 40 = 20 liters as per question we need to add water to get quantity 2 : 1 = > 40 / ( 20 + x ) = 1 / 2 = > 20 + x = 80 = > x = 60 liters option d"
Answer: d
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,600 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,600 , d ) 45,600 , e ) 48,500
Rationale: "median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.6 so , answer is d ."
Answer: d
Problem: if m and n are positive integers and m ^ 2 + n ^ 2 = 58 , what is the value of m ^ 3 + n ^ 3 ?
Options: a ) 72 , b ) 224 , c ) 370 , d ) 512 , e ) 1,600
Rationale: "you need to integers which squared are equal 58 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 stop . the integers ca n ' t be greater than 7 or we will score above 58 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 the only pair that matches is 7 ^ 2 + 3 ^ 2 = 58 . so 7 ^ 3 + 3 ^ 3 = 370 . answer c . )"
Answer: c
Problem: a circular ground whose radius is 15 metres , has a 1.2 metre - broad garden around it . what is the area of the garden in square metres ?
Options: a ) 118.67
b ) 116.67
c ) 117.67
d ) 120.56
e ) 120.57
Rationale: req . area = ï € [ ( 16.2 ) 2 â € “ ( 15 ) 2 ] = 22 â  „ 7 ã — ( 31.2 ã — 1.2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 ã — 31.2 ã — 1.2 ) / 7 = 117.67 sq m answer c
Answer: c
Problem: rahim bought 65 books for rs . 1160 from one shop and 50 books for rs . 920 from another . what is the average price he paid per book ?
Options: a ) rs . 18.28 , b ) rs . 20 , c ) rs . 18.08 , d ) rs . 28.08 , e ) rs . 38.08
Rationale: average price per book = ( 1160 + 920 ) / ( 65 + 50 ) = 2080 / 115 = rs . 18.08 answer : c
Answer: c
Problem: the ratio of the volumes of two cubes is 512 : 729 . what is the ratio of their total surface areas ?
Options: a ) 1 : 22 , b ) 81 : 12 , c ) 41 : 46 , d ) 41 : 19 , e ) 84 : 12
Rationale: "ratio of the sides = ³ √ 512 : ³ √ 729 = 8 : 9 ratio of surface areas = 82 : 92 = 41 : 46 answer : c"
Answer: c
Problem: x starts a business with rs . 45000 . y joins in the business after 7 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 18 : 5 , c ) 1 : 5 , d ) 3 : 1 , e ) 1 : 1
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 5 = 45 ã — 12 : 30 ã — 5 = 3 ã — 12 : 2 ã — 5 = 18 : 5 answer : option b"
Answer: b
Problem: if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the first part is ?
Options: a ) a ) 426 , b ) b ) 526 , c ) c ) 247 , d ) d ) 204 , e ) e ) 297
Rationale: given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 4 : 9 1 st part = 782 * 6 / 19 = rs . 247 answer : c
Answer: c
Problem: a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , 5 , 6 , and 7 , how many palindromes are possible ?
Options: a ) 35 , b ) 49 , c ) 105 , d ) 255 , e ) 343
Rationale: "there are 7 choices for each of the first three digits . the number of possible palindromes is 7 ^ 3 = 343 . the answer is e ."
Answer: e
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 63.50 , his capital is ?
Options: a ) 24,602 , b ) 28,888 , c ) 24,600 , d ) 24,628 , e ) 24,400
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 63.50 32 x - 31 x = 6350 * 4 x = 25,400 . answer : e"
Answer: e
Problem: in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 5 nches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 35 , e ) 43
Rationale: "his height was = 5 feet 5 inch = 5 + 60 = 65 inch . required % correction = 65 * ( 1.25 - 1 ) * 100 = 20 b"
Answer: b
Problem: a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 6 t seconds , then what is the length of the platform ?
Options: a ) l , b ) 3 l , c ) 5 l , d ) 7 l , e ) 9 l
Rationale: "the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 6 t ( l + p ) / ( l / t ) = 6 t p = 5 l the answer is c ."
Answer: c
Problem: a bus 15 m long is running with a speed of 40 km / hr . in what time will it pass a man who is skateboarding at 8 km / hr in the direction opposite to that in which the car is going ?
Options: a ) 1.125 , b ) 1.5 , c ) 1.75 , d ) 1.25 , e ) 1
Rationale: speed of bus relative to man = 40 + 8 = 48 km / hr . = 48 * 5 / 18 = 40 / 3 m / sec . time taken to pass the man = 5 * 3 / 40 = 1.125 sec . answer : a
Answer: a
Problem: the end of a blade on an airplane propeller is 10 feet from the center . if the propeller spins at the rate of 660 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 150 π , b ) 240 π , c ) 300 π , d ) 480 π , e ) 1,200 π
Rationale: distance traveled in 1 revolution = 2 π r = 2 π 10 / 5280 revolutions in one second = 660 revolutions in 60 seconds ( one minute ) = 660 * 60 total distance traveled = total revolutions * distance traveled in one revolution 660 * 60 * 2 π 10 / 5280 = 150 π a is the answer
Answer: a
Problem: victor gets 92 % marks in examinations . if these are 368 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 400 , d ) 288 , e ) 271
Rationale: "let the maximum marks be m then 92 % of m = 368 ⇒ 92 / 100 × m = 368 ⇒ m = ( 368 × 100 ) / 92 ⇒ m = 36800 / 92 ⇒ m = 400 therefore , maximum marks in the examinations are 400 . answer : c"
Answer: c
Problem: a train running at the speed of 300 km / hr crosses a pole in 15 seconds . what is the length of the train ?
Options: a ) 1200 m , b ) 1250 m , c ) 1300 m , d ) 1350 m , e ) 1450 m
Rationale: "speed = ( 300 * 5 / 18 ) m / sec = ( 250 / 3 ) m / sec length of the train = ( speed x time ) = ( 250 / 3 * 15 ) m = 1250 m . answer : b"
Answer: b
Problem: a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 23788 , d ) 10500 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 6 = 6 months . so there profit ratio = ( 3500 ã — 12 ) : ( 6 x ) = 2 : 3 â ‡ ’ x = 10500 answer : d"
Answer: d
Problem: the population of a village is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 10000 , b ) 12000 , c ) 13000 , d ) 14000 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 × 120 / 100 = 14400 e"
Answer: e
Problem: in a class of 30 students , 5 students did not borrow any books from the library , 12 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 5 , b ) 8 , c ) 15 , d ) 18 , e ) 20
Rationale: the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 32 - 12 = 20 books . answer : e .
Answer: e
Problem: two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 3 hours ?
Options: a ) 2.4 . , b ) 3.6 . , c ) 4.8 . , d ) 5.5 . , e ) 6.4
Rationale: "w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 3 hrs = 4 × rate of each carpenter x time = 4 × 2 / 5 × 3 = 4.8 desks c is the correct answer ."
Answer: c
Problem: mr . kutty has only hens and sheep . if the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep ?
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 6 : 13 , d ) 13 : 6 , e ) none of these
Rationale: let the total number of hens and sheep be x and y respectively . i . e . , x + y = 38 and 2 x + 4 y = 100 ∴ ratio = 13 : 6 answer d
Answer: d
Problem: a boat covers a certain distance downstream in 1 hour , while it comes back in 1.30 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ?
Options: a ) 10 , b ) 13 , c ) 11 , d ) 08 , e ) 15
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 − 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 1 1 ⁄ 2 hour . i . e . , distance travelled downstream in 1 hour = distance travelled upstream in 1 1 ⁄ 2 hour since distance = speed × time , we have ( x + 3 ) × 1 = ( x − 3 ) 3 / 2 ⇒ 2 ( x + 3 ) = 3 ( x − 3 ) ⇒ 2 x + 6 = 3 x − 9 ⇒ x = 6 + 9 = 15 kmph answer is e ."
Answer: e
Problem: if x is a positive number and 1 / 4 the square root of x is equal to 3 x , then x =
Options: a ) 1 / 16 , b ) 12 , c ) 1 / 12 , d ) 144 , e ) 1 / 144
Rationale: "1 / 4 of sqrt ( x ) = 3 x , which means that sqrt ( x ) = 12 x or x = 144 x ^ 2 - > divide by x 1 = 144 x x = 1 / 144 e ."
Answer: e
Problem: a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 15 days starting with sunday is
Options: a ) 280 , b ) 285 , c ) 290 , d ) 295 , e ) 570
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 15 ) = ( 8550 / 15 ) = 570 answer : option e"
Answer: e
Problem: in how many ways can 11 books on english and 9 books on french be placed in a row on a shelf so that two books on french may not be together ?
Options: a ) 220 . , b ) 240 , c ) 260 , d ) 280 , e ) 300
Rationale: we have 11 english and 9 french books , no french books should be adjacent . imagine 11 english books in a row and empty slots like below : * e * e * e * e * e * e * e * e * e * e * e * now if 9 french books would be placed in 12 empty slots , all french books will be separated by english books . so we can ` ` choose ' ' 9 empty slots from 12 available for french books , which is 12 c 9 = 220 . ans : a _________________
Answer: a
Problem: if 35 percent of 400 is 20 percent of x , then x =
Options: a ) 200 , b ) 350 , c ) 700 , d ) 900 , e ) 1,400
Rationale: "5 / 100 ( 400 ) = 2 / 10 ( x ) x = 700 . . answer : c"
Answer: c
Problem: the side of a rhombus is 26 m and length of one of its diagonals is 20 m . the area of the rhombus is ?
Options: a ) 488
b ) 429
c ) 418
d ) 480
e ) 410
Rationale: 262 – 102 = 242 d 1 = 20 d 2 = 48 1 / 2 * 20 * 48 = 480 answer : d
Answer: d
Problem: 80 370 ? 1550 2440 3530
Options: a ) 900 , b ) 840 , c ) 750 , d ) 860 , e ) 960
Rationale: "10 ^ 2 - 20 = 80 20 ^ 2 - 30 = 370 30 ^ 2 - 40 = 860 40 ^ 2 - 50 = 1550 50 ^ 2 - 60 = 2440 60 ^ 2 - 70 = 3530 . answer : d"
Answer: d
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 4 - percent solution ?
Options: a ) 35 , b ) 33 1 / 3 , c ) 21 , d ) 16 2 / 3 , e ) 15
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 4 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 4 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 4 x = 6 since you need a 15 l solution , you must evaporate 21 of the original 50 l solution to get a 4 % solution . answer is c ."
Answer: c
Problem: three coins are tossed . find the probability of at least 1 head and 1 tail ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 7 / 8 , e ) 1 / 8
Rationale: "n ( s ) = 2 ^ 3 = 8 . . . . ( 3 coins tossed ) let e is the event of getting at least 1 head and 1 tail n ( e ) = tth , htt , tht , hht , hth , thh = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 8 = 3 / 4 ans - c"
Answer: c
Problem: 10 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 90 , b ) 98 , c ) 35 , d ) 99 , e ) 80
Rationale: "though 2 * ( 10 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 9 , so he ' ll play 18 matches . similarly , second guy has to play with the rest of 8 as his 2 games with the first guy are already played . so he plays 16 matches . this continues like this and the total matches are 18 + 16 + 14 . . . + 2 18 + 16 + . . . + 2 = 2 ( 9 + 8 + . . . + 1 ) = 2 ( ( 9 * 10 ) / 2 ) = 9 * 10 = 90 . answer : a"
Answer: a
Problem: john is building a rectangular fence around a garden . the length will be 5 feet shorter than its width . if the total area of the garden is 176 square feet , what is the length of the diagonal ( in feet ) ?
Options: a ) between 18 and 19
b ) between 19 and 20
c ) between 20 and 21
d ) between 21 and 22
e ) between 22 and 23
Rationale: to solve this , we first need to set up an equation for the area of the garden . if x is the width , then we have x ( x - 5 ) = 176 . by putting the equation in standard form , we get x ^ 2 - 5 x - 176 = 0 . by using the quadratic formula , we get roots of - 11 and 16 . we know that x is the width , and x - 5 is the length , so by using the roots , we get 16 as the width ( x ) , and 11 as the length ( x - 5 ) . once we have this , we can use the pythagorean theorem to solve for the diagonal . plugging in the length and width , we will get d ^ 2 = 16 ^ 2 + 11 ^ 2 = 256 + 121 = 377 the square root of 377 is less than 20 , since 20 ^ 2 = 400 . going down a number , we can compute 19 ^ 2 = 361 < 377 . therefore , the length of the diagonal must be between 19 and 20 . the correct answer is b .
Answer: b
Problem: divide $ 450 among a , b in the ratio 1 : 4 . how many $ that a get ?
Options: a ) $ 90 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: "sum of ratio terms = 1 + 4 = 5 a = 450 * 1 / 5 = $ 90 answer is a"
Answer: a
Problem: 88 % of 370 + 24 % of 210 - ? = 118
Options: a ) 256 , b ) 258 , c ) 268 , d ) 358 , e ) none of these
Rationale: "let 88 % of 370 + 240 % of 210 - x = 118 then , x = ( 88 / 100 * 370 ) + ( 24 / 100 * 210 ) - 118 - 325.60 + 50.40 - 118 = 376 - 118 = 258 correct option : b"
Answer: b
Problem: a train passes a platform in 22 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 40 , b ) 50 , c ) 60 , d ) 30 , e ) 20
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 12 = > 300 + l = 15 × 22 = 330 = > l = 330 - 300 = 30 meter answer is d ."
Answer: d
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 184 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 434 , e ) 460
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 184 = > 4 x / 10 = 184 = > 4 x = 1840 = > x = 460 . answer : e"
Answer: e
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts four hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 8 , d ) d ) 5.5 , e ) e ) 5
Rationale: "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 4 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 4 + t ) = 40 * t t = 12 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 12 / 60 = 8 hrs time taken by a = 4 + t = 4 + 12 = 16 hrs time taken by k = 8 hrs so k starts 16 - 8 = 8 hrs after a . ( answer c )"
Answer: c
Problem: a and b together can complete work in 5 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 8 , c ) 15 , d ) 6 , e ) 7
Rationale: "explanation : ( a + b ) one day work = 1 / 5 now a does half of the work in 3 days so a can complete the whole work in 6 days a ’ s one day work = 1 / 6 b ’ s one day work = 1 / 5 - 1 / 6 = 1 / 30 b alone can complete the work in 30 days so half of the work in 15 days answer : option c"
Answer: c
Problem: a rectangular plot measuring 15 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 46 m , b ) 26 m , c ) 26 m , d ) 56 m , e ) 25 m
Rationale: "perimeter of the plot = 2 ( 15 + 50 ) = 130 m no of poles = 130 / 5 = 26 m answer : b"
Answer: b
Problem: if a train , travelling at a speed of 270 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 281 m , b ) 325 m , c ) 117 m , d ) 375 m , e ) 350 m
Rationale: "d d = 270 * 5 / 18 * 5 = 375 m"
Answer: d
Problem: a certain car uses one gallon of gasoline every 36 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 40 %
Rationale: "4 miles on the highway = 4 / 36 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 36 + 4 / 20 = 14 / 45 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 14 / 45 - 8 / 36 ) / ( 8 / 36 ) = 0.40 . answer : e ."
Answer: e
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along theoundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 145010 m , b ) 146400 m , c ) 153600 m , d ) 164500 m , e ) 167550 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m c"
Answer: c
Problem: the calendar of the year 2060 can be used again in the year ?
Options: a ) 2081 , b ) 2083 , c ) 2088 , d ) 1971 , e ) 1973
Rationale: "explanation : given year 2060 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2060 + 28 = 2088 answer : c"
Answer: c
Problem: mixture a is 40 percent alcohol , and mixture b is 80 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 50 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 1.5 , b ) 1.7 , c ) 2.3 , d ) 2.5 , e ) 2.4
Rationale: "( 80 - 50 ) / ( 50 - 40 ) = qa / qb 30 / 10 = qa / qb 3 / 1 = qa / qb qa = ( 3 / 5 ) * 4 = 12 / 5 = 2.4 approx answer : e"
Answer: e
Problem: the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 75 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75 % , b ) 80 % , c ) 145 % , d ) 150 % , e ) 180 %
Rationale: "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 75 percent to make square c length of each side of square c = 1.75 * 20 = 35 area of c = 35 ^ 2 = 1225 difference in areas of c and cummulative areas of a and b = 1225 - ( 400 + 100 ) = 725 percent is the area of square c greater than the sum of the areas of squares a and b = ( 725 / 500 ) * 100 % = 145 % answer c"
Answer: c
Problem: the temperature of a certain cup of coffee 15 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 15 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 15 a ) + 60 60 = 120 * ( 2 ^ - 15 a ) 60 / 120 = 2 ^ - 15 a 1 / 2 = 2 ^ - 15 a 2 ^ - 1 = 2 ^ - 15 a - 1 = - 15 a 1 / 15 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 15 * 30 ) + 60 f = 120 * ( 2 ^ - 2 ) + 60 f = 120 * ( 1 / 2 ^ 2 ) + 60 f = 120 * 1 / 4 + 60 f = 30 + 60 = 90 answer e !"
Answer: e