regisss/math_qa huggingface dataset:
Problem: a certain company ’ s profit in 1996 was 10 percent greater than its profit in 1995 , and its profit in 1997 was 20 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 32 % , d ) 35 % , e ) 38 %
Rationale: profit in 1995 - 100 profit in 1996 - 110 % increae profit in 1997 in comparison to 1995 = 10 + 110 * 20 % = 32 correct option : c
Answer: c
Problem: if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 11 .
Options: a ) 8 , b ) 5 , c ) 1 , d ) 3 , e ) 4
Rationale: "6 * 15 * 11 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 11 + 1 ) = ( √ 8 * 18 ) / 12 = ( √ 144 ) / 12 = 12 / 124 = 1 . answer is c"
Answer: c
Problem: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 8 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 8 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2400 . hence , ( r - p ) = ( 2400 - 900 ) = 1500 answer : b"
Answer: b
Problem: in a caravan , in addition to 50 hens , there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads in the caravan , the number of keepers is
Options: a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 20
Rationale: explanation : let number of keepers be x . then , total number of feet = 2 x 50 + 4 x 45 + 4 x 8 + 2 x = 2 x + 312 . total number of heads = 50 + 45 + 8 + x = 103 + x . therefore ( 2 x + 312 ) = ( 103 + x ) + 224 or x = 15 . answer : d
Answer: d
Problem: a 1500 m long train crosses a tree in 120 sec , how much time will it take to pass a platform 500 m long ?
Options: a ) 288 , b ) 160 , c ) 188 , d ) 188 , e ) 12
Rationale: "l = s * t s = 1500 / 120 s = 12.5 m / sec . total length ( d ) = 2000 m t = d / s t = 2000 / 12.5 t = 160 sec answer : b"
Answer: b
Problem: n is a positive integer . when n + 1 is divided by 6 , the remainder is 4 . what is the remainder when n is divided by 2 ?
Options: a ) 6 , b ) 5 , c ) 1 , d ) 3 , e ) 2
Rationale: n + 1 = 6 a + 4 i . e . n + 1 = 10 , 16 , 22 , 28 , . . . etc . i . e . n = 9 , 15 , 21 , 27 , . . . etc . when n is divided by 2 remainder is always 1 answer : c
Answer: c
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 2999 , b ) 1350 , c ) 2677 , d ) 2898 , e ) 2787
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 2 = rs . 1350 answerb"
Answer: b
Problem: if 9 / ( 5 + 3 / x ) = 1 , then x =
Options: a ) 3 , b ) 1 , c ) 3 / 4 , d ) - 1 / 3 , e ) - 3
Rationale: the expression 9 / ( 5 + 3 / x ) = 1 should have been equal to something . if 9 / ( 5 + 3 / x ) = 1 = > 9 x / ( 5 x + 3 ) = 1 = > 9 x = 5 x + 3 = > 4 x = 3 = > x = 3 / 4 correct option : c
Answer: c
Problem: if price of t . v set is reduced by 25 % , then its sale increases by 75 % , find net effect on sale value
Options: a ) 31 , b ) 32 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 25 + 75 + ( - 25 * 75 ) / 100 = - 25 + 75 - 19 = 31 answer : a"
Answer: a
Problem: 25 , 50 , 100 , 175 , 275 , ( . . . . )
Options: a ) 400 , b ) 300 , c ) 425 , d ) 450 , e ) 325
Rationale: "explanation : the pattern is 25 , 50 , 75 , 100 , etc . hence 125 = 400 answer : a"
Answer: a
Problem: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 9 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 19 , d ) 29 , e ) 39
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 9 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 9 * ( 2 / 3 ) ) days = > 20 days answer : b"
Answer: b
Problem: kathleen can paint a room in 3 hours , and anthony can paint an identical room in 4 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?
Options: a ) 8 / 15 , b ) 4 / 3 , c ) 15 / 8 , d ) 24 / 7 , e ) 15 / 4
Rationale: "( 1 / 3 + 1 / 4 ) t = 2 t = 24 / 7 answer : d"
Answer: d
Problem: how many prime numbers are between 25 / 8 and 213 / 6 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "25 / 8 = 4 - 213 / 6 = 36 - prime numbers between 4 and 36 are 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , and 31 - sign signifies that the number is marginally less . answer d"
Answer: d
Problem: on the number line , the number p is twice as many units from - 2 as - 2 is from 4 . if p is less than – 2 , what is the value of p ?
Options: a ) – 14 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: "distance between - 2 and 4 = 6 since number p is twice as many units from - 2 as - 2 is from 4 , therefore p can be - 14 since , p is less than - 2 , the value of p = - 14 answer a"
Answer: a
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 1 : 2 and 3 : 1 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 18 : 13 , b ) 16 : 13 , c ) 19 : 13 , d ) 14 : 11 , e ) 13 : 11
Rationale: "vessel a = 300 gallons - - > milk = 100 , water = 200 ; vessel b = 500 gallons - - > milk = 375 , water = 125 ; vessel a + b = 800 gallons - - > milk = 475 , water 325 . the ratio = 475 / 325 - - > 19 / 13 answer : c"
Answer: c
Problem: a bus travels first half distance between two places with a speed of 40 kmph and the rest half distance with a speed of 60 kmph . the average speed of the bus is ?
Options: a ) 48 kmph , b ) 78 kmph , c ) 28 kmph , d ) 18 kmph , e ) 98 kmph
Rationale: explanation : we know that speed = distance traveled / time taken let the total distance traveled by the car is 2 x km . then time taken by it to cover first half is hour . and for second half is hour . then average speed = total distance travelled / total time taken . i . e . = > = 48 kmph . answer : a
Answer: a
Problem: in a hostel there were 100 students . to accommodate 20 more students the average is decreased by rupees 5 . but total expenditure increased by rs . 400 . find the total expenditure of the hostel now ?
Options: a ) 54888 , b ) 2777 , c ) 5400 , d ) 1278 , e ) 2881
Rationale: "100 x + 400 = 12 ( x – 5 ) x = 50 100 * 50 + 400 = 5400 answer : c"
Answer: c
Problem: the ratio between the number of passengers travelling by i and ii class between the two railway stations is 1 : 50 , whereas the ratio of i and ii class fares between the same stations is 3 : 1 . if on a particular day rs . 1,325 were collected from the passengers travelling between these stations , then what was the amount collected from the ii class passengers ?
Options: a ) rs . 750 , b ) rs . 1000 , c ) rs . 850 , d ) rs . 1250 , e ) none of these
Rationale: let x be the number of passengers and y be the fare taken from passengers . 3 xy + 50 xy = 1325 = > xy = 25 amount collected from ii class passengers = 25 × 50 = rs . 1250 . answer : d
Answer: d
Problem: a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 38,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 15960 , c ) 14900 , d ) 14300 , e ) 14000
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 38000 × 21 / 50 = 15960 answer is b"
Answer: b
Problem: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 4.0 = ?
Options: a ) 1.07 , b ) 1.0 , c ) - 1.065 , d ) 1.71 , e ) 2.71
Rationale: "dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 1.065 answer c"
Answer: c
Problem: if â € œ * â €  is called â € œ + â €  , â € œ / â €  is called â € œ * â €  , â € œ - â €  is called â € œ / â €  , â € œ + â €  is called â € œ - â €  . 120 / 40 â € “ 30 * 20 - 5 = ?
Options: a ) 178.5 , b ) 156.6 , c ) 160.4 , d ) 163.6 , e ) 164.1
Rationale: "explanation : given : 120 / 40 â € “ 30 * 20 - 5 = ? substituting the coded symbols for mathematical operations , we get , 120 * 40 / 30 + 20 / 5 = ? 120 * 1.33 + 4 = ? 159.6 + 4 = 163.6 answer : d"
Answer: d
Problem: the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle . the shorter side of the triangle is 7 centimeters less than the longer side . find the length of the hypotenuse .
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: let a and b be the two sides of the triangle such that a is longer than b . the statement ` ` the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle ' ' may be fomulated by h = a + 2 or a = h - 2 the statement ` ` the shorter side of the triangle is 7 centimeters less than the longer side ' ' may be formulated . b = a - 7 or b = ( h - 2 ) - 7 = h - 9 we now use pythagora ' s theorem to write a third equation h 2 = a 2 + b 2 substitute a by h - 2 and b by h - 9 in the above equation to obtain an equation in one variable only . h 2 = ( h - 2 ) 2 + ( h - 9 ) 2 simplify and rewrite the above equation in standard form . h 2 - 22 h + 85 = 0 solve for h . h = 5 and h = 17 . only the solution h = 17 gives a and b positive and it is the length of the hypotenuse of the triangle . answer a
Answer: a
Problem: how long does a train 120 m long running at the speed of 70 km / hr takes to cross a bridge 145 m length ?
Options: a ) 13.9 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 13.9 sec , e ) 47.98 sec
Rationale: "speed = 70 * 5 / 18 = 19 m / sec total distance covered = 120 + 145 = 265 m . required time = 265 / 19 = 13.9 sec . answer : d"
Answer: d
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 650 , what is the least possible value of n ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "650 = 2 * 5 * 5 * 13 so the least value forncan be 13 . d"
Answer: d
Problem: a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?
Options: a ) 70 feet , b ) 52 feet , c ) 32 feet , d ) 12 feet , e ) 55 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 30 * breadth = 600 = > breadth = 20 feet area to be fenced = 2 b + l = 2 * 20 + 30 = 70 feet answer : option a"
Answer: a
Problem: two employees x and y are paid a total of rs . 560 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 254 , b ) s . 284 , c ) s . 290 , d ) s . 304 , e ) s . 380
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 560 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 560 ⇒ y [ 12 / 10 + 1 ] = 560 ⇒ 22 y / 10 = 560 ⇒ 22 y = 5600 ⇒ y = 5600 / 22 = rs . 254 ( approx ) a )"
Answer: a
Problem: calculate the sum of first 28 natural numbers .
Options: a ) 426 , b ) 406 , c ) 401 , d ) 409 , e ) 405
Rationale: "solution we know that ( 1 + 2 + 3 + . . . . . + 28 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 28 ) = ( 28 × 29 / 2 ) = 406 . answer b"
Answer: b
Problem: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land on the same side each time ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 16 , d ) 1 / 2 , e ) 1 / 32
Rationale: "must be either 4 tails or 4 heads 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 1 / 16 + 1 / 16 = 1 / 8 answer : a"
Answer: a
Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 3 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 3 ) . what is its perimeter ?
Options: a ) 32 , b ) 36 , c ) 38 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 4 lm = 10 kl = using distance formula 10 jm = using distance formula 8 sum of all is 32 a"
Answer: a
Problem: the c . p of 8 books is equal to the s . p of 16 books . find his gain % or loss % ?
Options: a ) 60 % , b ) 50 % , c ) 70 % , d ) 90 % , e ) 55 %
Rationale: "explanation : 8 cp = 16 sp 16 - - - 8 cp loss 100 - - - ? = > 50 % loss answer : b"
Answer: b
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 5000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 32000 , d ) 35000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 5000 = > total profit = 5000 * 7 = 35000 . answer : option d"
Answer: d
Problem: a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 1 day . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7
Rationale: b work 1 / 8 * 1 = 1 / 8 remaining work = 1 - 1 / 8 = 7 / 8 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocal 7 / 8 * remaining work = 8 / 7 * 1 / 4 = 2 / 7 answer : b
Answer: b
Problem: the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 4 : 3 . someone removes 6 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the weights of the items in the suitcase are 7 k , 4 k , and 3 k . if removing 6 pounds of clothes doubles the ratio of books to clothes , then 6 pounds represents half the weight of the clothes . 2 k = 6 pounds and then k = 3 pounds . the electronics weigh 3 ( 3 ) = 9 pounds . the answer is e ."
Answer: e
Problem: a bag consists of 50 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 9 / 10
Rationale: "bag consists of 50 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 50 - 5 - 9 = 36 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 50 + 36 / 50 = 45 / 50 = 9 / 10 hence , answer will be e ."
Answer: e
Problem: how many integers between 100 and 200 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 46 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "the total numbers between 100 and 200 , inclusive , is 101 . 3 * 34 = 102 and 3 * 66 = 198 so the number of multiples of 3 is 33 . 5 * 20 = 100 and 5 * 40 = 200 so the number of multiples of 5 is 21 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 13 = 195 so the number of multiples of 15 is 7 . thus the total number is 101 - 33 - 21 + 7 = 54 . the answer is e ."
Answer: e
Problem: for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 22 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 7
Rationale: mean = ( x + x + 2 + x + 4 + x + 7 + x + 22 ) / 5 = ( 5 x + 35 ) / 5 = x + 7 median = x + 4 thus mean - median = x + 7 - ( x + 4 ) = 3 answer = d
Answer: d
Problem: pavan travelled for 11 hours . he covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph . find the distance travelled by pavan ?
Options: a ) 398 km , b ) 892 km , c ) 387 km , d ) 300 km , e ) 230 km
Rationale: "let the distance travelled be x km . total time = ( x / 2 ) / 30 + ( x / 2 ) / 25 = 11 = > x / 60 + x / 50 = 11 = > ( 5 x + 6 x ) / 300 = 11 = > x = 300 km answer : d"
Answer: d
Problem: 3 / 4 of 1 / 2 of 2 / 5 of 5100 = ?
Options: a ) 392 , b ) 229 , c ) 765 , d ) 493 , e ) 540
Rationale: "c 765 ? = 5100 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 765"
Answer: c
Problem: in order to obtain an income of rs . 900 from 20 % stock at rs . 102 , one must make an investment of
Options: a ) rs . 6000 , b ) rs . 4590 , c ) rs . 4560 , d ) rs . 4500 , e ) rs . 4570
Rationale: "explanation : market value = rs . 102 . required income = rs . 900 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 20 ( ie , 20 % of the face value 100 ) , investment = rs . 102 to obtain rs . 900 , investment = 102 / 20 ã — 900 = rs . 4590 answer : option b"
Answer: b
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 10 ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 11 / 9 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 10 + 1 ) / ( 10 - 1 ) = 11 / 9 = 11 / 9 answer : d"
Answer: d
Problem: if the price of a certain bond on may 1 st was 1 / 2 the price of the bond on june 1 st and the price of the bond on july 1 st was 50 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 75 % , c ) 120 % , d ) 133 1 / 3 % , e ) 160 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 1 / 2 * 12 = 6 ; the price on july 1 st = 6 * 1.5 = 9 . the average price of the bond on may 1 st and july 1 st = ( 6 + 9 ) / 2 = 7.5 . the price of the bond on june 1 st ( 12 ) is 8 / 5 times ( 160 % ) the average price of the bond on may 1 st and july 1 st . answer : e ."
Answer: e
Problem: an investment compounds annually at an interest rate of 33.34 % what is the smallest investment period by which time the investment will more than triple in value ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 4
Rationale: "assume initial amount is x annual interest is 34.1 % so after 1 year the amount will become x * ( 100 + 33.34 ) / 100 = > x * 4 / 3 now we need to find n for x * ( 4 / 3 ) ^ n = 3 x or in other words n = 4 e"
Answer: e
Problem: a no . when divided by 220 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 67 ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 11 , e ) 14
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Problem: a and b ’ s salaries together amount to rs . 3,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is b ’ s salary ?
Options: a ) 777 , b ) 750 , c ) 789 , d ) 776 , e ) 881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 3000 4 b = 3000 = > b = 750 answer b"
Answer: b
Problem: ritesh and co . generated revenue of rs . 1,700 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 18.38 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 1,700 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1700 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1700 . = > 13,600 . hence , the total revenue by end of 2007 is rs . 13,600 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 13600 ) × 100 . = > 18.38 % . answer : a"
Answer: a
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 1000 , b ) 3889 , c ) 8908 , d ) 3780 , e ) 2709
Rationale: "1120 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1000 answer : a"
Answer: a
Problem: the radius of a cylindrical vessel is 7 cm and height is 5 cm . find the whole surface of the cylinder ?
Options: a ) 281 , b ) 528 , c ) 440 , d ) 767 , e ) 1981
Rationale: "r = 7 h = 5 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 12 ) = 528 answer : b"
Answer: b
Problem: a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 5400 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 15000 , c ) rs 16000 , d ) rs 17000 , e ) none of these
Rationale: "explanation : s . i . = p ∗ r ∗ t / 100 = > p = s . i . ∗ 100 / r ∗ t = > p = 5400 ∗ 100 / 12 ∗ 3 = rs 15000 option b"
Answer: b
Problem: in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 12 % . what is population of after 2 year .
Options: a ) 139 , b ) 141 , c ) 142 , d ) 143 , e ) 144
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 11 % so total man = 150 * . 88 = 132 women will be = 175 - 132 = 43 so population after two years = [ 135 ^ 2 + 43 ^ 2 ] ^ . 5 = 138.8 = 139 so population after two year = 139 answer : a"
Answer: a
Problem: evaluate : 58 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 50 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 58 - 12 * 3 * 2 = 58 - 8 = 50 correct answer b"
Answer: b
Problem: jenny has recently moved house and is working out her optimal commute . she can take an indirect route which involves taking a bus for 1 mile and then walk 0.75 miles . or she can take a direct route and walk for 1.5 miles and this takes her 30 minutes . what is the most amount time that the bus journey can take for jenny to be indifferent between the two routes assuming travel time is her only concern ?
Options: a ) 5 minutes , b ) 10 minutes , c ) 15 minutes , d ) 20 minutes , e ) 25 minutes
Rationale: if jenny can walk 1.5 miles in 30 minutes , then she can talk 0.75 miles in half the time i . e . 15 minutes . for jenny to be indifferent between the two routes , the two journeys must have the same travel time . the direct route has a travel time of 30 minutes ( walking ) . the indirect route has a travel time of 15 minutes ( walking ) plus the bus journey . for the two routes to be the same the bus journey must take 15 minutes ( 30 - 15 ) . answer : c
Answer: c
Problem: seller selling an apple for rs . 15 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 18 , e ) 20
Rationale: "sp = 15 loss = cp 16 loss = cp − sp = cp − 15 ⇒ cp 16 = cp − 15 ⇒ 15 cp 16 = 15 ⇒ cp 16 = 1 ⇒ cp = 16 c"
Answer: c
Problem: if the volume of a cube is x ^ 3 cubic units , what is the number of square units in the surface area of the cube ?
Options: a ) x ^ 2
b ) x ^ 3
c ) x ^ 6
d ) 6 x ^ 2
e ) 6 x ^ 3
Rationale: the question basically asks you to calculate the surface area of the cube . volume of the cube = x ^ 3 this means each side of the cube = x hence area of each side = x ^ 2 total surfaces in a cube = 6 total surface area = 6 * x 2 correct option : d
Answer: d
Problem: the area of a square field is 28808 sq m . how long will a lady take to cross the field diagonally at the rate of 7.2 km / hr ?
Options: a ) 2.5 min , b ) 3 min , c ) 2 min , d ) 4 min , e ) 4.5 min
Rationale: "area of a square field = 28808 sq m let the side of square = a a ^ 2 = 28808 = > a = 169.73 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 169.73 = 240 speed of lady = 7.2 km / hour = 7200 m / hour = 120 m / min time taken by lady to cross the field diagonally = 240 / 120 = 2 min answer c"
Answer: c
Problem: if a town of 35,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 36000 , b ) b . 37000 , c ) c . 38000 , d ) d . 39000 , e ) e . 40000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Problem: there are 12 slate rocks , 17 pumice rocks , and 8 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 5 / 36 , b ) 7 / 64 , c ) 9 / 83 , d ) 11 / 111 , e ) 13 / 135
Rationale: "12 / 37 * 11 / 36 = 11 / 111 the answer is d ."
Answer: d
Problem: one day a car rental agency rented 3 / 4 of its cars , including 5 / 6 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 13 / 20 , b ) 11 / 15 , c ) 7 / 10 , d ) 4 / 7 , e ) 2 / 5
Rationale: "the cars with cd players which were not rented is ( 1 / 6 ) ( 3 / 5 ) = 1 / 10 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 1 / 10 ) / ( 1 / 4 ) = 2 / 5 the answer is e ."
Answer: e
Problem: how many words , with or without meaning , can be formed using all letters of the word red using each letter exactly once ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: the word red has exactly 3 letters which are all different . therefore the number of words that can be formed = number of permutations of 3 letters taken all at a time . = p ( 3 , 3 ) = 3 ! = 3 x 2 × 1 = 6 answer : a
Answer: a
Problem: of the 65 cars on a car lot , 30 have air - conditioning , 45 have air bag , and 12 have both air - conditioning and air bag . how many of the cars on the lot have neither air - conditioning nor air bag ?
Options: a ) 2 , b ) 8 , c ) 10 , d ) 15 , e ) 18
Rationale: "total - neither = all air conditioning + all air bags - both or 65 - neither = 30 + 45 - 12 = 63 . = > neither = 2 , hence c . answer : c"
Answer: c
Problem: a and b can do a piece of work in 2 days . with the help of c they finish the work in 1 days . c alone can do that piece of work in ?
Options: a ) 1.5 days , b ) 4 days , c ) 3 days , d ) 1 day , e ) 2 days
Rationale: c = 1 / 1 – 1 / 2 = 1 / 2 = > 2 days answer : e
Answer: e
Problem: four 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 ) 5 , b ) 3 , c ) 4 , d ) 6 , e ) 1
Rationale: "rate of one machine = 1 job / ( 20 * 4 ) days let x = number of machines needed to complete the job in 10 days 1 / ( 4 * 20 ) * 10 * x = 1 job x = 8 8 - 4 = 4 answer : c"
Answer: c
Problem: a car gets 32 miles to the gallon . if it is modified to use a solar panel , it will use only 80 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?
Options: a ) 84 , b ) 88 , c ) 92 , d ) 96 , e ) 100
Rationale: originally , the distance the car could go on a full tank was 12 * 32 = 384 miles . after it has been modified , the car can go 32 / 0.8 = 40 miles per gallon . on a full tank , the car can go 12 * 40 = 480 miles , thus 96 miles more . the answer is d .
Answer: d
Problem: john bought 9.25 m of cloth for $ 434.75 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 58 , d ) 56 , e ) 54
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 434.75 cost per metre = 434.75 ÷ 9.25 the cost of the cloth per metre = $ 47 answers : b"
Answer: b
Problem: the average of 60 results is 40 and the average of other 40 results is 60 . what is the average of all the results ?
Options: a ) 24 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: "answer sum of 100 result = sum of 60 result + sum of 40 result . = 60 x 40 + 40 x 60 = 4800 / 100 correct option : c"
Answer: c
Problem: 3 , 7,12 , 18,25 , . . . . . . . . . . . . . . 6 th terms
Options: a ) 43 , b ) 53 , c ) 63 , d ) 33 , e ) 78
Rationale: "3 + 4 = 7 7 + 5 = 12 12 + 6 = 18 18 + 7 = 25 25 + 8 = 33 answer : d"
Answer: d
Problem: a person was asked to state his age in years . his reply was , ` ` take my age 3 years hence , multiply it by 4 and subtract 4 times my age 3 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 92 , c ) 27 , d ) 24 , e ) 19
Rationale: explanation : let the present age of person be x years . then , 4 ( x + 3 ) - 4 ( x - 3 ) = x < = > ( 4 x + 12 ) - ( 4 x - 12 ) = x < = > x = 24 . . answer : d
Answer: d
Problem: there are cats got together and decided to kill the mice of 999984 . 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 ) 996,1004 , d ) 791,1009 , e ) 931,1009
Rationale: "999984 can be written as 1000000 â € “ 16 = 10002 â € “ 42 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 4 ) * ( 1000 - 4 ) = ( 1004 ) * ( 996 ) given that number of cats is less than number if mice . so number of cats is 996 and number of mice were 1004 answer c"
Answer: c
Problem: 100 kg of an alloy a is mixed with 200 kg of alloy b . if alloy a has lead and tin in the ratio 5 : 3 and alloy b has tin and copper in the ratio 2 : 3 , then the amount of tin in the new alloy is ?
Options: a ) 100.6 kg , b ) 120.3 kg , c ) 117.5 kg , d ) 110.8 kg , e ) 114 kg
Rationale: "quantity of tin in 100 kg of a = 100 * 3 / 8 = 37.5 kg quantity of tin in 200 kg of b = 200 * 2 / 5 = 80 kg quantity of tin in the new alloy = 37.5 + 80 = 117.5 kg answer is c"
Answer: c
Problem: a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 1 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 30 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 13 , b ) 18 , c ) 12 , d ) 15 , e ) 17
Rationale: "total vehicle = 1 / 3 of speedster + 2 / 3 of others . speedster convertibles = 1 / 3 total vehicle * 4 / 5 given : 2 / 3 constitutes 30 vehicles . hence 1 / 3 constitutes 15 speedster convertibls = 15 * 4 / 5 = 12 c"
Answer: c
Problem: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 35 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 18 , d ) 45 , e ) 01
Rationale: "explanation : as there is meal for 70 adults and 35 have their meal , the meal left can be catered to 35 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 35 adults = 45 children hence , the meal can be catered to 45 children . answer : d"
Answer: d
Problem: the monthly rent of a shop of dimension 10 feet × 10 feet is rs . 1300 . what is the annual rent per square foot of the shop ?
Options: a ) 43 , b ) 156 , c ) 68 , d ) 87 , e ) 92
Rationale: "sol . monthly rent per square feet = 1300 / ( 10 * 10 ) = 13 & annual rent per square feet = 12 * 13 = 156 answer : b"
Answer: b
Problem: a candidate got 35 % of the votes polled and he lost to his rival by 2280 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 2665 , d ) 2888 , e ) 7600
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2280 100 % - - - - - - - - - ? = > 7600 answer : e"
Answer: e
Problem: it takes 3 workers a total of 9 hours to build a giant machine with each worker working at the same rate . if 3 workers start to build the machine at 11 : 00 am , and one extra worker per hour is added beginning at 2 : 00 pm , at what time will the machine be complete ?
Options: a ) 5 : 15 , b ) 5 : 26 , c ) 5 : 37 , d ) 5 : 48 , e ) 5 : 59
Rationale: "3 workers build 1 / 9 of a machine in one hour . 1 worker builds 1 / 27 of a machine in one hour . in the first 3 hours , 3 workers build 3 * ( 1 / 27 ) * 3 = 9 / 27 of a machine from 2 : 00 to 3 : 00 , 4 workers build another 4 / 27 . the total is 13 / 27 . from 3 : 00 to 4 : 00 , 5 workers build another 5 / 27 . the total is 18 / 27 . from 4 : 00 to 5 : 00 , 6 workers build another 6 / 27 . the total is 24 / 27 . to build another 3 / 27 , 7 workers need ( 3 / 7 ) * 60 minutes which is about 26 minutes . the machine is complete at about 5 : 26 . the answer is b ."
Answer: b
Problem: the ratio of the volumes of a cube to that of the sphere which will fit inside the cube is ?
Options: a ) 6.862 kg
b ) 6.838 kg
c ) 6.632 kg
d ) 6.832 kg
e ) 6.834 kg
Rationale: 52 * 40 * 29 = 60320 48 * 36 * 27 = 46650 - - - - - - - - - - - - 13664 13664 * 1 / 2 = 6832 = > 6.832 kg answer : d
Answer: d
Problem: a and b start walking towards each other at 1 pm at speed of 5 kmph and 7 kmph . they were initially 24 km apart . at what time do they meet ?
Options: a ) 4 pm , b ) 6 pm , c ) 3 pm , d ) 10 pm , e ) 5 pm
Rationale: "time of meeting = distance / relative speed = 24 / 7 + 5 = 24 / 12 = 2 hrs after 1 pm = 3 pm answer is c"
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 27 seconds . what is the length of the train ?
Options: a ) 186 m , b ) 176 m , c ) 450 m , d ) 150 m , e ) 765 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 27 ) m = 450 m . answer : c"
Answer: c
Problem: fresh grapes contain 75 % by weight while dried grapes contain 25 % water by weight . what is the weight of dry grapes available from 200 kg of fresh grapes ?
Options: a ) 40.00 kg , b ) 45.50 kg , c ) 66.67 kg , d ) 80.56 kg , e ) 90.00 kg
Rationale: "from the question we know : 200 kg * 75 % = 150 kg of water in the fresh grapes 200 kg - 150 kg of water = 50 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 25 % of the weight of the dry graps is water and we know that 50 kg is non - water mass we can set up the following equation : x = 1 / 4 ( x ) + 50 kg 3 / 4 ( x ) = 50 kg x = 66.67 kg answer - c"
Answer: c
Problem: the ratio of the volumes of two cubes is 1000 : 3375 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 4 : 9 , c ) 729 : 1331 , d ) 27 : 121 , e ) none of these
Rationale: "ratio of the sides = â ³ â ˆ š 1000 : â ³ â ˆ š 3375 = 10 : 15 ratio of surface areas = 10 ^ 2 : 15 ^ 2 = 100 : 225 = 4 : 9 answer : b"
Answer: b
Problem: a man goes into a barbershop and gets a $ 15 haircut . he pays the barber with a $ 20 bill , but the barber does n ' t have change because it is an especially slow day . the barber goes to the flower shop next to his own and trades the $ 20 bill for a $ 10 dollar bill and two $ 5 bills . then he gives the man his $ 5 in change . later the lady from the flower shop confronts the barber and tells him that the $ 20 bill he gave her was counterfeit . the barber agrees and he gives the lady a different $ 20 bill . later that day he tries to figure out how much money he lost . what did he lose ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 12 , d ) $ 15 , e ) $ 20
Rationale: he lost $ 5 . the lady from the flower shop gave him $ 20 in change , but eventually got $ 20 back . she broke even . the man who got the haircut gave the barber nothing ( except counterfeit money ) but got $ 5 back from the barber . so the barber lost only $ 5 , and gave a free haircut .
Answer: a
Problem: if the cost price of 72 articles is equal to the selling price of 60 articles , then what is the percent profit ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "let x be the cost price of one article . let y be the selling price of one article . 60 y = 72 x y = 1.2 x the answer is c ."
Answer: c
Problem: of all the homes on gotham street , 1 / 3 are termite - ridden , and 5 / 8 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 8
Rationale: "the fraction of homes which are termite - infested but not collapsing is 3 / 8 * 1 / 3 = 1 / 8 the answer is e ."
Answer: e
Problem: what will be the compound interest on a sum of rs . 22,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 8908.42 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 22000 * ( 1 + 12 / 100 ) 3 ] = 22000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 30908.42 c . i . = ( 30908.42 - 22000 ) = rs . 8908.42 answer : a"
Answer: a
Problem: of the votes cast on a certain proposal , 68 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
Options: a ) 300 , b ) 340 , c ) 380 , d ) 420 , e ) 460
Rationale: "let x be the total number of votes cast . 0.6 x = 0.4 x + 68 0.2 x = 68 x = 340 the answer is b ."
Answer: b
Problem: a box is in the shape of a semicircle with a radius of 12 . what is the approximate perimeter of the semicircle ?
Options: a ) 54
b ) 62
c ) 25
d ) 34
e ) 60
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 12 + 2 * 12 = 61.68 approximately 62 answer b
Answer: b
Problem: a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates x apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: "number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates x / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c"
Answer: c
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 4 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 120
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 5 x + 2 / 3 x + 4 x - 13 / 15 x = 4 2 / 15 x = 4 = > so x = ( 15 / 2 ) * 4 = 30 km answer a"
Answer: a
Problem: a tree of height 36 m is on one edge of a road broke at a certain height . it fell in such a way that the top of the tree touches the other edge of the road . if the breadth of the road is 12 m , then what is the height at which the tree broke ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree . from the diagram , ( 36 − x ) 2 = x 2 + 122 ( 36 − x ) 2 = x 2 + 122 ⇒ 1296 − 72 x + x 2 = x 2 + 144 ⇒ 1296 − 72 x + x 2 = x 2 + 144 ⇒ 72 x = 1296 − 144 ⇒ 72 x = 1296 − 144 ⇒ x = 16 answer : a
Answer: a
Problem: if y is the smallest positive integer such that 3,675 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 12
Rationale: "i just tried plugging in the numbers and found out that 12 * 3675 = 44 , 100 , which is a square of 210 e"
Answer: e
Problem: if a person walks at 16 km / hr instead of 12 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 , b ) 65 , c ) 70 , d ) 61 , e ) 60
Rationale: "let the actual distance traveled be x km . then , x / 12 = ( x + 20 ) / 16 x - 60 = > x = 60 km . answer : e"
Answer: e
Problem: a man is 29 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 27 years , e ) 16 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 29 ) + 2 = 2 ( x + 2 ) x + 31 = 2 x + 4 x = 27 . answer : d"
Answer: d
Problem: the average of 25 results is 18 . the average of first 12 of them is 10 and that of last 12 is 20 . find the 13 th result ?
Options: a ) 60 , b ) 75 , c ) 90 , d ) 100 , e ) 110
Rationale: 13 th result = sum of 25 results - sum of 24 results = 18 * 25 - 12 * 10 - 12 * 20 = 450 - 120 - 240 = 90 answer is c
Answer: c
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 36 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) a ) 5 , b ) b ) 8 , c ) c ) 6 , d ) d ) 2 , e ) e ) 1
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 36 kg joins the group , total weight of boys = 30 x + 36 so 30 x + 36 = 31 ( x + 1 ) = > x = 5 . answer : a"
Answer: a
Problem: a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 685 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 2 , d ) 17 , e ) 19
Rationale: "30 * 25 = 750 685 - - - - - - - - - - - 65 25 + 7.50 = 32.5 62 / 32.5 = 2 c"
Answer: c
Problem: a box measuring 72 inches long by 48 inches wide by 24 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 17 , b ) 18 , c ) 54 , d ) 108 , e ) 162
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 8 is the biggest number that could divide all three , 72 , 48 and 24 . thus side of cube must be 8 , and total number of cubes = 72 / 8 * 48 / 8 * 24 / 8 = 162 ans e it is ."
Answer: e
Problem: 80 370 860 1550 2440 ?
Options: a ) 900 , b ) 840 , c ) 750 , d ) 860 , e ) 3530
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 : e"
Answer: e
Problem: if the cost price of 12 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 40 % gain , d ) 40 % loss , e ) 52 % loss
Rationale: "explanation : 12 cp = 25 sp cost price cp = 25 selling price sp = 12 formula = ( sp - cp ) / cp * 100 = ( 12 - 25 ) / 25 * 100 = 52 % loss answer : option e"
Answer: e
Problem: the cost of an article is decreased by 50 % . if the original cost is $ 200 , find the decrease cost .
Options: a ) 330 , b ) 200 , c ) 150 , d ) 100 , e ) 91
Rationale: original cost = $ 200 decrease in it = 50 % of $ 200 = 50 / 100 ã — 200 = 10000 / 100 = $ 100 therefore , decrease cost = $ 200 - $ 100 = $ 100 answer : d
Answer: d
Problem: what is the 16 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 2 nd , 4 th , 6 th , . . . ) to the right of the decimal point is alternating by 2 , 0 , 7 thus 16 th digit is 0 . answer : a ."
Answer: a
Problem: of the 3 - digit integers greater than 700 , how many have two digits t that are equal to each other and the remaining digit different from the other two ?
Options: a ) 90 , b ) 82 , c ) 80 , d ) 45 , e ) 36
Rationale: three - digit integers greater than 700 : 701 to 999 , inclusive . possible values for hundreds - digit - - > 7 , 89 possible values for tens - digit and ones - digit - - > 0 , 1 , 23 , 45 , 67 , 89 when hundreds - digit and tens - digit are the same : ( 3 x 1 x 10 ) - 3 = 27 - - - > we minus three to exclude 777 , 888 and 999 when hundreds - digit and ones - digit are the same : ( 3 x 10 x 1 ) - 3 = 27 - - - > we minus three to exclude 777 , 888 and 999 when tens - digit and hundreds - digit are the same : [ ( 3 x 10 x 1 ) - 3 ] - 1 = 26 - - - > we minus three to exclude 777 , 888 and 999 ; we minus one to exclude 700 t = 27 + 27 + 26 = 80 answer : c
Answer: c
Problem: the ages of two person differ by 20 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10
Rationale: "let their ages be x and ( x + 20 ) years . then , 5 ( x - 5 ) = ( x + 20 - 5 ) = > 4 x = 40 = > x = 10 their present ages are 30 years and 10 year . answer : a"
Answer: a
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 10 % ?
Options: a ) 20 % , b ) 28 % , c ) 27 % , d ) 35 % , e ) 70 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 90 2 / 3 sp 1 = 90 sp 1 = 135 100 - - - 35 = > 35 % answer : d"
Answer: d
Problem: out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many w applicants majored in political science and had a gpa higher than 3.0 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35
Rationale: "total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) w = 20 - 15 = 5 answer : a"
Answer: a
Problem: the average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 58 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 73 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 58 + 10 x 1.5 58 + 15 = 73 kg ans : ' b '"
Answer: b
Problem: the price of a car and ac are in the ratio 3 : 2 . if the scooter costs $ 500 more than the ac . then the price of the ac ?
Options: a ) 1500 , b ) 200 , c ) 1700 , d ) 2000 , e ) 2500
Rationale: let the price of the car and ac is 3 x and 2 x 3 x - 2 x = 500 x = 500 price of ac = 3 * 500 = $ 1500 answer is a
Answer: a
Problem: a shopkeeper sold an article offering a discount of 4 % and earned a profit of 44 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 24 , b ) 28 , c ) 30 , d ) 32 , e ) 50
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 144 let marked price be rs . x . then , 96 / 100 x = 144 x = 14400 / 96 = rs . 150 now , s . p . = rs . 150 , c . p . = rs . 100 profit % = 50 % . answer : e"
Answer: e
Problem: the cost per pound of green tea and coffee were the same in june . in july , the price of coffee shot up by 100 % and that of green tea dropped by 70 % . if in july , a mixture containing equal quantities of green tea and coffee costs $ 3.45 for 3 lbs , how much did a pound of green tea cost in july ?
Options: a ) $ 4 , b ) $ 0.3 , c ) $ 1 , d ) $ 3 , e ) $ 1.65
Rationale: lets assume price of coffee in june = 100 x price of green tea in june = 100 x price of coffee in july = 200 x ( because of 100 % increase in price ) price of green tea in july = 30 x ( because of 70 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of green tea in july will be = 300 x + 45 x = 345 x as per question 345 x = 3.45 $ x = 0.01 s so the price of tea in july = 30 x = 30 x 0.01 = 0.3 $ / pound answer b
Answer: b
Problem: the average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew , who weighs 53 kg is replaced by a new man . find the weight of the new man .
Options: a ) 69 , b ) 72 , c ) 75 , d ) 71 , e ) none of them
Rationale: "total weight increased = ( 1.8 x 10 ) kg = 18 kg . : . weight of the new man = ( 53 + 18 ) kg = 71 kg . answer is d"
Answer: d