regisss/math_qa huggingface dataset:
Problem: a vendor sells 20 percent of the pears he had and throws away 50 percent of the remainder . the next day , the vendor sells 20 percent of the remaining pears and throws away the rest . in total , what percent of his pears does the vendor throw away ?
Options: a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72
Rationale: let x be the original number of pears . on day one , the vendor throws away ( 0.5 ) ( 0.8 ) x = 0.4 x . the remaining pears are ( 0.5 ) ( 0.8 ) x = 0.4 x . on day two , the vendor throws away ( 0.8 ) ( 0.4 ) x = 0.32 x . the vendor throws away a total of 0.4 x + 0.32 x = 0.72 x . the vendor throws away 72 percent of the pears . the answer is e .
Answer: e
Problem: john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 80 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 80 = 20 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 20 / 100 ) * 100 = ( 0.2 ) * 100 = 20 % . a"
Answer: a
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 75 . what is that number ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 9
Rationale: "explanation : let the number be v . then , 3 ( 2 x + 9 ) = 75 . 2 x + 9 = 25 = > 2 x = 16 = > x = 8 answer : d ) 8"
Answer: d
Problem: the value of 489.1375 x 0.0483 x 1.956 / 0.0873 x 92.581 x 99.749 is closest to :
Options: a ) 0.48 , b ) 5.8 , c ) 0.58 , d ) 0.058 , e ) 0.0058
Rationale: = 489.1375 x 0.0483 x 1.956 / 0.0873 x 92.581 x 99.749 = 489 x 0.05 x 2 / 0.09 x 93 x 100 = 489 / 9 x 93 x 10 = 163 / 279 x 1 / 10 = 0.58 / 10 = 0.058 ( or ) 0.06 . answer is d .
Answer: d
Problem: an uneducated retailer marks all his goods at 50 % above the cost price and thinking that he will still make 15 % profit , offers a discount of 15 % on the marked price . what is his actual profit on the sales ?
Options: a ) 12.50 % , b ) 27.50 % , c ) 14 % , d ) 14.50 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 150 . s . p . = 85 % of rs . 150 = rs . 127.5 . ∴ gain % = 27.50 % . answer b"
Answer: b
Problem: on teacher ' s day , sweets were to be equally distributed among 190 children in a school . actually , on the teacher ' s day , 70 children were absent and therefore each child got 14 sweets extra . how many sweets did each child get on that day ?
Options: a ) 18 , b ) 22 , c ) 28 , d ) 32 , e ) 38
Rationale: total children = 190 . let each student gets x chocolates if all were present . so , total chocolates = 190 x . 70 students were absent . so , no of extra chocolates distributed among 120 students , = 14 * 70 = 980 . now , total chocolates = 190 x 120 * ( x + 14 ) = 190 120 x + 1680 = 190 x 70 x = 1680 x = 24 . total no of chocolates = 24 * 190 = 4560 . no of chocolates each student gets on that day = 4560 / 120 = 38 . answer : option e
Answer: e
Problem: x , a , z , and b are single digit positive integers . x = ¼ a . z = ¼ b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 33 , b ) 36 , c ) 44 , d ) 63 , e ) 66
Rationale: from the given equations , a = 4 x , b = 4 z ( 10 a + b ) - ( 10 x + z ) = 40 x + 4 z - 10 x - z = 30 x + 3 z = 3 ( 10 x + z ) therefore the resultant should be divisible by 3 which is n ' t possible only in the case of c . hence c is the answer
Answer: c
Problem: in what time will a train 140 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 3.5 sec , b ) 4.25 sec , c ) 5 sec , d ) 12.5 sec , e ) 6 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 140 / 40 = 3.5 sec . answer : a"
Answer: a
Problem: if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 157.20 , b ) 157.29 , c ) 157.50 , d ) 157.30 , e ) 157.23
Rationale: "( 3500 * 1.5 * 3 ) / 100 = > 157.50 answer : c"
Answer: c
Problem: if a : b is 2 : 3 and b : c is 3 : 4 then a : c is equal to
Options: a ) 2 : 3 , b ) 6 : 7 , c ) 5 : 6 , d ) 1 : 2 , e ) 3 : 4
Rationale: "since a : b = 2 : 3 and b : c = 3 : 4 , we can deduce that a : b : c = 2 : 3 : 4 so , a : c = 2 : 4 = 1 : 2 . d is the correct answer ."
Answer: d
Problem: carl can wash all the windows of his house in 6 hours . his wife maggie can wash all the windows in 5 hours . how many hours will it take for both of them working together to wash all the windows ?
Options: a ) 2 , b ) 2 1 / 4 , c ) 11 8 / 2 , d ) 4 1 / 2 , e ) 5
Rationale: "work hrs = ab / ( a + b ) = 30 / 11 = 11 8 / 2 answer is c"
Answer: c
Problem: on a two - dimensional coordinate plane , the line z = x ^ 2 - x ^ 3 touches the x - axis in how many places ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: apparently it ' s z = x ^ 2 - x ^ 3 instead of z = x ^ 2 - z ^ 3 . in this case : the x - intercept is the value ( s ) of x for z = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c .
Answer: c
Problem: find the value of 72514 x 9999 = m ?
Options: a ) 725067486 , b ) 436567874 , c ) 653658791 , d ) 725117481 , e ) 357889964
Rationale: "72514 x 9999 = 72514 x ( 10000 - 1 ) = 72514 x 10000 - 72514 x 1 = 725140000 - 72514 = 725067486 a"
Answer: a
Problem: a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 9 feet , and the sum of the lengths of the painted sides is 37 feet , find out the area of the parking space in square feet ?
Options: a ) 120 , b ) 122 , c ) 124 , d ) 128 , e ) 126
Rationale: "length = 9 feet breadth = 37 − 92 = 14 feet area = 9 × 14 = 126 square feet answer is e ."
Answer: e
Problem: a man ' s speed with the current is 20 kmph and speed of the current is 1 kmph . the man ' s speed against the current will be
Options: a ) 11 kmph , b ) 12 kmph , c ) 18 kmph , d ) 17 kmph , e ) none of these
Rationale: explanation : speed with current is 20 , speed of the man + it is speed of the current speed in s ɵ ll water = 20 - 1 = 19 now speed against the current will be speed of the man - speed of the current = 19 - 1 = 18 kmph answer : c
Answer: c
Problem: if | x - 12 | = 100 , what is the sum of all the possible values of x ?
Options: a ) - 12 , b ) - 22 , c ) 24 , d ) 36 , e ) 42
Rationale: "there will be two cases x - 12 = 100 or x - 12 = - 100 = > x = 112 or x = - 88 sum of both the values will be - 88 + 112 = 24 answer is c"
Answer: c
Problem: calculate the l . c . m of 4 / 9 , 5 / 7 , 9 / 13 , 7 / 15 is :
Options: a ) 1230 , b ) 1290 , c ) 1260 , d ) 1240 , e ) 2260
Rationale: "required l . c . m = l . c . m . of 4 , 5 , 9 , 7 / h . c . f . of 9 , 7 , 13 , 15 = 1260 / 1 = 1260 answer is c"
Answer: c
Problem: kanul spent $ 3000 in buying raw materials , $ 2000 in buying machinery and 10 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 5555.555 , b ) $ 5543.22 , c ) $ 5568.000 , d ) $ 5366.521 , e ) $ 5365.66
Rationale: let the total amount be x then , ( 100 - 10 ) % of x = 3000 + 2000 90 % of x = 5000 90 x / 100 = 5000 x = $ 50000 / 9 x = $ 5555.555 answer is a
Answer: a
Problem: the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 5 | + 4 is equal to :
Options: a ) – 7 , b ) 7 , c ) 20 , d ) 12 , e ) 14
Rationale: x ^ 2 - 8 x + 17 = | x - 5 | rhs can be - ve or + ve x ^ 2 - 9 x + 22 = 0 x ^ 2 - 7 x + 12 = 0 x = 11,4 , 3,2 we test all 3 values in original equation , all ok . thus , sum = 11 + 4 + 3 + 2 = 20 ans ( c )
Answer: c
Problem: 1.20 can be expressed in terms of percentage as
Options: a ) 120 % , b ) 0.120 % , c ) 1.20 % , d ) 0.209 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 1.20 * 100 = 120 answer : option a"
Answer: a
Problem: if the radius of a cylinder is doubled and height 5 times , what is the new volume of the cylinder divided by the old one ?
Options: a ) 8 . , b ) 2 . , c ) 6 . , d ) 20 . , e ) 10 .
Rationale: "let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 2 r ) ^ 2 ( 5 h ) v ' = 20 v d ) 20"
Answer: d
Problem: ( x ) + 4671 + 6514 - 7687 = 19190 . calculate the value of x
Options: a ) 15615 , b ) 15692 , c ) 15687 , d ) 15112 , e ) 15690
Rationale: "x + 4671 + 6514 - 7687 = 19190 = x + 4671 + 6514 = 19190 + 7687 = x + 11185 = 26877 = x = 26877 - 11185 = 15692 answer is b"
Answer: b
Problem: in some quantity of ghee , 60 % is pure ghee and 40 % is vanaspati . if 10 kg of pure ghee is added , then the strength of vanaspati ghee becomes 20 % . the original quantity was ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 18 , e ) 22
Rationale: let the original quantity be x then , vanaspati ghee in xkg = 40 x / 100 kg = 2 x / 5 kg ( 2 x / 5 ) / ( x + 10 ) = 20 / 100 2 x / ( 5 x + 50 ) = 1 / 5 x = 10 answer is a
Answer: a
Problem: a motorist travels for 6 hours , the first half at 60 kmph and the rest at 48 kmph . find the distance traveled by him .
Options: a ) 234 , b ) 124 , c ) 324 , d ) 452 , e ) 352
Rationale: distance = 3 * 60 + 3 * 48 = 180 + 144 = 324 km answer c .
Answer: c
Problem: in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the error percent in the area calculated from these measurements .
Options: a ) 0.8 % , b ) 0.2 % , c ) 0.4 % , d ) 0.9 % , e ) 0.6 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 105 / 100 * x ) * ( 96 / 100 * y ) = 504 / 500 * xy . error in measurement = 504 / 500 * xy ) - xy = 4 / 500 * xy . error % = [ 4 / 500 * xy * 1 / xy * 100 ] % = 4 / 5 = 0.8 % . answer is a"
Answer: a
Problem: in a group of ducks and cows , the total number of legs are 24 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 24 more than twice the number of heads = > 2 ( d + 2 c ) = 24 + 2 ( c + d ) = > d + 2 c = 12 + c + d = > 2 c = 12 + c = > c = 12 i . e . , total number of cows = 12 answer is a ."
Answer: a
Problem: a can do a piece of work in 6 days . b can do it in 5 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 8.7 days , b ) 2.0 days , c ) 6.6 days , d ) 7.5 days , e ) 4.4 days
Rationale: "c = 1 / 2 - 1 / 6 - 1 / 5 = 2 / 15 = > 7.5 days answer : d"
Answer: d
Problem: if 250 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 65 , b ) 66 , c ) 62 , d ) 69 , e ) 97
Rationale: "the question actually asks the highest power of 10 which divides 250 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 250 factorial will have 62 as - 250 / 5 = 50 50 / 5 = 10 10 / 5 = 2 so answer will be ( c ) 62"
Answer: c
Problem: a machine , working at a constant rate , manufactures 72 staplers in 28 minutes . how many staplers does it make in 1 hr 52 min ?
Options: a ) 268 , b ) 262 , c ) 300 , d ) 288 , e ) 250
Rationale: "change 1 hr 52 min to 112 min . for this , we need to set up a simple proportion of staplers per time 72 / 28 = s / 112 . the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . we can cancel the common factor of 28 in the two denominators . 72 / 28 * 28 = s / 112 * 28 72 / 1 = s / 4 s = 4 * 72 s = 288 the machine would be 288 staplers in 1 hr 52 min . answer : d"
Answer: d
Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 1 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
Options: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22
Rationale: "p ( 1 and not 2 ) = 1 / 8 * ( 1 - 3 / 5 ) = 1 / 20 . answer : a ."
Answer: a
Problem: when a = x + ( 2 / x ) and b = x - ( 2 / x ) , ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = ?
Options: a ) 2 , b ) 256 , c ) 8 , d ) 16 , e ) 32
Rationale: - - > ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = { ( 2 ) ^ ( a ^ 2 - b ^ 2 ) } = 2 ^ ( a - b ) ( a + b ) . since a - b = 4 / x and a + b = 2 x , 2 ^ ( a - b ) ( a + b ) = 2 ^ ( 4 / x ) ( 2 x ) = 2 ^ 8 = 256 answer is b
Answer: b
Problem: if ( 4 - x ) / ( 4 + x ) = x , what is the value of x ^ 2 + 5 x - 4 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: ( 4 - x ) = x * ( 4 + x ) ( 4 - x ) = 4 x + x ^ 2 0 = x ^ 2 + 5 x - 4 the answer is a .
Answer: a
Problem: walking with 4 / 5 of my usual speed , i miss the bus by 5 minutes . what is my usual time ?
Options: a ) 145 , b ) 5617 , c ) 15 , d ) 20 , e ) 12
Rationale: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 5 4 - - - - - - - - - ? è 20 answer : d"
Answer: d
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 45 kg , then the weight of b is :
Options: a ) 31 kg , b ) 32 kg , c ) 33 kg , d ) 35 kg , e ) none of these
Rationale: "explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 … . ( i ) a + b = ( 40 x 2 ) = 80 … . ( ii ) b + c = ( 45 x 2 ) = 90 … . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 170 … . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 35 . b ’ s weight = 35 kg . answer : d"
Answer: d
Problem: evaluate : 35 - 12 * 3 * 2 = ?
Options: a ) 62 , b ) 52 , c ) 32 , d ) 27 , e ) 22
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 35 - 12 * 3 * 2 = 35 - 8 = 27 correct answer d"
Answer: d
Problem: a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 4 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 6 / 9
Rationale: "income = salary ( s ) + tips = s + s * 5 / 4 = s * 9 / 4 tips = s * 5 / 4 fraction of his income came from tips = ( s * 5 / 4 ) / ( s * 9 / 4 ) = 5 / 9 answer : d"
Answer: d
Problem: in a fort , there are 1200 soldiers . if each soldier consumes 3 kg per day , the provisions available in the fort will last for 30 days . if some more soldiers join , the provisions available will last for 25 days given each soldier consumes 2.5 kg per day . find the number of soldiers joining the fort in that case ?
Options: a ) 273 , b ) 528 , c ) 539 , d ) 538 , e ) 723
Rationale: "assume x soldiers join the fort . 1200 soldiers have provision for 1200 ( days for which provisions last them ) ( rate of consumption of each soldier ) = 1200 ( 30 ) ( 3 ) kg also provisions available for ( 1200 + x ) soldiers is ( 1200 + x ) ( 25 ) ( 2.5 ) kg as the same provisions are available = > 1200 ( 30 ) ( 3 ) = ( 1200 + x ) ( 25 ) ( 2.5 ) x = [ 1200 ( 30 ) ( 3 ) ] / [ ( 25 ) ( 2.5 ) ] - 1200 x = 528 answer : option b"
Answer: b
Problem: 19 people went to a hotel for combine dinner party 13 of them spent rs . 79 each on their dinner and rest spent 4 more than the average expenditure of all the 19 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 1492 , d ) 1496 , e ) none of these
Rationale: solution : let average expenditure of 19 people be x . then , 19 x = 13 * 79 + 6 * ( x + 4 ) ; or , 19 x = 13 * 79 + 6 x + 24 ; or , x = 80.84 ; so , total money spent = 80.84 * 19 = rs . 1536.07 . answer : option e
Answer: e
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 81 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7000 , b ) 8100 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 81 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 81 = > total appeared candidates in state b = 81 x 100 = 8100 = > total appeared candidates in state a = total appeared candidates in state b = 8100
Answer: b
Problem: find the compound ratio of ( 3 : 2 ) , ( 4 : 3 ) and ( 1 : 4 ) is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 3 : 2
Rationale: "required ratio = 3 / 2 * 4 / 3 * 1 / 4 = 1 / 2 = 1 : 2 answer is a"
Answer: a
Problem: a ( 5 , w ^ 2 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 11 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: "y = x ^ 2 + 11 w ^ 2 = 5 ^ 2 + 11 w ^ 2 = 36 w = 6 answer d"
Answer: d
Problem: how many positive integers less than 5,000 are evenly divisible by neither 16 nor 21 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 16 5000 / 16 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 16 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 16 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4514 answer a ."
Answer: a
Problem: a girl walks at a speed of 5 kmph . how much time does he take to walk a distance of 30 km ?
Options: a ) 10 hrs , b ) 2 hrs , c ) 3 hrs , d ) 5 hrs , e ) 6 hrs
Rationale: time = distance / speed = 30 / 5 = 6 hours . answer is e
Answer: e
Problem: a man â € ™ s current age is ( 2 / 5 ) of the age of his father . after 10 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 39
Rationale: "let , father â € ™ s current age is a years . then , man â € ™ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 10 ] = ( 1 / 2 ) ( a + 10 ) 2 ( 2 a + 50 ) = 5 ( a + 10 ) a = 50 d"
Answer: d
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 34 ?
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 34 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 3 more to make it 34 m + 34 answer - a"
Answer: a
Problem: a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and thereby decreases his average by 0.4 . the number of wickets taken by him till the last match was :
Options: a ) 64 , b ) 72 , c ) 80 , d ) 85 , e ) none of the above
Rationale: "let the number of wickets taken till the last match be x . then , 12.4 x + 26 / x + 5 = 12 ⇒ 12.4 x + 26 = 12 x + 60 ⇒ 0.4 x = 34 ⇒ x = 34 ⁄ 0.4 = 340 ⁄ 4 = 85 . answer d"
Answer: d
Problem: working together , tim and tom can type 12 pages in one hour . if they would be able to type 14 pages in one hour if tom increases his typing speed by 25 % , what is the ratio of tom ' s normal typing speed to that of tim ?
Options: a ) 2 / 1 , b ) 1 / 2 , c ) 1 / 3 , d ) 4 / 1 , e ) 1 / 4
Rationale: "lets say tim types x pages an hour and tom types y pages an hour . we know that x + y = 12 tom increase speed by 25 % means he will type 1.25 y pages an hour . so we get x + 1.25 y = 14 we need to know the ratio of tom ' s speed to tim ' s speed . this is going to be proportional to the number of pages each can type in an hour , hence ( y / x ) . subtracting both : 0.25 y = 2 so y = 8 . . . so x = 4 ( y / x ) = 8 / 4 = 2 / 1 answer is ( a )"
Answer: a
Problem: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 9 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 95 , d ) 90 , e ) 66
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 9 total people can seat = 81 + 9 = 90 answer : d"
Answer: d
Problem: the average of temperatures at noontime from monday to friday is 25 ; the lowest one is 15 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 50 , d ) 45 , e ) 75
Rationale: average = 25 , sum of temperatures = 25 * 5 = 125 as the min temperature is 15 , max would be 125 - 4 * 15 = 65 - - > the range = 65 ( max ) - 15 ( min ) = 50 answer : c
Answer: c
Problem: what will be the compound interest on a sum of rs . 27,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.77 , b ) s . 10123.21 , c ) s . 10933.05 , d ) s . 10123.28 , e ) s . 10123.21
Rationale: "amount = [ 27000 * ( 1 + 12 / 100 ) 3 ] = 27000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 37933.0 c . i . = ( 37933.056 - 27000 ) = rs . 10933.05 answer : c"
Answer: c
Problem: a merchant marks goods up by 75 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 22.5 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: let p be the original price of the goods and let x be the rate after the markup . ( 1.75 p ) * x = 1.225 p x = 1.225 / 1.75 = 0.7 which is a discount of 30 % . the answer is c .
Answer: c
Problem: a , b and c rents a pasture for rs . 1130 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 199 , c ) 351 , d ) 156 , e ) 122
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 1130 = 351 answer : c"
Answer: c
Problem: how many multiples of 2 are there between 1 and 54 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "26 multiples of 2 between 1 and 54 exclusive . from 2 * 1 upto 2 * 26 , ( 1,2 , 3,4 , . . . , 26 ) . hence , 26 multiples ! correct option is d"
Answer: d
Problem: at what rate percent per annum will a sum of money double in 2 years .
Options: a ) 34 % , b ) 50 % , c ) 11.5 % , d ) 20 % , e ) 21.5 %
Rationale: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 2 ) ] % = 50 % per annum . answer : b"
Answer: b
Problem: the sum of 2 consecutive numbers is definitely :
Options: a ) positive . , b ) divisible by 2 . , c ) divisible by 3 . , d ) divisible by 4 . , e ) divisible by 5 .
Rationale: "if 1 st term is x : x + ( x + 1 ) = 2 x + 1 - - - > positive if 2 nd term is x : ( x - 1 ) + x = 2 x - 1 - - - > positive a"
Answer: a
Problem: four concentric circles r given . the radius of 1 st circle is x . next is 2 x , then 3 x and 4 x . given that area b / w 2 nd and 1 st is a and 4 th and 3 rd circles being b . find ratio of a to b
Options: a ) 2 : 7
b ) 1 : 7
c ) 3 : 5
d ) 3 : 7
e ) 3 : 4
Rationale: area of first circle = pi * ( x ) ^ 2 = pi * x ^ 2 area of second circle = pi * ( 2 x ) ^ 2 = 4 * pi * x ^ 2 area of third circle = pi * ( 3 x ) ^ 2 = 9 * pi * x ^ 2 area of fourth circle = pi * ( 4 x ) ^ 2 = 16 * pi * x ^ 2 area b / w 1 st and 2 nd circles = 3 * pi * x ^ 2 area b / w 3 rd and 4 th circles = 7 * pi * x ^ 2 so ratio = 3 : 7 answer : d
Answer: d
Problem: a grocery shop has a sale of rs . 6335 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 5091 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6335 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6335 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 33909 + x = 39000 = > x = 39000 − 33909 = 5091 answer : d"
Answer: d
Problem: two numbers have a h . c . f of 9 and a product of two numbers is 1800 . find the l . c . m of the two numbers ?
Options: a ) 200 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 1800 / 9 = 200 . answer : a"
Answer: a
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 4 eggs . if the cost of each pound of rice is $ 0.33 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.22 , b ) 0.44 , c ) 0.55 , d ) 22 , e ) 55
Rationale: a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 33 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 4 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 8 eggs = 8 / 12 * 33 = 22 cents . answer : d .
Answer: d
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 14000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 28
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 14000 x 7 ) + 6000 ( x - 7 ) x = 28 . answer e"
Answer: e
Problem: a man buys rs . 48 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 36
Rationale: "dividend on rs . 48 = rs . 9 / 100 x 48 = rs . 4.32 . rs . 12 is an income on rs . 100 . rs . 4.32 is an income on rs . 100 / 12 x 4.32 = rs . 36 . answer : option e"
Answer: e
Problem: a can do a piece of work in 20 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 55 , e ) 10
Rationale: "8 / 20 + 6 / x = 1 x = 10 days answer : e"
Answer: e
Problem: the ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250 . the sum of the numbers is :
Options: a ) 30 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let the numbers be 3 x , 4 x and 5 x then , 9 x 2 + 16 x 2 + 25 x 2 = 1250 50 x 2 = 1250 x = 5 sum of numbers = 3 x + 4 x + 5 x = 12 x = 60 answer c 60"
Answer: c
Problem: elena ’ s bread recipe calls for 8 ounces of butter for each 14 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 56
Rationale: "solving through algebra route : 8 b + 14 f = x amount if we multiply this equation with 4 we get : 32 b + 56 f = 4 x therefore , we got 32 ounces of butter and 4 x amount of quantity when we use 56 ounces of floor . ans : e"
Answer: e
Problem: solution a is 20 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 7
Rationale: "let : x = ounces taken from solution a ( 20 % salt ) y = ounces taken from solution b ( 80 % salt ) to prepare 50 ounce 50 % salt . first equation is simple : x + y = 50 to get another equation so as to be able to solve , compute salt contents . 20 % of x + 80 % of y = 50 % of 50 or x / 5 + 4 / 5 * y = 25 or x + 4 y = 125 solve two equations to get : x = 25 y = 25 so solutions has to mix in 1 : 1 oops 4 : 4 answer : c"
Answer: c
Problem: a man can row at 6 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 2.4 km , b ) 2.6 km , c ) 2.9 km , d ) 4.4 km , e ) 5.6 km
Rationale: "explanation : speed in still water = 6 kmph speed of the current = 1 kmph speed downstream = ( 6 + 1 ) = 7 kmph speed upstream = ( 6 - 1 ) = 5 kmph let the required distance be x km total time taken = 1 hour â ‡ ’ x / 7 + x / 5 = 1 â ‡ ’ 5 x + 7 x = 35 â ‡ ’ 12 x = 35 â ‡ ’ x = 2.9 km answer : option c"
Answer: c
Problem: 5 kilograms of oranges contained 95 % of water . if the next day the concentration of water decreased by 5 % , what was the new weight of the oranges , in kilograms ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: five kilograms of oranges contained 95 % of water . if the next day the concentration of water decreased by 5 % , what was the new weight of the oranges , in kilograms ? ( a ) 30 ( b ) 25 ( c ) 15 ( d ) 10 ( e ) 5 if b is the answer , then the question means that the concentration of water the newt day became 90 % . out of 5 kilograms 95 % , or 4.75 kilograms was water and 0.25 kilograms was non - water . the next day , after some water evaporated , oranges became 90 % water and 10 % of non - water , so the next day 0.25 kilograms of non - water composed 10 % of oranges , which means that the new weight of the oranges was x * 0.10 = 0.25 - - > x = 25 kilograms . answer : b .
Answer: b
Problem: the mean of 20 values was 150 . it was detected on rechecking that one value 160 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 151.25 , d ) 148 , e ) none of the above
Rationale: corrected mean = 150 × 20 − 135 + 160 / 20 = 3000 − 135 + 160 / 20 = 3025 / 20 = 151.25 answer c
Answer: c
Problem: the present population of a town is 200 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 220 , e ) 250
Rationale: "p = 200 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 200 * ( 1 + 10 / 100 ) = 200 * ( 11 / 10 ) = 220 ( approximately ) answer is d"
Answer: d
Problem: at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 19 employees are trained to work in the family buffet , 18 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 2 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "39 = 19 + 18 + 12 - 2 - 2 x 2 x = 19 + 18 + 12 - 2 - 39 = 45 - 37 = 8 x = 4 c"
Answer: c
Problem: if n is a prime number greater than 7 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 7 , square it and see what would be the remainder upon division of it by 12 . n = 11 - - > n ^ 2 = 121 - - > remainder upon division 121 by 12 is 1 . answer : b ."
Answer: b
Problem: if sushi rows 27 km upstream and 81 km down steam taking 9 hours each , then the speed of the stream
Options: a ) 12 kmph , b ) 13 kmph , c ) 22 kmph , d ) 20 kmph , e ) 15 kmph
Rationale: speed upstream = 27 / 9 = 3 kmph speed down stream = 81 / 3 = 27 kmph speed of stream = ½ ( 27 - 3 ) = 12 kmph answer : a
Answer: a
Problem: a rich aristocrat decided that he would give every man rs . 45 and every women rs . 60 . only one nineth of the man and only one twelfth of the women collected their dues . can u tell me how much money thath aristocrat spent if their were 3552 people in total
Options: a ) 17760 , b ) 18540 , c ) 16320 , d ) 14640 , e ) 15640
Rationale: iman = 45 and 1 women = 60 then 1 / 9 man = 1 / 9 * 45 = 5 and 1 / 12 of women = 1 / 12 * 60 = 5 total people 3552 = 3552 * 5 = 17760 answer : a
Answer: a
Problem: 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour slower than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 6 m / h - - > 3 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 3 ^ 2 d ^ 2 = 25 = 5 answer option a
Answer: a
Problem: a fill pipe can fill 1 / 3 of cistern in 20 minutes in how many minutes , it can fill 3 / 4 of the cistern ?
Options: a ) 15 min , b ) 45 min , c ) 25 min , d ) 40 min , e ) 50 min
Rationale: "1 / 3 of the cistern can fill in 20 min 3 / 4 of the cistern can fill in = 20 * 3 * 3 / 4 = 45 min answer is b"
Answer: b
Problem: the length of the bridge , which a train 145 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 76 m , b ) 178 m , c ) 230 m , d ) 187 m , e ) 176 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 145 + x ) / 30 = 25 / 2 = > 2 ( 145 + x ) = 750 = > x = 230 m . answer : c"
Answer: c
Problem: a cube is divided into 125 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "each side of the cube has 5 x 5 = 25 cubelets . only the interior cubelets are painted one colour . on each side , 3 x 3 = 9 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 9 = 54 the answer is d ."
Answer: d
Problem: indu gave bindu rs . 3750 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 1 , b ) 2 , c ) 6 , d ) 4 , e ) 9
Rationale: "3750 = d ( 100 / 4 ) 2 d = 6 answer : c"
Answer: c
Problem: for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 37 , the mean is how much greater than the median ?
Options: a ) 6 , b ) 1 , c ) 2 , d ) 4 , e ) 7
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 37 ) / 5 = ( 5 x + 50 ) / 5 = x + 10 median = x + 4 thus mean - median = x + 10 - ( x + 4 ) = 6 answer = a"
Answer: a
Problem: the flow of water through a drainage pipe was monitored for a 3 - hour period . in the second hour , the rate of flow was 36 gallons per hour , which was 50 percent faster than the rate of flow for the first hour . if 25 percent more water flowed through the pipe in the third hour than it did in the second , how many gallons of water flowed through the pipe during the entire 3 hours ?
Options: a ) 106.25 , b ) 105.5 , c ) 105.75 , d ) 106 , e ) 105.0
Rationale: rate of flow of water in second hour = 36 gallons per hour rate of flow of water in first hour = 36 / ( 3 / 2 ) = 24 gallons per hour rate of flow of water in third hour = ( 125 / 100 ) * 36 = ( 5 / 4 ) * 36 = 45 gallons per hour number of gallons of water that flowed through the pipe during the entire 3 hours = 24 + 36 + 45 = 105 gallons answer e
Answer: e
Problem: running at the same constant rate , 6 identical machines can produce a total of 330 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2200 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 330 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 330 x = ( 10 x 4 x 330 ) / ( 6 ) x = 2200 . answer : c"
Answer: c
Problem: if a light flashes every 6 seconds , how many times will it flash in 1 / 4 of an hour ?
Options: a ) 51 , b ) 151 , c ) 251 , d ) 351 , e ) 451
Rationale: "in 1 / 4 of an hour there are 15 * 60 = 900 seconds the number of 6 - second intervals = 900 / 6 = 150 after the first flash , there will be 150 more flashes for a total of 151 . the answer is b ."
Answer: b
Problem: a sum of rs . 1360 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 300 , e ) none
Rationale: "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 13660 = > 17 x / 12 = 13660 = > 13660 x 12 / 17 = rs . 960 hence , b ’ s share = rs . ( 960 / 4 ) = rs . 240 . answer c"
Answer: c
Problem: find the compound interest on $ 20000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 1648.64 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 1020.45
Rationale: "principle = $ 20000 rate = 2 % half yearly = 4 half years amount = 20000 * ( 1 + 2 / 100 ) ^ 4 = 20000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 21648.64 c . i . = 21648.64 - 20000 = $ 1648.64 answer is b"
Answer: b
Problem: 78 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 26 , d ) 15 , e ) 16
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 78 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 78 x 5 x 12 x = ( 78 x 5 x 12 ) / ( 30 x 6 ) x = 26 . answer : c"
Answer: c
Problem: can you find a 6 digit number under 5 lakh such that the sum of it ' s digits is 43 ?
Options: a ) 588338 , b ) 499449 , c ) 399826 , d ) 788392 , e ) 622975
Rationale: b the required number is 499449 . the maximum sum of a number under 5 lakh will be of the number 499999 i . e . 49 . thus the required number must be close to 499999 . the root of 499999 ~ 707.106 by calculating the square of 707 , we get 499849 which is the answer .
Answer: b
Problem: a real estate agent received a 6 % commission on the selling price of a house . if his commission was $ 8880 , what was the selling price of the house ?
Options: a ) $ 234000 , b ) $ 227000 , c ) $ 148000 , d ) $ 479000 , e ) $ 337,000
Rationale: 6 % x = 8,880 : x = selling price of house . x = $ 148,000 : solve for x correct answer c .
Answer: c
Problem: there is a total of 84 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 2 / 7 . what is the probability that the marble will be either red or blue ?
Options: a ) 3 / 7 , b ) 11 / 14 , c ) 13 / 28 , d ) 19 / 28 , e ) 29 / 42
Rationale: p ( red or blue ) = 1 - p ( white ) - p ( green ) = 28 / 28 - 7 / 28 - 8 / 28 = 13 / 28 the answer is c .
Answer: c
Problem: ( x + 7 ) is a factor in x ^ 2 - mx - 35 . what is the value of m ?
Options: a ) - 3 , b ) - 2 , c ) - 4 , d ) - 5 , e ) - 6
Rationale: "i solved the second degree equation and found it like this : x ^ 2 - mx - 35 ( x - 5 ) ( x + 7 ) x = 5 or x = - 7 substituting both values for x in the equation we find : x ^ 2 - mx - 35 = > ( - 7 ) ^ 2 - m ( - 7 ) = 35 = > 49 + 7 m = 35 = > 7 m = 35 - 49 = - 14 = > m = - 2 and with 5 , using a similar process we end up with : ( 5 ) ^ 2 - m ( 5 ) = 35 - 10 = 5 m m = - 2 ao , ans b"
Answer: b
Problem: the product of two positive integers is 575 and their difference is 2 . what is the bigger number ?
Options: a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29
Rationale: "let ' s use trial and error to find the two numbers . 27 * 25 = 675 ( too high ) 25 * 23 = 575 the answer is c ."
Answer: c
Problem: at a certain pizza parlor , the diameter of a large pizza is 40 % larger than the diameter of a small pizza . what is the percent increase in total amount of pizza , from a small to a large ?
Options: a ) 20 % , b ) 40 % , c ) 64 % , d ) 80 % , e ) 96 %
Rationale: a real world problem — - yum ! — - but again , the specifics of the shape don ’ t matter . diameter increases 40 % , so k = 1.4 in this case . “ amount of pizza ” just means the area of the circle , so k ^ 2 = ( 1.4 ) ^ 2 = 1.96 , which is the multiplier for a 96 % increase . that ’ s the percent increase in area . answer = e
Answer: e
Problem: on a map , 2.5 inches represent 40 miles . how many miles approximately is the distance if you measured 155 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 990.4 , b ) 970 , c ) 972 , d ) 976.4 , e ) 975
Rationale: "1 inch = 2.54 cm 2.5 inch = 2.54 * 2.5 cm 6.35 cm = 40 miles 155 cms = 40 / 6.35 * 155 = 976.4 miles answer : d"
Answer: d
Problem: the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 48 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: 20 x + 48 = 21 ( x – 5 ) x = 57 answer : c
Answer: c
Problem: if two integers x , y ( x > y ) are selected from - 4 to 4 ( inclusive ) , how many cases are there ?
Options: a ) 27 , b ) 30 , c ) 33 , d ) 36 , e ) 39
Rationale: "there are 9 integers from - 4 to 4 inclusive . 9 c 2 = 36 . the answer is d ."
Answer: d
Problem: a man is 24 years older than his son . in four years , his age will be twice the age of his son . the present age of the son is
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then â € ¹ = â € º ( x + 24 ) + 4 = 2 ( x + 4 ) â € ¹ = â € º x + 28 = 2 x + 8 x = 20 . answer c"
Answer: c
Problem: a car is purchased on hire - purchase . the cash price is $ 23 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly instalments . interest is charged at 12 % p . a . what is the monthly instalment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 515 , d ) $ 543 , e ) $ 552
Rationale: "explanation : cash price = $ 23 000 deposit = 10 % ã — $ 23 000 = $ 2300 loan amount = $ 23000 â ˆ ’ $ 2300 number of payments = 60 = $ 20700 i = p * r * t / 100 i = 12420 total amount = 20700 + 12420 = $ 33120 regular payment = total amount / number of payments = 552 answer : e"
Answer: e
Problem: on the number line , if x is halfway between - 8 and 4 , and if y is halfway between - 2 and 6 , what number is halfway between x and y ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: x = - 2 and y = 2 . the answer is c .
Answer: c
Problem: a survey was sent to 90 customers , 15 of whom responded . then the survey was redesigned and sent to another 50 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 28 % , e ) 63 %
Rationale: "rate of first survey = 15 / 90 rate of second survey = 9 / 50 % response rate increase ( 9 / 50 - 15 / 90 ) / ( 15 / 90 ) = 8 % answer is c = 8 %"
Answer: c
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 50 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 86 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 50 % more than company a ' s assets which is 150 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 75 a + b = 175 kw = 150 kw / ( a + b ) * 100 = 150 / 175 * 100 = 85.7 % or 86 % answer : c"
Answer: c
Problem: a rectangular field is to be fenced on three sides leaving a side of 80 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 44 ft , b ) 97 ft , c ) 22 ft , d ) 11 ft , e ) 66 ft
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 80 x breadth = 680 breadth = 8.5 feet area to be fenced = 2 b + l = 2 ( 8.5 ) + 80 = 97 feet answer : b ) 97 ft"
Answer: b
Problem: rs . 120 are divided among a , b , c such that a ' s share is rs . 20 more than b ' s and rs . 20 less than c ' s . what is b ' s share
Options: a ) rs 10 , b ) rs 20 , c ) rs 24 , d ) rs 28 , e ) none of these
Rationale: explanation : let c = x . then a = ( x � 20 ) and b = ( x � 40 ) . x + x - 20 + x - 40 = 120 or x = 60 . a : b : c = 40 : 20 : 60 = 2 : 1 : 3 . b ' s share = rs . 120 * ( 1 / 6 ) = rs . 20 answer : b
Answer: b
Problem: a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 5 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if average of 3 is 5 so sum of 3 should be 15 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 6 and 6 so a has to be 3 b"
Answer: b
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 10 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 10 , c ) 20 , d ) 16 , e ) 12
Rationale: "7 * 5 : 10 * x = 7 : 10 x = 20 answer : c"
Answer: c
Problem: a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 25 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 2 / 5 . hence , c is the correct answer ."
Answer: c
Problem: if x is an integer such that 0 < x < 12 , 1 < x < 15 , 10 > x > 5 , 11 > x > 8 , and x + 2 < 12 , then x is
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "0 < x < 12 , 1 < x < 15 , - 5 < x < 10 8 < x < 11 x < 10 from above : 8 < x < 10 - - > x = 9 . answer : d ."
Answer: d
Problem: a sum of money lent out at s . i . amounts to rs . 660 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) s . 440 , b ) s . 500 , c ) s . 540 , d ) s . 740 , e ) s . 516
Rationale: "s . i for 5 years = ( 1020 - 660 ) = rs . 360 . s . i . for 2 years = 360 / 5 * 2 = rs . 144 . principal = ( 660 - 144 ) = rs . 516 . answer : e"
Answer: e
Problem: what number has a 5 : 1 ratio to the number 8 ?
Options: a ) 22 , b ) 40 , c ) 88 , d ) 52 , e ) 12
Rationale: 5 : 1 = x : 8 x = 40 answer : b
Answer: b
Problem: for an agricultural experiment , 500 seeds were planted in one plot and 200 were planted in a second plot . if exactly 30 percent of the seeds in the first plot germinated and exactly 50 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 35.7 % , b ) 25 % , c ) 32 % , d ) 30.8 % , e ) 60 %
Rationale: "from the first plot 0.30 * 500 = 150 ; from the second plot 0.50 * 200 = 100 ; total percent = ( 150 + 100 ) / ( 500 + 200 ) = 0.357 . answer : a ."
Answer: a