regisss/math_qa huggingface dataset:
Problem: two stations a and b are 110 km apart on a straight line . one train starts from a at 5 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 11 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: "suppose they meet x hours after 5 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 8 a . m . answer : c"
Answer: c
Problem: a circular ground whose diameter is 40 metres , has a garden of area 1100 m ^ 2 around it . what is the wide of the path of the garden ?
Options: a ) 8.07 , b ) 7.07 , c ) 6.07 , d ) 7.0 , e ) 8.5
Rationale: "req . area = ï € [ ( 20 ) 2 â € “ ( r ) 2 ] = 22 â  „ 7 ã — ( 400 - r ^ 2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] ie ) 22 / 7 ( 400 - r ^ 2 ) = 1100 , ie ) r ^ 2 = 50 , r = 7.07 m answer b"
Answer: b
Problem: in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 4 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "the choices give away the answer . . 36 machines take 4 hours to fill 4 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 12 / 4 = 6 ans b"
Answer: b
Problem: a man gains 20 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 140 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 120 / 100 ) x = 6 x / 5 new s . p . = 2 ( 6 x / 5 ) = 12 x / 5 profit = 12 x / 5 - x = 7 x / 5 profit % = ( profit / c . p . ) * 100 = > ( 7 x / 5 ) * ( 1 / x ) * 100 = 140 % option b"
Answer: b
Problem: if the cost price is 90 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 11 % , c ) 13 % , d ) 21 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 90 profit = $ 10 profit % = 10 / 90 * 100 = 25 / 6 = 11 % approximately answer is b"
Answer: b
Problem: marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 10,000 and the marginal cost is $ 200 , and the total cost is $ 40,000 , what is the value of n ?
Options: a ) 30 , b ) 50 , c ) 60 , d ) 80 , e ) 150
Rationale: "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 40,000 = $ 10,000 + n * $ 200 - - > n = 150 . answer : e ."
Answer: e
Problem: 7 does not occur in 1000 . so we have to count the number of times it appears between 1 and 999 . any number between 1 and 999 can be expressed in the form of xyz where 0 < x , y , z < 9 .
Options: a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 470
Rationale: 1 . the numbers in which 7 occurs only once . e . g 7 , 17 , 78 , 217 , 743 etc this means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits ( i . e 0 to 9 with the exception of 7 ) you have 1 * 9 * 9 = 81 such numbers . however , 7 could appear as the first or the second or the third digit . therefore , there will be 3 * 81 = 243 numbers ( 1 - digit , 2 - digits and 3 - digits ) in which 7 will appear only once . in each of these numbers , 7 is written once . therefore , 243 times . 2 . the numbers in which 7 will appear twice . e . g 772 or 377 or 747 or 77 in these numbers , one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7 ) . there will be 9 such numbers . however , this digit which is not 7 can appear in the first or second or the third place . so there are 3 * 9 = 27 such numbers . in each of these 27 numbers , the digit 7 is written twice . therefore , 7 is written 54 times . 3 . the number in which 7 appears thrice - 777 - 1 number . 7 is written thrice in it . therefore , the total number of times the digit 7 is written between 1 and 999 is 243 + 54 + 3 = 300 option b
Answer: b
Problem: a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 16 km ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 7
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 16 t = 16 / 2 = 8 answer : c"
Answer: c
Problem: in 1982 and 1983 , company b ’ s operating expenses were $ 12.0 million and $ 15.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 5 5 / 9 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 %
Rationale: profit in 1982 = 15.6 - 12 = 3.6 million $ profit in 1983 = 18.8 - 15 = 3.8 million $ percentage increase in profit = ( 3.8 - 3.6 ) / 3.6 * 100 % = 5 5 / 9 % answer b
Answer: b
Problem: peter can cover a certain distance in 1 hr . 24 min . by covering two - third of the distance at 4 kmph and the rest at 5 kmph . find the total distance .
Options: a ) 4 km , b ) 5 km , c ) 6 km , d ) 7 km , e ) 8 km
Rationale: time = distance / speed let total distance travelled be x in 84 / 60 hrs 2 / 3 rd of x travelled in 4 km / hr 1 / 3 rd of distance travelled in 5 km / hr 2 x / ( 3 * 4 ) + x / ( 3 * 5 ) = 84 / 60 x = 6 km answer : c
Answer: c
Problem: if the area of a circle decreases by 20 % , then the radius of a circle decreases by
Options: a ) 20 %
b ) 18 %
c ) 36 %
d ) 11 %
e ) none of these
Rationale: if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 20 ) % = ( 100 − 10 √ 80 ) % = 100 - 89 = 11 % answer d
Answer: d
Problem: if n is a natural number , then ( 6 n ^ 2 + 6 n ) is always divisible by ?
Options: a ) 6 only , b ) 6 and 12 , c ) 12 only , d ) by 18 only , e ) none of these
Rationale: "( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . correct option : b"
Answer: b
Problem: two trains 140 m and 180 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 11.52 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 10.2 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 180 = 320 m . required time = 320 * 9 / 250 = 11.52 sec . answer : a"
Answer: a
Problem: the average of first seven multiples of 8 is :
Options: a ) 9 , b ) 16 , c ) 15 , d ) 32 , e ) 10
Rationale: "explanation : ( 8 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 8 x 28 / 7 = 32 answer : d"
Answer: d
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability j that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability j is 2 / 3 . d"
Answer: d
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 54 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 54 2 l ^ 2 / 3 = 54 l ^ 2 = 81 l = 9 cm the answer is d ."
Answer: d
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 3 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 25 , b ) 43 , c ) 42 , d ) 40 , e ) 18
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 3 w = 120 = > w = 40 answer d"
Answer: d
Problem: dacid obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 98 , b ) 78 , c ) 76 , d ) 87 , e ) 75
Rationale: "average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : e"
Answer: e
Problem: 16 ltr of water is added with 24 ltr of a solution containing 90 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 48 % , b ) 52 % , c ) 54 % , d ) 60 % , e ) 70 %
Rationale: "we have a 24 litre solution containing 90 % of alcohol in the water . = > quantity of alcohol in the solution = 24 ã — 90 / 100 now 16 litre of water is added to the solution . = > total quantity of the new solution = 24 + 16 = 40 percentage of alcohol in the new solution = 24 ã — 90 / 100 40 ã — 100 = 24 ã — 9010040 ã — 100 = 24 ã — 2.25 / 100 = 54 % c"
Answer: c
Problem: a bag contains 3 white marbles and 3 black marbles . if each of 3 girls and 3 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 15 , d ) 1 / 20 , e ) 1 / 25
Rationale: first , total ways to select for all boys and girls , i . e 6 ! / ( 3 ! * 3 ! ) = 6 * 5 * 4 * 3 * 2 * 1 / 3 * 2 * 1 * 3 * 2 * 1 = 20 then there are one two way girls can have all same colors , either white or black . the number of ways in which 3 girls can select 3 white balls = 3 c 3 = 1 the number of ways in which 3 girls can select 3 black balls = 3 c 3 = 1 therefore , total favorable outcomes / total outcomes = 2 / 20 = 1 / 10 b
Answer: b
Problem: a cube has four of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
Options: a ) 1 : 4 , b ) 1 : 3 , c ) 1 : 2 , d ) 2 : 5 , e ) 2 : 11
Rationale: "let x be the area of each face of the cube . the area painted red is 4 ( x / 2 ) = 2 x the area painted white is 4 ( x / 2 ) + 2 x = 4 x the ratio of red to white is 2 x : 4 x which is 1 : 2 . the answer is c ."
Answer: c
Problem: if a book is sold at 5 % profit instead of 5 % loss , it would have brought rs 13 more . find out the cost price of the book
Options: a ) 75 , b ) 72 , c ) 130 , d ) 70 , e ) 80
Rationale: "let c . p . of the book be rs . ’ x ’ given , 1.05 x - 0.95 x = 13 = > 0.1 x = 13 = 13 / 0.1 = rs 130 answer : c"
Answer: c
Problem: if 4 and 8 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 3 , c ) 8 , d ) 14 , e ) 56
Rationale: 60 n / 4 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 2 * 2 * 2 * 2 * 2 = 3 * 5 * n / 8 must be an integer for this to be true n must multiple of 8 , thus min of n = 8 hence c
Answer: c
Problem: if 3 ^ 8 x 3 ^ 7 = 3 ^ n what is the value of n ?
Options: a ) 20 , b ) 18 , c ) 17 , d ) 16 , e ) 15
Rationale: "3 ^ 8 * 3 ^ 7 = 3 ^ n or 3 ^ 8 + 7 = 3 ^ n n = 15 e"
Answer: e
Problem: in karthik ' s opinion , his weight is greater than 55 kg but less than 62 kg . his brother does not agree with karthik and he thinks that karthik ' s weight is greater than 50 kg but less than 60 kg . his father ' s view is that his weight can not be greater than 58 kg . if all of them are correct in their estimation , what is the average of different probable weights of karthik ?
Options: a ) 54.5 , b ) 56.5 , c ) 59.2 , d ) 61 , e ) 62
Rationale: explanation : solution : assume karthik ' s weight be x kg . according to karthik , 55 < x < 62 according to karthik ; s brother , 50 < x < 60 . according to karthik ' s mother , x < 58 . the values satisfying all the above conditions are 56 and 57 . . ' . required average = ( 56 + 57 ) / 2 = 56.5 . answer : b
Answer: b
Problem: two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 200 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 15 sec , e ) 20 sec
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 200 + 200 ) / 20 = 20 sec . answer : e"
Answer: e
Problem: if 20 men can build a wall 66 metres long in 8 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 283.8 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 8 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 8 * 20 ) = 283.8 mtrs answer : a"
Answer: a
Problem: how many odd numbers between 10 and 1,300 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 17
Rationale: "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 17 numbers . answer : e ."
Answer: e
Problem: the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 770 the other is
Options: a ) 330 , b ) 90 , c ) 270 , d ) 250 , e ) 350
Rationale: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 770 = 90 answer is b ."
Answer: b
Problem: a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.20 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?
Options: a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.68 , d ) $ 102.07 , e ) $ 105.3
Rationale: "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.68 or 2 ) 25 + 25 + 25 = $ 96.60 c"
Answer: c
Problem: the distance between west - town to east - town is 15 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 2 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 7 . , c ) 10 . , d ) 12 . , e ) 15 .
Rationale: "time taken by the birds to meet = 15 / ( 2 + 1 ) = 5 mins distance traveled by the bird traveling from west - town = 2 * 5 = 10 answer : c"
Answer: c
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 10 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) 42 , b ) 36 , c ) 46 , d ) 38 , e ) 40
Rationale: "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 10 strikes , there would be 9 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 12 ' o clock , the 10 strikes and 9 intervals will take 2 * ( 10 + 9 ) = 38 secs d d"
Answer: d
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 20 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 22 , b ) 98 , c ) 60 , d ) 88 , e ) 24
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 20 = 3 x = > x = 10 / 3 . so , speed of the faster train = 20 / 3 = 20 / 3 * 18 / 5 = 24 km / hr . answer : e"
Answer: e
Problem: if a and b get profits of rs . 6,000 and rs . 4,000 respectively at the end of year then ratio of their investments are
Options: a ) 4 : 1 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5
Rationale: "suppose a and b is ratio of investment . so a : b = 6000 + 4000 a : b = 10000 a / ( a + b ) * 10000 = 6000 2 a = 3 b a / b = 3 / 2 i . e 3 : 2 answer : c"
Answer: c
Problem: on dividing 171 by a number , the quotient is 8 and the remainder is 3 . find the divisor .
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "d = ( d - r ) / q = ( 171 - 3 ) / 8 = 168 / 8 = 21 d"
Answer: d
Problem: 40 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 780 , b ) 200 , c ) 210 , d ) 220 , e ) 230
Rationale: "or , if there are n persons then no . of shakehands = nc 2 = 40 c 2 = 780 answer : a"
Answer: a
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 21000 . a ' s share is ?
Options: a ) 2999 , b ) 2778 , c ) 7000 , d ) 2889 , e ) 6612
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 21000 = 7000 answer : c"
Answer: c
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 15 more blue balls than white balls , and thrice as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 15 more blue balls than white balls . . . equation # 2 : y = 15 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 3 y solve equation # 2 for z : z = y - 15 now , we can replace both x and z with y in equation # 1 3 y + y + ( y - 15 ) = 100 5 y - 15 = 100 5 y = 115 y = 23 there are 23 blue balls . this is 15 more than the number of white balls , so z = 8 . that ' s the answer . just as a check , x = 69 , and 69 + 23 + 8 = 100 . answer = 8 , ( a )"
Answer: a
Problem: how long does a train 150 m long traveling at 36 kmph takes to cross a signal post ?
Options: a ) 8 sec , b ) 15 sec , c ) 20 sec , d ) 10 sec , e ) 22 sec
Rationale: d = 150 m s = 36 * 5 / 18 = 10 t = 150 * 1 / 10 = 15 sec answer : b
Answer: b
Problem: a car dealership has 40 cars on the lot , 20 % of which are silver . if the dealership receives a new shipment of 80 cars , 50 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the number of silver cars is 0.2 * 40 + 0.5 * 80 = 48 the percentage of cars which are silver is 48 / 120 = 40 % the answer is c ."
Answer: c
Problem: the two lines y = x and x = - 7 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 18.5 , b ) 21.5 , c ) 24.5 , d ) 27.5 , e ) 30.5
Rationale: "the point of intersection is ( - 7 , - 7 ) . the triangle has a base of length 7 and a height of 7 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 7 * 7 = 24.5 the answer is c ."
Answer: c
Problem: a train 125 m long passes a man , running at 3 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 79 , e ) 48
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 3 ) km / hr . x - 3 = 45 = > x = 48 km / hr . answer : option e"
Answer: e
Problem: if 16 ^ y = 4 ^ 14 , what is y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: 16 ^ y = 4 ^ 2 y = 4 ^ 14 2 y = 14 y = 7 the answer is e .
Answer: e
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 105 games will be played during the tournament . find the number of participants .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "let p be the number of participants . pc 2 = 105 ( p ) ( p - 1 ) = 210 = 15 * 14 p = 15 the answer is a ."
Answer: a
Problem: a train running at the speed of 90 km / hr crosses a pole in 6 seconds . find the length of the train .
Options: a ) 150 meter , b ) 100 meter , c ) 105 meter , d ) 120 meter , e ) 130 meter
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time ( 25 ) * 6 = 150 meter answer : a"
Answer: a
Problem: jen has a jar of jam , and she ate 1 / 3 of the jam for lunch . if jen ate 1 / 7 of the remaining jam for dinner , what fraction of the jam was left after dinner ?
Options: a ) 2 / 7 , b ) 3 / 7 , c ) 4 / 7 , d ) 9 / 14 , e ) 11 / 14
Rationale: let x be the amount of jam at the beginning . after lunch , the remaining jam was ( 2 / 3 ) x . after dinner , the remaining jam was ( 6 / 7 ) ( 2 / 3 ) x = ( 4 / 7 ) x . the answer is c .
Answer: c
Problem: a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.42 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?
Options: a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.78 , d ) $ 98.77 , e ) $ 105.3
Rationale: "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.77 or 2 ) 25 + 25 + 25 = $ 96.75 d"
Answer: d
Problem: the radius of the two circular fields is in the ratio 3 : 7 the area of the first field is what percent less than the area of the second ?
Options: a ) 82.9 % , b ) 84.2 % , c ) 81.0 % , d ) 80.6 % , e ) 81.6 %
Rationale: "r = 3 ï € r 2 = 9 r = 7 ï € r 2 = 49 49 ï € â € “ 40 ï € 100 - - - - ? = > 81.6 % . answer : e"
Answer: e
Problem: the distance between west - town to east - town is 20 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 4 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 7 . , c ) 10 . , d ) 16 . , e ) 15 .
Rationale: time taken by the birds to meet = 20 / ( 4 + 1 ) = 4 mins distance traveled by the bird traveling from west - town = 4 * 4 = 16 answer : d
Answer: d
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 6,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 3,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 6,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 6,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 480 = 0.10 x combine terms and subtract 0.08 x from both sides : 70 = 0.02 x divide both sides by 0.02 : 3,500 = x your answer is a ."
Answer: a
Problem: if p ^ 2 – 13 p + 40 = s , and p is a positive integer between 1 and 10 , inclusive , what is the probability that s < 0 ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 10
Rationale: p 2 – 13 p + 40 = s so ( p – 8 ) ( p – 5 ) = s for q to be negative , the expressions ( p – 8 ) and ( p – 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p – 8 ) and ( p – 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer ) . that means that there are only two integer values for p , 6 and 7 , that would yield a negative q . with a total of 10 possible p values , only 2 yield a negative q , so the probability is 2 / 10 or 1 / 5 . the correct answer is b .
Answer: b
Problem: a and b complete a work in 6 days . a alone can do it in 10 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 3.78 days , c ) 3.25 days , d ) 3.15 days , e ) 2.75 days
Rationale: "1 / 6 + 1 / 10 = 8 / 30 = 4 / 15 15 / 4 = 3.75 days answer : a"
Answer: a
Problem: 5 * 2 is a 3 digit number with * is a missing digit . if the number is divisible by 6 , the missing digit is
Options: a ) 0 , b ) 2 , c ) 5 , d ) 7 , e ) 9
Rationale: sol . let the number be 5 x 2 . clearly , it is divisible by 2 . now , 5 + x + 2 = ( 7 + x ) must be divisible by 3 . so , x = 2 . answer b
Answer: b
Problem: how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 38 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 2 , b ) 5 , c ) 8 , d ) 15 , e ) 25
Rationale: selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 38 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 50 - 40 ) / ( 40 - 38 ) = 5 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 8 lbs . answer ( c )
Answer: c
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 600 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 438 , b ) 446 , c ) 452 , d ) 462 , e ) 470
Rationale: "number of newborns that can die in first month = 1 / 10 * 600 = 60 survived = 540 number of newborns that can die in second month = 1 / 10 * 540 = 54 survived = 486 number of newborns that can die in third month = 1 / 10 * 486 = 48 survived = 438 answer : a"
Answer: a
Problem: three interviewers , a , b , and c are interviewing 40 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer b admitted 15 applicants , a admitted 17 applicants , and c admitted 20 applicants , at least how many applicants get the admission ?
Options: a ) 8
b ) 2
c ) 6
d ) 0
e ) 12
Rationale: if b admitted 15 are overlapping with a admission of 17 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : d
Answer: d
Problem: 0 , 1 , 5 , 14 , 30 , ____
Options: a ) 25 , b ) 35 , c ) 45 , d ) 65 , e ) 55
Rationale: "0 , 1,5 , 14 , 30 , . . . . . 0 + 1 * 1 = 1 1 + 2 * 2 = 5 5 + 3 * 3 = 14 14 + 4 * 4 = 30 so 30 + 5 * 5 = 55 answer : e"
Answer: e
Problem: the security gate at a storage facility requires a 4 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be odd , how many lock codes are possible ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 720 , e ) 1440
Rationale: x - x - x - x - x - - > there are 4 odd digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 4 - x - x - 3 . other x ' s can take following values : 4 - 5 - 4 - 3 - - > 4 * 5 * 4 * 3 = 240 . answer : b .
Answer: b
Problem: if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 4 ] ] ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 19 , e ) 28
Rationale: "[ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 4 ] ] = 4 ^ 2 + 2 * 4 + 4 = 28 . option e"
Answer: e
Problem: in a forest 110 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,500 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 150 tagged deers comprise 10 % of total # of deers - - > total # of deers = 110 * 10 = 1,100 . answer : d ."
Answer: d
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 4240 , what is the length of the plot in metres ?
Options: a ) 20 , b ) 200 , c ) 50 , d ) 400 , e ) 140
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 4240 [ 4 l - 40 ] = 4240 / 26.50 = 160 4 l = 200 l = 200 / 4 = 50 meters . answer : c"
Answer: c
Problem: in the new budget the price of milk rose by 20 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?
Options: a ) 7.5 % , b ) 9.1 % , c ) 10.9 % , d ) 16.67 % , e ) 15 %
Rationale: reduce in consumption = r / ( 100 + r ) * 100 % = 20 / 120 * 100 = 16.67 % answer is d
Answer: d
Problem: evaluate 64 / . 08
Options: a ) 800 , b ) 500 , c ) 505 , d ) none of these , e ) 506
Rationale: "explanation : 64 / . 08 = 6400 / 8 = 800 option a"
Answer: a
Problem: two airplanes take off from one airfield at noon . one flies due east at 206 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ?
Options: a ) 412 , b ) 332 , c ) 400 , d ) 483 , e ) 566
Rationale: "a in two hours : the plane flying east will be 412 miles away from airport . the other plane will be 566 miles away from airport . 566 / 412 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 412 miles apart . a"
Answer: a
Problem: 96 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0
Rationale: "should be simple . 0.96 * 5 / 8 = 4.8 / 8 = 0.6 correct option : c"
Answer: c
Problem: a man goes downstream at 14 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 0 kmph , b ) 4 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 3 kmph
Rationale: speed of the stream = 1 / 2 ( 14 - 8 ) kmph = 3 kmph . correct option : e
Answer: e
Problem: the ratio of radius of a circle and the side of a square is 2 : 11 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 7 , c ) 8 : 77 , d ) 4 : 121 , e ) none
Rationale: "radius / side = 2 / 11 ⇒ area of circle / area of square = 4 / 121 answer : d"
Answer: d
Problem: a train overtakes two person who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . the length of the train is :
Options: a ) 45 m , b ) 50 m , c ) 54 m , d ) 72 m , e ) none of these
Rationale: let actual speed of train = s m / sec and length of train = l m . then , s - 2 × 5 / 18 = l 9 ⇒ 9 s = l + 5 . . . … ( i ) and s - 4 × 5 ⁄ 18 = l ⁄ 10 ⇒ 90 s = 9 l + 100 . . . . . ( ii ) by ( i ) & ( ii ) , we get l = 50 m . answer b
Answer: b
Problem: a is twice as good a workman as b and together they finish a piece in 18 days . in how many days will a alone finish the work ?
Options: a ) 25 days , b ) 26 days , c ) 23 days , d ) 45 days , e ) 27 days
Rationale: "sol . ( a ’ s 1 day ’ s work ) : ) ( b ’ s 1 days work ) = 2 : 1 . ( a + b ) ' s 1 day ' s work = 1 / 18 divide 1 / 18 in the ratio 2 : 1 . : . a ’ s 1 day ' s work = ( 1 / 18 * 2 / 3 ) = 1 / 27 hence , a alone can finish the work in 27 days . ans : e"
Answer: e
Problem: on dividing a number by 56 , we get 26 as remainder . on dividing the same number by 8 , what will be the remainder ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "number = 56 x + 26 ( ∵ since the number gives 26 as remainder on dividing by 56 ) = ( 7 × 8 × x ) + ( 3 × 8 ) + 2 hence , if the number is divided by 8 , we will get 2 as remainder . answer : a"
Answer: a
Problem: if the wheel is 12 cm then the number of revolutions to cover a distance of 1240 cm is ?
Options: a ) 11 , b ) 14 , c ) 16 , d ) 12 , e ) 19
Rationale: "2 * 22 / 7 * 12 * x = 1240 = > x = 16 answer : c"
Answer: c
Problem: ( ab ) x − 2 = ( ba ) x − 7 . what is the value of x ?
Options: a ) 1.5 , b ) 4.5 , c ) 7.5 , d ) 9.5 , e ) 8.7
Rationale: explanation : ( a / b ) x − 2 = ( b / a ) x − 7 ⇒ ( a / b ) x − 2 = ( a / b ) − ( x − 7 ) ⇒ x − 2 = − ( x − 7 ) ⇒ x − 2 = − x + 7 ⇒ x − 2 = − x + 7 ⇒ 2 x = 9 ⇒ x = 92 = 4.5 option b
Answer: b
Problem: a and b together can do a piece of work in 6 days and a alone can do it in 10 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 18 days , c ) 15 days , d ) 21 days , e ) 22 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 10 work in 1 day b alone can do ( 1 / 6 - 1 / 10 ) = 1 / 15 work in 1 day = > complete work can be done in 15 days by b answer : option c"
Answer: c
Problem: jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 94 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 102
Rationale: total score on 3 tests = 94 * 3 = 282 jerry wants the average to be = 96 hence total score on 4 tests should be = 96 * 4 = 384 score required on the fourth test = 384 - 282 = 102 option e
Answer: e
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 18000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "0.036 * 10 ^ 5 can be written as 3600 18000 * 10 ^ ( - 3 ) can be written as 18 required = 3600 / 18 = 200 answer : b"
Answer: b
Problem: an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4400 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 5500 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: 4 - - - 4400 5 - - - ? = > 5500 answer : b
Answer: b
Problem: it takes avery 3 hours to build a brick wall while tom can do it in 2.5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 25 minutes . , b ) 30 minutes . , c ) 40 minutes . , d ) 55 minutes , e ) 1 hour and 20 minutes
Rationale: "avery ' s efficiency is 100 / 3 = 33 % tom ' s = 100 / 2.5 = 40 % they worked together for 1 hour and finished 73 % of the job remaining = 27 % tom will complete 40 % in 60 minutes , 20 % in 30 minutes and , 7 % in 60 * 7 / 40 minutes = 10.5 minutes time taken by tom to finish the remaining on his own = 30 + 10.5 = 40.5 minutes ( adjusting for the 0.333 ) ~ 40 minutes answer : c"
Answer: c
Problem: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is ?
Options: a ) 127 , b ) 688 , c ) 200 , d ) 121 , e ) 123
Rationale: "let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"
Answer: c
Problem: the current of a stream runs at the rate of 3 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) a ) 7.24 , b ) b ) 2 , c ) c ) 8.5 , d ) d ) 6.67 , e ) e ) 3
Rationale: "s = 3 m = x ds = x + 3 us = x - 3 6 / ( x + 3 ) + 6 / ( x - 3 ) = 2 x = 7.24 answer : a"
Answer: a
Problem: an article with cost price of 180 is sold at 15 % profit . what is the selling price ?
Options: a ) 198 , b ) 200 , c ) 204 , d ) 207 , e ) 210
Rationale: "sp = 1.15 * 180 = 207 answer : d"
Answer: d
Problem: the average monthly salary of 15 employees in an organisation is rs . 1800 . if the manager ' s salary is added , then the average salary increases by rs . 150 . what is the manager ' s monthly salary ?
Options: a ) rs . 3601 , b ) rs . 3618 , c ) rs . 4200 , d ) rs . 3619 , e ) rs . 3610
Rationale: "manager ' s monthly salary = rs . ( 1950 * 16 - 1800 * 15 ) = rs . 4200 answer : c"
Answer: c
Problem: 8 machines , each working at the same constant rate , together can complete a certain job in 24 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 16 days ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 24 to 16 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 8 = 12 so we need 12 - 8 = 4 more machines . answer : c"
Answer: c
Problem: a group of boy scouts and girls scouts is going on a rafting trip . 52 % of the scouts arrived with signed permission slips . if 40 % of the scouts were boy scouts and 62.5 % of the boy scouts arrived with signed permission slips , then what percentage of the children were girl scouts who arrived with signed permission slips ?
Options: a ) 27 , b ) 28 , c ) 29 , d ) 30 , e ) 31
Rationale: "we do n ' t know how many scouts went on the trip , so let ' s assume 100 scouts went on the trip ( since we only are concerned with percents in the answer ) 40 % were boy scouts so 40 % of 100 = 40 were boy scouts 62.5 % of the boy scouts brought their permission slips signed , so . 625 * 40 = 25 boy scouts had signed slips 15 boy scouts did not 52 % of all the scouts had signed slips , so . 52 * 100 = 52 in total had signed slips thus 52 - 25 = 27 girl scouts had signed slips thus the percentage of scouts who were girl scouts arriving with signed permission slips is 27 / 100 = . 27 = 27 % a"
Answer: a
Problem: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 % fescue . if a mixture of x and y contains 30 % ryegrass , what percent of the weight of the mixture is x ?
Options: a ) 10 % , b ) 33 1 / 3 % , c ) 40 % , d ) 50 % , e ) 66 2 / 3 %
Rationale: "assuming the weight of the mixture to be 100 g * * , then the weight of ryegrass in the mixture would be 30 g . also , assume the weight mixture x used in the mixture is xg , then the weight of mixture y used in the mixture would be ( 100 - x ) g . so we can now equate the parts of the ryegrass in the mixture as : 0.4 x + 0.25 ( 100 - x ) = 30 0.4 x + 25 - 0.25 x = 30 0.15 x = 5 x = 5 / 0.15 = 500 / 15 = 100 / 3 so the weight of mixture x as a percentage of the weight of the mixture = ( weight of x / weight of mixture ) * 100 % = ( 100 / 3 ) / 100 * 100 % = 33 % answer : b"
Answer: b
Problem: a , b and c invests rs . 4000 , rs . 3000 and rs . 2000 in a business . after one year b removed his money ; a and c continued the business for one more year . if the net profit after 2 years be rs . 2400 , then b ' s share in the profit is ?
Options: a ) 276 , b ) 289 , c ) 480 , d ) 400 , e ) 278
Rationale: "4 * 24 : 3 * 12 : 2 * 24 8 : 3 : 4 3 / 15 * 2400 = 480 answer : c"
Answer: c
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 3 hours to fill the tank . the leak can drain all the water in ?
Options: a ) 10 hr , b ) 14 hr , c ) 12 hr , d ) 9 hr , e ) 15 hr
Rationale: "work done by the leak in 1 hour = 1 / 2 - 3 / 7 = 1 / 14 leak will empty the tank in 14 hrs answer is b"
Answer: b
Problem: the cost of 16 pens and 8 pencils is rs . 352 and the cost of 4 pens and 4 pencils is rs . 96 . find the cost of each pen ?
Options: a ) rs . 32 , b ) rs . 28 , c ) rs . 36 , d ) rs . 25 , e ) none of these
Rationale: "let the cost of each pen and pencil be ' p ' and ' q ' respectively . 16 p + 8 q = 352 - - - ( 1 ) 4 p + 4 q = 96 8 p + 8 q = 192 - - - ( 2 ) ( 1 ) - ( 2 ) = > 8 p = 160 = > p = 20 answer : e"
Answer: e
Problem: if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 55 minutes ?
Options: a ) 80 , b ) 100 , c ) 150 , d ) 180 , e ) 220
Rationale: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 55 minutes the population increases by 55 x 4 = 220 people . answer . e ."
Answer: e
Problem: five 6 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 32 , b ) 1 / 1296 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: the three dice can fall in 6 * 6 * 6 * 6 * 6 = 7776 ways . hence the probability is 6 / 7776 = 1 / 1296 answer : b
Answer: b
Problem: in the junior basketball league there are 21 teams , 1 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 11 .
Rationale: "total teams = 21 bad teams = ( 1 / 3 ) * 21 = 7 rich teams = 10 so maximum value that the both rich and bad can take will be 10 . so e = 11 can not be that value . ans e ."
Answer: e
Problem: a and b undertake to do a piece of work for rs . 1200 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of a .
Options: a ) 500 , b ) 600 , c ) 750 , d ) 800 , e ) none of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 1200 * 4 / 8 ) = rs . 600 , b ' s share = rs . ( 1200 * 3 / 8 ) = rs . 450 c ' s share = rs . [ 1200 - ( 300 + 225 » ) = rs . 150 . answer is b"
Answer: b
Problem: a can do a half of certain work in 60 days and b one third of the same in 35 days . they together will do the whole work in .
Options: a ) 56 days , b ) 420 days , c ) 46 days , d ) 560 days , e ) 96 days
Rationale: "a = 120 days b = 105 days 1 / 120 + 1 / 105 = 45 / 2520 = 1 / 56 = > 56 days answer : a"
Answer: a
Problem: if p is a prime number greater than 3 , find the remainder when p ^ 2 + 15 is divided by 12 .
Options: a ) 6 , b ) 4 , c ) 0 , d ) 8 , e ) 7
Rationale: "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 15 = 36 n ^ 2 + 12 n + 1 + 15 = 36 n ^ 2 + 12 n + 12 + 4 if p = 6 n - 1 , then p ^ 2 + 15 = 36 n ^ 2 - 12 n + 1 + 15 = 36 n ^ 2 - 12 n + 12 + 4 when divided by 12 , it must leave a remainder of 4 . the answer is b ."
Answer: b
Problem: a merchant marks his goods up by 40 % and then offers a discount of 10 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 8 % , b ) 14 % , c ) 26 % , d ) 15 % , e ) 17 %
Rationale: "let the price be 100 . the price becomes 140 after a 40 % markup . now a discount of 10 % on 126 . profit = 126 - 100 26 % answer c"
Answer: c
Problem: if a and b are positive numbers , and a ^ 3 + b ^ 3 = 100 , then the greatest possible value of a is between :
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
Rationale: "if a = 4.5 and b is a bit more than 2 , then a ^ 3 + b ^ 3 can equal 100 . if a > 5 , then a ^ 3 + b ^ 3 > 100 . the answer is c ."
Answer: c
Problem: the average age of 18 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?
Options: a ) 9 , b ) 31 , c ) 56 , d ) 72 , e ) 90
Rationale: age of the 15 th student = 18 * 15 - ( 14 * 5 + 16 * 9 ) = 270 - 214 = 56 years answer is c
Answer: c
Problem: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 1800 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 16,200 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 22,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 1800 triples to $ 5400 , in 28 years , it will again triple to $ 5400 * 3 = $ 16,200 answer a"
Answer: a
Problem: a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) s . 240 , b ) s . 140 , c ) s . 340 , d ) s . 50 , e ) s . 90
Rationale: "a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 300 and 200 . difference in profit share = 420 - 280 = 140 answer : b"
Answer: b
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 27.675 , c ) 30 , d ) data inadequate , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 × ( 100 + 23.5 ) / ( 100 − 5 ) = 100 × 247 / 190 = 130 hence , required % profit = 130 – 100 = 30 % answer c"
Answer: c
Problem: p and q started a business investing rs 10000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 2 : 7 , b ) 2 : 6 , c ) 17 : 6 , d ) 2 : 3 , e ) 7 : 8
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 10000 : 15000 = 10 : 15 = 2 : 3 option d"
Answer: d
Problem: 0.99999 + 0.11112 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.111 , e ) 1.11111
Rationale: "0.99999 + 0.11112 = 0.99999 + 0.11111 + 0.00001 = ( 0.99999 + 0.00001 ) + 0.11111 = 1 + 0.11111 = 1.11111 e"
Answer: e
Problem: the perimeter of one square is 40 cm and that of another is 20 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 11.2 √ 2 , b ) 13 √ 2 , c ) 23 √ 2 , d ) 12 √ 4 , e ) 13 √ 9
Rationale: "4 a = 40 4 a = 20 a = 10 a = 5 a 2 = 100 a 2 = 25 combined area = a 2 = 125 = > a = 11.2 d = 11.2 √ 2 answer : a"
Answer: a
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 860 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 680 , d ) s . 700 , e ) s . 720
Rationale: "s . i . for 1 year = rs . ( 860 - 815 ) = rs . 45 . s . i . for 3 years = rs . ( 45 x 3 ) = rs . 135 . principal = rs . ( 815 - 135 ) = rs . 680 . answer : option c"
Answer: c
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 874 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 638 , c ) s . 698 , d ) s . 700 , e ) s . 760
Rationale: "s . i . for 1 year = rs . ( 874 - 815 ) = rs . 59 . s . i . for 3 years = rs . ( 59 x 3 ) = rs . 177 . principal = rs . ( 815 - 177 ) = rs . 638 . answer : option b"
Answer: b
Problem: the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 3 / 8 is given by ?
Options: a ) 7 / 98 , b ) 1 / 48 , c ) 1 / 98 , d ) 1 / 96 , e ) 3 / 42
Rationale: 2 / 3 * 6 / 7 * 1 / 3 * 3 / 8 = 36 / 504 = 3 / 42 answer : e
Answer: e
Problem: find the quantities of two types of rice to be mixed , first variety is of rs . 12 per kg and second variety is of rs . 20 per kg . to get 12 kg of rice mixture worth rs . 15 per kg ? ( in kg )
Options: a ) 3.5 , 8.5 , b ) 7 , 5 , c ) 7.5 , 4.5 , d ) 8 , 4 , e ) 8 , 5
Rationale: from allegation & mixture ratio = c - m / m - d = 20 - 15 / 15 - 12 = 5 / 3 . from the option c r = 7.5 / 4.5 = 5 / 3 answer : c
Answer: c