regisss/math_qa huggingface dataset:
Problem: pipe a can fill a tank in 2 hours . due to a leak at the bottom , it takes 3 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 10 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "let the leak can empty the full tank in x hours 1 / 2 - 1 / x = 1 / 3 = > 1 / x = 1 / 2 - 1 / 3 = ( 3 - 2 ) / 6 = 1 / 6 = > x = 6 . answer : d"
Answer: d
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 752 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 752 - 640 = 112 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 112 / 28 = 28 / 7 = 4 total hrs = 40 + 4 = 44 answer c 44"
Answer: c
Problem: if the weight of 12 meters long rod is 12.2 kg . what is the weight of 6 meters long rod ?
Options: a ) 7.2 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 6.1 kg , e ) none
Rationale: "answer ∵ weight of 12 m long rod = 12.2 kg ∴ weight of 1 m long rod = 12.2 / 12 kg ∴ weight of 6 m long rod = 12.2 x 6 / 12 = 6.1 kg option : d"
Answer: d
Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 45000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 4 : 3
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 45000 × 9 = 45 × 12 : 45 × 9 = 3 × 12 : 2 × 9 = 4 : 3 answer is e ."
Answer: e
Problem: find the fraction which has the same ratio to 2 / 5 that 3 / 7 has to 6 / 5
Options: a ) 2 / 4 , b ) 6 / 78 , c ) 4 / 7 , d ) 3 / 5 , e ) 1 / 7
Rationale: "p : 2 / 5 = 3 / 7 : 6 / 5 as the product of the means is equal to the product of the extremes . p * 6 / 5 = 2 / 5 * 3 / 7 p * 6 / 5 = 6 / 35 p = 1 / 7 = > p = 1 / 7 answer : e"
Answer: e
Problem: a student traveled 25 percent of the distance of the trip alone , continued another 20 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 150
Rationale: "let x be the total length of the trip . 0.25 x + 20 miles + 0.5 x = x 20 miles = 0.25 x x = 80 miles the answer is b ."
Answer: b
Problem: david obtained 72 , 60 , 35 , 62 and 84 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 62.6 , c ) 87 , d ) 165 , e ) 11
Rationale: explanation : average = ( 72 + 60 + 35 + 62 + 84 ) / 5 = 313 / 5 = 62.6 . answer : b
Answer: b
Problem: mohit sold an article for $ 12000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
Options: a ) 16000 , b ) 25000 , c ) 10000 , d ) 18000 , e ) 17000
Rationale: "let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 12000 - 10 / 100 ( 12000 ) = 12000 - 1200 = $ 10800 = > 1.08 x = 10800 = > x = 10000 c"
Answer: c
Problem: a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 1.80 , what total number of pens and pencils did the customer purchase ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "answer : algebraically , the question looks like this : 2.5 = 0.35 x + 0.25 y there are three possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 and 3 pencils for $ 0.25 each . that ' s 3 pens and 3 pencils for a total of 6 pens and pencils . choice ( a ) is correct ."
Answer: a
Problem: what profit percent is made by selling an article at a certain price , if by selling at 1 / 2 rd of that price , there would be a loss of 20 % ?
Options: a ) 20 % , b ) 29 % , c ) 60 % , d ) 27 % , e ) 28 %
Rationale: "sp 2 = 1 / 2 sp 1 cp = 100 sp 2 = 80 1 / 2 sp 1 = 80 sp 1 = 160 100 - - - 160 = > 60 % answer : c"
Answer: c
Problem: williams works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 10 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 5 / 8 , b ) 7 / 8 , c ) 6 / 8 , d ) 2 / 9 , e ) 1 / 7
Rationale: "first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 10 x total tips for all months = 6 * x + 10 x = 16 x tips for august / total tips for all months = 10 x / 16 x = 5 / 8 answer : a"
Answer: a
Problem: how many seconds will it take for a car that is traveling at a constant rate of 77 miles per hour to travel a distance of 21 yards ? ( 1 mile = 1,160 yards )
Options: a ) . 1 , b ) 0.3 , c ) 0.6 , d ) 2 , e ) 1.6
Rationale: "speed = 77 miles / hr = 37.64 yard / s distance = 21 yards time = distance / speed = 21 / 37.64 = 0.6 sec ans - c"
Answer: c
Problem: by selling an article at rs . 400 , a profit of 25 % is made . find its cost price ?
Options: a ) 228 , b ) 320 , c ) 287 , d ) 480 , e ) 811
Rationale: "sp = 400 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 400 * [ 100 / ( 100 + 25 ) ] = 400 * [ 100 / 125 ] = rs . 320 answer : b"
Answer: b
Problem: a certain galaxy is known to comprise approximately 4 x 10 ^ 12 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 80,000 , d ) 12,000 , e ) 80,000
Rationale: "total no . of stars on galaxy = 4 * 10 ^ 12 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 4 * 10 ^ 12 / 50 * 10 ^ 6 = 40 * 10 ^ 4 / 5 = 80000 therefore answer is c"
Answer: c
Problem: 12.5 % of 192 = 50 % of ?
Options: a ) 48 , b ) 96 , c ) 24 , d ) none of these , e ) can not be determined
Rationale: "answer let 12.5 % of 192 = 50 % of a , ⇒ ( 12.5 x 192 ) / 100 = ( 50 x a ) / 100 ∴ a = ( 12.5 x 192 ) / 50 = 48 correct option : a"
Answer: a
Problem: a 9 % stock yields 25 % . the market value of the stock is :
Options: a ) rs 45 , b ) rs 25 , c ) rs 40 , d ) rs 39 , e ) rs 36
Rationale: "explanation : for an income of rs . 25 , investment = rs . 100 . for an income of rs 9 , investment = rs . 100 / 25 x 9 = rs 36 market value of rs . 100 stock = rs 36 answer is e"
Answer: e
Problem: find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 asquotient and the 15 as remainder ?
Options: a ) 1245 , b ) 1567 , c ) 1678 , d ) 1335 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Problem: ‘ a ’ completes a work in 12 days . ‘ b ’ completes the same work in 15 days . ‘ a ’ started working alone and after 3 days b joined him . how many days will they now take together to complete the remaining work ?
Options: a ) 5 , b ) 8 , c ) 6 , d ) 4 , e ) none of these
Rationale: work done by ‘ a ’ in 3 days = 1 ⁄ 12 × 3 = 1 ⁄ 4 ∴ remaining work = 1 - 1 ⁄ 4 = 3 ⁄ 4 work done by a and b together = 12 × 15 / 27 = 20 / 3 ∴ remaining work done by a and b together in = 3 ⁄ 4 × 20 ⁄ 3 = 5 days answer a
Answer: a
Problem: the sum of ages of 5 children born 3 years different each is 50 years . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 16 , e ) 17
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . x + 12 = 4 + 12 = 16 d"
Answer: d
Problem: in a coconut grove , ( x + 2 ) trees yield 40 nuts per year , x trees yield 120 nuts per year and ( x – 2 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "( x + 2 ) × 40 + x × 120 + ( x − 2 ) × 180 / ( x + 2 ) + x + ( x − 2 ) = 100 ⇒ 340 x − 280 / 3 x = 100 ⇒ 40 x = 280 ⇒ x = 7 answer e"
Answer: e
Problem: find value for x from given equation ? x + 1 = - 3
Options: a ) 1 , b ) x = - 4 , c ) - 3 , d ) - 5 , e ) 5
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = - 3 - 1 2 . simplify both sides : x = - 4 b"
Answer: b
Problem: rectangular tile each of size 25 cm by 65 cm must be laid horizontally on a rectangular floor of size 150 cm by 390 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 50 , b ) 40 , c ) 25 , d ) 36 , e ) 45
Rationale: "area of tile = 25 * 65 = 1625 area of floor = 150 * 390 = 58500 no of tiles = 58500 / 1625 = 36 so , the no of tile = 36 answer : d"
Answer: d
Problem: of the 3,600 employees of company x , 1 / 6 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 13 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "welcome , just post the question and the choices let ' s see , the way i did it was 1 / 6 are clerical out of 3600 so 600 are clerical 600 reduced by 1 / 4 is 1200 * 1 / 4 so it reduced 150 people , so there is 450 clerical people left but since 150 people left , it also reduced from the total of 3600 so there are 3450 people total since 450 clerical left / 3450 people total you get ( a ) 13 % answer : a"
Answer: a
Problem: the area of a triangle is with base 3 m and height 6 m ?
Options: a ) 88 m 2 , b ) 9 m 2 , c ) 66 m 2 , d ) 77 m 2 , e ) 31 m 2
Rationale: "1 / 2 * 3 * 6 = 9 m 2 answer : b"
Answer: b
Problem: 9886 + x = 13200 , then x is ?
Options: a ) 3327 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: "answer x = 13200 - 9886 = 3314 option : e"
Answer: e
Problem: if x is a sum of all even integers on the interval 13 . . . 45 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 16 , c ) 26 , d ) 52 , e ) 1014
Rationale: "x = 14 + 16 + . . . + 44 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 44 ) / 2 * 16 = 29 * 16 . gcd of 16 and 29 * 16 is 16 . answer : b ."
Answer: b
Problem: in a stream running at 2 kmph , a motor boat goes 6 km upstream and back again to the starting point in 33 minutes . find the speed of the motorboat in still water .
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) none of them
Rationale: let the speed of the motarboat in still water be x kmph . then , 6 / x + 2 + 6 / x - 2 = 33 / 60 11 x 2 - 240 x - 44 = 0 11 x 2 - 242 x + 2 x - 44 = 0 ( x - 22 ) ( 11 x + 2 ) = 0 x = 22 . answer is a
Answer: a
Problem: a cistern is filled by a tap in 5 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 60 , b ) 62 , c ) 64 , d ) 66 , e ) 68
Rationale: "filling rate - leak rate = net rate 1 / 5.5 - leak rate = 1 / 6 leak rate = 2 / 11 - 1 / 6 = 1 / 66 the answer is d ."
Answer: d
Problem: ajay bought 15 kg of dal at the rate of rs 14.50 per kg and 10 kg at the rate of rs 13 per kg . he mixed the two and sold the mixture at the rate of rs 15 per kg . what was his total gain in this transaction ?
Options: a ) rs 1.10 , b ) rs 11 , c ) rs 16.50 , d ) rs 27.50 , e ) none of these
Rationale: explanation : cost price of 25 kg = rs . ( 15 x 14.50 + 10 x 13 ) = rs . 347.50 . sell price of 25 kg = rs . ( 25 x 15 ) = rs . 375 . profit = rs . ( 375 — 347.50 ) = rs . 27.50 . answer : d
Answer: d
Problem: speed of a boat in standing water is 10 kmph and speed of the stream is 2 kmph . a man can rows to a place at a distance of 100 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 24 hours , b ) 21 hr 30 min , c ) 20 hr 50 min , d ) 18 hr 15 min , e ) 22 hrs
Rationale: speed upstream = 8 kmph speed downstream = 12 kmph total time taken = 100 / 8 + 100 / 12 = 20 hours 50 min answer is c
Answer: c
Problem: shekar scored 76 , 65 , 82 , 67 and 95 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 77 , c ) 75 , d ) 85 , e ) 90
Rationale: explanation : average = ( 76 + 65 + 82 + 67 + 95 ) / 5 = 385 / 5 = 77 hence average = 77 answer : b
Answer: b
Problem: if in a race of 110 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 16 m , c ) 11 m , d ) 22 m , e ) 15 m
Rationale: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 110 * 5 ) / 25 = 22 m hence , a beats b by 22 m . answer d"
Answer: d
Problem: a small company reduced its faculty by approximately 20 percent to 195 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 224 , e ) e ) 244
Rationale: "if x is the original number of employees , then after 20 % reduction in employees number is . 80 x but we are given . 80 x = 195 x = 244 so the original number of employees is 244 correct answer - e"
Answer: e
Problem: a part of certain sum of money is invested at 9 % per annum and the rest at 15 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 6 , b ) 4 : 9 , c ) 5 : 3 , d ) 4 : 1 , e ) 4 : 2
Rationale: "15 : 9 = 5 : 3 answer : c"
Answer: c
Problem: if 3 men or 4 women can reap a field in 43 days how long will 7 men and 5 women take to reap it ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 19
Rationale: "explanation : 3 men reap 1 / 43 field in 1 day 1 man reap 1 / ( 3 x 43 ) 4 women reap 1 / 43 field in 1 day 1 woman reap 1 / ( 43 x 4 ) 7 men and 5 women reap ( 7 / ( 3 x 43 ) + 5 / ( 4 x 43 ) ) = 1 / 12 in 1 day 7 men and 5 women will reap the field in 12 days answer : option b"
Answer: b
Problem: the smallest number when increased by ` ` 3 ` ` is exactly divisible by 510 , 4590 , and 105 is :
Options: a ) 630 , b ) 633 , c ) 150 , d ) 140 , e ) 627
Rationale: lcm = 630 630 - 3 = 627 answer : e
Answer: e
Problem: if the perimeter of square region d and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of d
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pd ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pd = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Problem: a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 3 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 / 3 = s * 8 / 3 tips = s * 8 / 3 fraction of his income came from tips = ( s * 5 / 3 ) / ( s * 8 / 3 ) = 5 / 8 answer : c"
Answer: c
Problem: if ( c - a ) / ( c - b ) = 3 , then ( 5 b - 5 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 3.33 , e ) 2.5
Rationale: "let ' s say c = 7 , b = 5 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 3.33 answer d ( hopefully ) ) )"
Answer: d
Problem: rachel and sarah spent $ 8 for gasoline , $ 15.65 for their lunch , and $ 5 apiece for gifts for grandma . grandma gave each of them $ 10 . if the girls left home with a total of $ 50 , how much do they have for the return trip ?
Options: a ) $ 36.35 , b ) $ 26.35 , c ) $ 16.35 , d ) $ 46.35 , e ) $ 56.35
Rationale: $ 50 + $ 20 = $ 70 what they left with plus $ 10 to each $ 8 + $ 15.65 + $ 10 = $ 33.65 what they spent ( gifts are $ 5 + $ 5 ) $ 70 - $ 33.65 = $ 36.35 left correct answer a
Answer: a
Problem: in the fifth grade at parkway elementary school there are 420 students . 320 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 , d ) 65 , e ) 108
Rationale: "total students = 420 boys = 320 , girls = 100 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 100 - 35 = 65 . correct option : d"
Answer: d
Problem: p and q invested in a shop . the profits were divided in the ratio of 2 : 4 respectively . if p invested rs . 500000 , the amount invested by q is :
Options: a ) 5000000 , b ) 4000000 , c ) 1000000 , d ) 6000000 , e ) none
Rationale: "suppose q invested rs . y . then , 500000 / y = 2 / 4 or y = [ 500000 x 4 / 2 ] = 1000000 . answer c"
Answer: c
Problem: 1939392 * 625
Options: a ) 1212120010 , b ) 1212120000 , c ) 1212120011 , d ) 1212121010 , e ) 1212121000
Rationale: "explanation : trick : when multiplying with 5 n 5 n then put n zeros to the right of multiplicand and divide the number with 2 n 2 n so using this we can solve this question in much less time . 1939392 × 5 ( 4 ) = 1939392000016 = 1212120000 option b"
Answer: b
Problem: if ( m - 8 ) is a factor of m ^ 2 - qm - 24 , then q =
Options: a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
Rationale: "( m - 8 ) ( m - a ) = m ^ 2 - qm - 24 a = - 3 q = 8 + a = 5 = b"
Answer: b
Problem: peter invests a sum of money and gets back an amount of $ 815 in 3 years . david invests an equal amount of money and gets an amount of $ 870 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
Options: a ) 670 , b ) 650 , c ) 698 , d ) 744 , e ) 700
Rationale: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 870 - 815 = 55 interest earned for 3 years = 55 * 3 = 165 amount invested = 815 - 165 = 650 answer : b"
Answer: b
Problem: the ratio of the adjacent angles of a parallelogram is 5 : 13 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 168 ° , b ) 134 ° , c ) 156 ° , d ) 224 ° , e ) none of these
Rationale: "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 5 x + 13 x = 180 ° or , 18 x = 180 ° or , x = 10 ° hence the angles of the parallelogram are 50 ° and 130 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 50 ° + 84 ° = 134 ° answer : b"
Answer: b
Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turn on to be white , if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ?
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 9 , d ) 3 / 7 , e ) 4 / 7
Rationale: "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b"
Answer: b
Problem: half a number plus 5 is 13 . what is the number ?
Options: a ) 8 , b ) 16 , c ) 10 , d ) 11 , e ) 12
Rationale: "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 13 ( 1 / 2 ) x = 13 - 5 ( 1 / 2 ) x = 8 x = 16 correct answer is b"
Answer: b
Problem: a hare and a jackal are running a race . 3 leaps of the hare are equal to 4 leaps of the jackal . for every 6 leaps of the hare , the jackal takes 7 leaps . find the ratio of the speed of the hare to the speed of the jackal .
Options: a ) 64 : 25 , b ) 8 : 7 , c ) 5 : 8 , d ) 25 : 64 , e ) 6 : 7
Rationale: the hare takes 6 leaps and the jackal takes 7 leaps . 1 hare leap = 4 / 3 jackal leaps thus the hare ' s 6 leaps = 6 * ( 4 / 3 ) = 8 jackal leaps . the ratio of their speeds is 8 : 7 . the answer is b .
Answer: b
Problem: on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 15
Rationale: "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 c"
Answer: c
Problem: a , b and c enter into a partnership by investing $ 15000 , $ 21000 and $ 27000 respectively . at the end of 8 months , b receives $ 1540 as his share . find the share of a .
Options: a ) $ 800 , b ) $ 900 , c ) $ 1000 , d ) $ 1100 , e ) $ 1200
Rationale: "the ratio of capital of a , b and c = 15000 : 21000 : 27000 = 5 : 7 : 9 a ' s share = ( 5 / 7 ) * 1540 = $ 1100 the answer is d ."
Answer: d
Problem: a is twice as good as workman as b and together they finish a piece of work in 18 days . in how many days will a alone finish the work ?
Options: a ) 27 , b ) 26 , c ) 29 , d ) 25 , e ) 24
Rationale: "a : b = 2 : 1 ab ' s together wrk in 18 days a ; s alone is 1 / 18 * 2 / 3 = 27 days answer : a"
Answer: a
Problem: when a number is divided by 6 & then multiply by 12 the answer is 15 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.6 , d ) 7.5 , e ) 6.5
Rationale: "if $ x $ is the number , x / 6 * 12 = 15 = > 2 x = 15 = > x = 7.5 d"
Answer: d
Problem: by selling 15 pens for a rupee a woman loses 25 % . how many for a rupee should he sell in order to gain 25 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 10 , e ) 65
Rationale: "d 85 % - - - 15 125 % - - - ? 85 / 125 * 15 = 10"
Answer: d
Problem: if the perimeter of square region z and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of z
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pz ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pz = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 9 years hence ?
Options: a ) 22 , b ) 77 , c ) 78 , d ) 98 , e ) 71
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 9 years , their ages will be 49 and 29 . sum of their ages = 49 + 29 = 78 . answer : c"
Answer: c
Problem: a , band c can do a piece of work in 35 days , 20 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 16 days
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 35 + 1 / 20 = 11 / 140 ( a + c ) ' s 1 day ' s work = 1 / 35 + 1 / 55 = 18 / 385 work done in 2 day ' s = 11 / 140 + 18 / 385 = 48 / 383 48 / 383 th work done in 2 days work done = 383 / 48 * 2 = 16 days ( approx ) answer : e"
Answer: e
Problem: aram ’ s car was fined when he gave joe and peter a ride , so they decided to help aram pay the fine . joe paid $ 3 more than 1 / 4 of the fine and peter paid $ 3 less than 1 / 3 of the fine , leaving pay $ 4 less than 1 / 2 the fine to complete the payment . what fraction of the fine did aram pay ?
Options: a ) $ 13 , b ) $ 15 , c ) $ 20 , d ) $ 28 , e ) $ 48
Rationale: as given aram ' payment is [ 1 ] [ / 2 ] * fine - 4 i . e total fine = 2 * ( sam ' s payment + 4 ) now , as everything looks integer , fine should be able to divide by 4 and 3 . because joe ' s contribution has 1 / 4 of the fine and peter ' s contribution has 1 / 3 of the fine so , that leads me to following : options , aram ' s pay , total fine ( f ) , f / 4 , f / 3 a ) , 13 , 34 , no i . e 34 / 4 , no i . e 34 / 3 b ) , 14 , 38 , no , no c ) , 20 , 48 , yes yes , no need to further go on as we have got f / 4 and f / 3 correct , just for confirmation we go further d ) , 28 , 64 , yes , no e ) , 48 , 104 , yes , no correct answer is c
Answer: c
Problem: what is 992 * 992 ?
Options: a ) 974,169 , b ) 974,219 , c ) 984,064 , d ) 985,219 , e ) 985,369
Rationale: "if you take a base of 1000 then 992 is 8 less than 1000 to get the product of 992 x 992 write like this 992 - 8 ( as 8 less than base 1000 ) 992 - 8 now 8 x 8 = 64 and 992 - 8 = 984 so 992 x 992 = 984064 . . . ( bingo the answer is c . you can even have a shortcut . . . . . . 8 x 8 = 64 . . . only answer choice has last three digits as 64 . . so no need to calculate 992 - 8 . after you get 8 x 8 you can straight way pick answer choice c ."
Answer: c
Problem: the mean of 50 observations was 36 . it was found later that an observation 43 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 36.1 , c ) 36.2 , d ) 36.4 , e ) none
Rationale: "solution correct sum = ( 36 x 50 + 43 - 23 ) = 1820 . â ˆ ´ correct mean = 1820 / 50 = 36.4 . answer d"
Answer: d
Problem: due to construction , the speed limit along an 5 - mile section of highway is reduced from 52 miles per hour to 36 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 3.12 , b ) b ) 8 , c ) c ) 10 , d ) d ) 2.57 , e ) e ) 24
Rationale: "old time in minutes to cross 5 miles stretch = 5 * 60 / 52 = 5 * 15 / 13 = 5.76 new time in minutes to cross 5 miles stretch = 5 * 60 / 36 = 5 * 5 / 3 = 8.33 time difference = 2.57 ans : d"
Answer: d
Problem: it is currently 7 : 16 pm . at what time in the morning was it exactly 19,443 minutes earlier ?
Options: a ) 7 : 11 , b ) 7 : 13 , c ) 7 : 17 , d ) 7 : 19 , e ) 7 : 21
Rationale: converting 19,443 minutes to hours , we get 19,443 / 60 = 324 r 3 ; that is 324 hours and 3 minutes . all of the answers are during the same hour of the morning , thus the hours can be assumed to bring us into the 7 am hour evenly from 7 : 16 pm . thus 324 hours ago was 7 : 16 am . take an extra 3 minutes off , and it was 7 : 13 am . b
Answer: b
Problem: 52 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 30.33 , b ) 34.44 , c ) 26.1 , d ) 28.0 , e ) 21.0
Rationale: "explanation : let the two parts be ( 52 - x ) and x . then , 10 ( 52 - x ) + 22 x = 780 = > 12 x = 260 = > x = 21.66 . bigger part = ( 52 - x ) = 30.33 . answer : a ) 30.33"
Answer: a
Problem: the price of 2 sarees and 4 shirts is $ 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?
Options: a ) 3800 , b ) 3300 , c ) 2400 , d ) 4200 , e ) 1400
Rationale: c $ 2400 let the price of a saree and a shirt be $ x and $ y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = $ ( 12 x 200 ) = $ 2400 .
Answer: c
Problem: on dividing 271 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 30
Rationale: "d = ( d - r ) / q = ( 271 - 1 ) / 9 = 270 / 9 = 30 e )"
Answer: e
Problem: working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exactly 12 days . if b starts , they take half a day more . how long does it take to complete the task if they both work together ?
Options: a ) 4 , b ) 4.5 , c ) 6 , d ) 8 , e ) 6.5
Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 6 no . of days when b works = 6 → 6 x + 6 y = 1 when b starts : no . of days when a works = 6.5 no . of days when b works = 5.5 → 6.5 x + 5.5 y = 1 solving the above two equations for xy x = 1 / 12 y = 1 / 12 → total work done by ab in a day = 1 / 12 + 1 / 12 = 2 / 12 = 1 / 6 → no . of days to complete the work when both work together = 6 answer : c"
Answer: c
Problem: on dividing a number by 5 , we get 3 as remainder . what will the remainder when the square of the this number is divided by 5 ?
Options: a ) 0 , b ) 5 , c ) 8 , d ) 9 , e ) 4
Rationale: "explanation : let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x ^ 2 = ( 5 k + 3 ) ^ 2 = ( 25 k ^ 2 + 30 k + 9 ) = 5 ( 5 k ^ 2 + 6 k + 1 ) + 4 on dividing x 2 by 5 , we get 4 as remainder . e )"
Answer: e
Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm .
Options: a ) 370 cm 2 , b ) 365 cm 2 , c ) 380 cm 2 , d ) 384 cm 2 , e ) 394 cm 2
Rationale: "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 24 x 32 ) cm 2 = 384 cm 2 answer : option d"
Answer: d
Problem: a taxi leaves point a 4 hours after a bus left the same spot . the bus is traveling 30 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in two hours .
Options: a ) 40 , b ) 42 , c ) 45 , d ) 48 , e ) 49
Rationale: "let the speed of bus be v - 30 , speed of taxi be v the bus travelled a total of 6 hrs and taxi a total of 2 hrs . hence 6 * ( v - 30 ) = 2 v 6 v - 180 = 2 v 4 v = 180 v = 45 mph c"
Answer: c
Problem: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 15 ) both lie on the line defined by the equation x = ( y / 5 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "x = ( y / 5 ) - ( 2 / 5 ) , and so y = 5 x + 2 . the slope is 5 . ( n + 15 - n ) / ( m + p - m ) = 5 p = 3 the answer is c ."
Answer: c
Problem: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 7 : 7 : 8 . if the shop carries 330 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154
Rationale: "let us assume the number of dogs , cats and bunnies to be 7 x , 7 x and 8 x total dogs and bunnies = 15 x . and we are given that 15 x = 330 . hence x = 22 . dogs = 7 x = 7 * 22 = 154 ( option e )"
Answer: e
Problem: of the 150 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 10 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 10 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 10 answer : option a"
Answer: a
Problem: if y is the smallest positive integer such that 7,700 multiplied by y is the square of an integer , then y must be
Options: a ) 29 , b ) 58 , c ) 63 , d ) 74 , e ) 77
Rationale: "7700 = 5 * 5 * 2 * 2 * 7 * 11 , so we need one 7 and one 11 to make it a square of a number . so 7 * 11 = 77 ans : e"
Answer: e
Problem: a bookstore has a shelf that contains biographies which normally sell for $ 20 each and mysteries that normally sell for $ 12 each . during a sale , the biographies and mysteries are discounted at different rates so that a customer saves a total of $ 19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries . if the sum of the discount rates for the two types of books is 38 percent , what is the discount rate on mysteries ?
Options: a ) 18 % , b ) 29.68 % , c ) 19.68 % , d ) 29 % , e ) 68 %
Rationale: "let b be the discount on biographies and m be the discount on mysteries so . , b + m = 0.38 - - - - - ( 1 ) and ( 20 * 5 + 12 * 3 ) - ( 20 * 5 * ( 1 - b ) + 12 * 3 * ( 1 - m ) ) = 19 - - > 100 ( 1 - ( 1 - b ) ) + 36 ( 1 - ( 1 - m ) = 19 100 b + 36 m = 19 - - - - - - ( 2 ) solving 12 . , we get m = 0.2968 = 29.68 % b"
Answer: b
Problem: find the ones digit of 73 ^ 320
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 320 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer d ."
Answer: d
Problem: the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 152 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 152 , c ) 156 , d ) 144 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 152 . so , total number of ducks and frogs in the pond , = 2 * 152 = 304 . therefore , number of frogs , = ( 304 * 39 ) / 76 = 156 . answer : option c"
Answer: c
Problem: the side of a square is increased by 30 % then how much % does its area increases ?
Options: a ) 52.65 , b ) 69 , c ) 50.75 , d ) 42.75 , e ) 52.75
Rationale: "a = 100 a 2 = 10000 a = 130 a 2 = 16900 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 6900 100 - - - - - - - ? = > 69 % answer : b"
Answer: b
Problem: the “ connection ” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b . for instance , the smallest common multiple of 8 and 12 is 24 , and the product of 8 and 12 is 96 , so the connection between 8 and 12 is 24 / 96 = 1 / 4 the positive integer y is less than 20 and the connection between y and 6 is equal to 1 / 1 . how many possible values of y are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: since “ connection ” between y and 6 is 1 / 1 then lcm ( 6 , y ) = 6 y , which means that 6 and y are co - prime ( they do not share any common factor but 1 ) , because if the had any common factor but 1 then lcm ( 6 , y ) would be less than 6 y . so , we should check how many integers less than 20 are co - prime with 6 , which can be rephrased as how many integers less than 20 are not divisible by 2 or 3 ( 6 = 2 * 3 ) . there are ( 18 - 2 ) / 2 + 1 = 9 multiples of 2 in the range from 0 to 20 , not inclusive ; there are ( 18 - 3 ) / 3 + 1 = 6 multiples of 3 in the range from 0 to 20 , not inclusive ; there are 3 multiples of 6 in the range from 0 to 20 , not inclusive ( 6 , 12 , 18 ) - overlap of the above two sets ; total multiples of 2 or 6 in the range from 0 to 20 , not inclusive is 9 + 6 - 3 = 12 ; total integers in the range from 0 to 20 , not inclusive is 19 ; hence , there are total of 19 - 12 = 7 numbers which have no common factor with 6 other than 1 : 1 , 5 , 7 , 11 , 13 , 17 and 19 . answer : a .
Answer: a
Problem: the probability of two events a and b are 0.15 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6
Rationale: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 15 + . 40 - . 15 = . 40 but the probability of neither a nor b = 1 - . 40 = 0.60 answer : e"
Answer: e
Problem: ( 0.8 ) ( power 3 ) - ( 0.5 ) ( power 3 ) / ( 0.8 ) ( power 2 ) + 0.40 + ( 0.5 ) ( power 2 ) is :
Options: a ) 0.6 , b ) 0.5 , c ) 0.35 , d ) 0.3 , e ) none of them
Rationale: "given expression = ( 0.8 ) ( power 3 ) - ( 0.5 ) ( power 3 ) / ( 0.8 ) ( power 2 ) + ( 0.8 x 0.5 ) + ( 0.5 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.8 - 0.5 ) = 0.30 answer is d ."
Answer: d
Problem: if the length of the sides of two cubes are in the ratio 7 : 1 , what is the ratio of their total surface area ?
Options: a ) 7 : 1 , b ) 14 : 1 , c ) 21 : 1 , d ) 42 : 1 , e ) 49 : 1
Rationale: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 7 x ) ^ 2 = 294 x ^ 2 . the ratio of surface areas is 49 : 1 . the answer is e ."
Answer: e
Problem: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 110.60 , what was the total value of the item ?
Options: a ) $ 2160 , b ) $ 2370 , c ) $ 2580 , d ) $ 2790 , e ) $ 2950
Rationale: "let x be the value of the item . 0.07 * ( x - 1000 ) = 110.60 x = 2580 the answer is c ."
Answer: c
Problem: on a trip covering 400 km , a bicyclist travels the first 100 km at 20 km per hour and the remainder of the distance at 15 km per hour . what is the average speed , in km per hour , for the entire trip ?
Options: a ) 15.5 , b ) 16.0 , c ) 16.5 , d ) 17.0 , e ) 17.5
Rationale: time 1 = 100 / 20 = 5 hours time 2 = 300 / 15 = 20 hours total time = 25 hours average speed = 400 / 25 = 16 km / hr the answer is b .
Answer: b
Problem: eighteen years ago , a father was 3 times as old as his son . now the father is only twice as old his son . then the sum of the present ages of the son and the father is :
Options: a ) 53 , b ) 108 , c ) 77 , d ) 107 , e ) 109
Rationale: explanation : let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 18 ) = 3 ( x - 18 ) = > x = 36 required sum = ( 2 x + x ) = 108 years . answer : option d
Answer: d
Problem: how many pieces can a square pizza be cut into by making 5 linear cuts ?
Options: a ) 16 , b ) 17 , c ) 13 , d ) 14 , e ) 15
Rationale: "1 cut can make 2 pieces a second cut can make 4 pieces by cutting through 2 pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces a"
Answer: a
Problem: the area of a parallelogram is 128 sq m . then the area of a triangle formed by its diagonal is - - - - - - - - - - ?
Options: a ) 128 m
b ) 64 m
c ) 64 m ^ 2
d ) 128 m ^ 2
e ) none
Rationale: b * h / 2 = 128 / 2 = 64 m . ans : ( b )
Answer: b
Problem: a person crosses a 1080 m long street in 14 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 4.5 , c ) 4.6 , d ) 5.4 , e ) 5.5
Rationale: "speed = 1080 / ( 12 x 60 ) m / sec = 1.3 m / sec . converting m / sec to km / hr = 1.3 x ( 18 / 5 ) km / hr = 4.6 km / hr . answer : c"
Answer: c
Problem: if x is a prime number , and x - 1 is the median of the set { x - 1 , 3 x + 3 , 2 x - 4 } , then what is the average ( arithmetic mean ) of the set ?
Options: a ) 2 , b ) 5 / 3 , c ) 3 , d ) 10 / 3 , e ) 14 / 3
Rationale: if x is a prime number , and x - 1 is the median of the set { x - 1 , 3 x + 3 , 2 x - 4 } , then what is the average ( arithmetic mean ) of the set ? a . 2 b . 5 / 3 c . 3 d . 10 / 3 e . 14 / 3 solution : x - 1 is the median of the set , implies if we arrange the set in ascending order , the set would be [ 2 x - 4 , x - 1 , 3 x + 3 ] . this means that : 2 x - 4 < x - 2 < 3 x + 3 solving inequality gives x > - 2 and x < 3 . since x is prime number and the only prime number < 3 is 2 , so put x = 2 . hence set becomes : [ 0 , 1 , 9 ] and avg = 10 / 3 . d
Answer: d
Problem: the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 223 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 – 2552 = 208 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 208 2 x = 358 x = 179 runs answer a"
Answer: a
Problem: the sector of a circle has radius of 21 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 49.5 + 42 = 91.5 cm answer : a"
Answer: a
Problem: 8.008 / 1.001
Options: a ) 0.008 , b ) 8 , c ) 0.8 , d ) 80 , e ) 800
Rationale: "answer is 8 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 8008 / 1001 = 8 answer b"
Answer: b
Problem: the radius of a semicircle is 7 . what is the approximate perimeter of the semicircle ?
Options: a ) 36
b ) 25
c ) 15
d ) 28
e ) 37
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 7 + 2 * 7 = 35.98 approximately 36 answer a
Answer: a
Problem: a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , one boggies were detached . the train now crosses a telegraph post in
Options: a ) 16.5 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) none of these
Rationale: length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 18 = 10 m / s now , length of train = 11 ã — 15 = 165 m â ˆ ´ required time = 165 â  „ 10 = 16.5 sec . answer a
Answer: a
Problem: if a sum of money doubles itself in 8 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 13 , d ) 13.5 , e ) 14
Rationale: explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 8 ) = 12.5 option b
Answer: b
Problem: natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 2 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.75 , d ) 5 , e ) 7.5
Rationale: "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 2 km / hour x / 3 = 2 x = 6 km the average speed while climbing = distance / time = 6 / 4 = 1.5 km / h the answer is a ."
Answer: a
Problem: the average ( arithmetic mean ) of 4 positive integers is 30 . if the average of 2 of these integers is 15 , what is the greatest possible value that one of the other 2 integers can have ?
Options: a ) 55 , b ) 89 , c ) 100 , d ) 109 , e ) 115
Rationale: "a + b + c + d = 120 a + b = 30 c + d = 90 greatest possible = 89 ( just less than 1 ) answer = b"
Answer: b
Problem: the length of the bridge , which a train 135 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 76 m , b ) 178 m , c ) 240 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 , ( 135 + x ) / 30 = 25 / 2 = > 2 ( 135 + x ) = 750 = > x = 240 m . answer : c"
Answer: c
Problem: carol spends 1 / 4 of her savings on a stereo and 1 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 1 / 2 , e ) 7 / 12
Rationale: "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 3 ) ( 1 / 4 ) s = ( 2 / 3 ) * ( 1 / 4 ) * s = ( 1 / 6 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 6 ) / s = 5 / 12 answer : c"
Answer: c
Problem: jancy had 100 currency notes in all , some of which are of rs 70 denomination and the remaining of rs 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount ( in rs ) did she have in the denomination of rs 50 ?
Options: a ) 103 , b ) 102 , c ) 100 , d ) 105 , e ) 106
Rationale: let the number of 50 - rupee notes = x then , the number of 70 - rupee notes = ( 100 – x ) 50 x + 70 ( 100 – x ) = 5000 : x = 100 answer : c
Answer: c
Problem: a line that passes through ( – 1 , – 4 ) and ( 4 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
Rationale: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 4 + 1 ) = > 5 k = k + 4 = > k = 1 ans b it is !"
Answer: b
Problem: a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 25 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 20 % , b ) 25 % , c ) 28.5 % , d ) 30 % , e ) 32 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.25 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 25 % income the savings increased by 100 % . or s = . 25 i or s = 25 % of income b is the answer"
Answer: b
Problem: the contents of a certain box consist of 24 apples and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be apples ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 46 , e ) 50
Rationale: "apples = ( apples + kiwi + x ) * 0.3 24 = ( 30 + 24 + x ) * 0.3 x = 26 . answer : b ."
Answer: b
Problem: p and q can complete a work in 80 days and 48 days respectively . p alone started the work and q joined him after 16 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 40 days
Rationale: explanation : work done by p in 1 day = 1 / 80 work done by q in 1 day = 1 / 48 work done by p in 16 days = 16 ã — ( 1 / 80 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 80 + 1 / 48 = 1 / 30 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 1 / 30 ) = 24 total days = 16 + 24 = 40 answer : option e
Answer: e