regisss/math_qa huggingface dataset:
Problem: the sum of three consecutive numbers is 102 . the greatest among these three number is :
Options: a ) 26 , b ) 35 , c ) 29 , d ) 30 , e ) 31
Rationale: "let the numbers be x , x + 1 and x + 2 then , x + ( x + 1 ) + ( x + 2 ) = 102 3 x = 102 x = 33 greatest number , ( x + 2 ) = 35 . answer : b"
Answer: b
Problem: a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 40 % impurities to the product . find the net profit percentage of the dealer ?
Options: a ) 94 % , b ) 87.5 % , c ) 55 % , d ) 56.25 % , e ) 36 %
Rationale: "the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 50 % impurities to the product . it means that he is selling $ 5 worth of product for $ 7.5 . so his profit is $ 7.5 - $ 4 = $ 3.5 and his profit percent is ( 3.5 / 4 ) * 100 = 87.5 % answer : - b"
Answer: b
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 52 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) s . 53.30 , b ) s . 53.22 , c ) s . 51.219 , d ) s . 53.18 , e ) s . 51.10
Rationale: explanation : sum = ( 52 * 100 ) / ( 2 * 5 ) = rs . 520 amount = [ 520 * ( 1 + 5 / 100 ) 2 ] = rs . 573.3 c . i . = ( 573.3 - 520 ) = rs . 53.30 . answer : a
Answer: a
Problem: 29 persons can repair a road in 16 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 12.88 , b ) 3.88 , c ) 13.88 , d ) 15 , e ) 18.8
Rationale: "let the required number of days be x more persons , less days ( indirect proportion ) more hours , less days ( indirect proportion ) hence we can write as ( persons ) 29 : 30 } : : x : 16 ( hours ) 5 : 6 29 * 5 * 16 = 30 * 6 * x x = 12.88 answer : a"
Answer: a
Problem: the income tax in country x is 8 % of any income up to $ 5000 . for incomes over $ 5000 , an 8 % tax is imposed on the first $ 5000 , and a 10 % tax is imposed on the portion of the total income in excess of $ 5000 . if perry paid $ 950 in income tax last month , then what was perry ' s income ?
Options: a ) $ 10500 , b ) $ 11000 , c ) $ 13000 , d ) $ 13500 , e ) $ 14,000
Rationale: given : for incomes over $ 5,000 , an 8 % tax is imposed on the first $ 5,000 , and a 10 % tax is imposed on the portion of the total income in excess of $ 5000 . if perry paid $ 950 in income tax last month , then what was perry ' s income ? for first 5000 , 8 % tax then we get 400 $ as tax . now perry paid 950 $ tax . . . we need to check which option is going to yield 550 $ on the remaining amount . a . $ 10,500 - 5000 = 5500 , then we get 10 % tax , we get 550 $ . . . ( $ 10,500 - 5000 - here already for 5000 $ we have calculated the tax and we need to tally for the remaining amount ) 550 + 400 = 950 $ . . . hence this is the option . answer : option a .
Answer: a
Problem: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: c 130 % let c . p . be $ 100 . then , s . p . = $ 123.50 let marked price be $ x . then , 95 / 100 x = 123.50 x = 12350 / 95 = $ 130 now , s . p . = $ 130 , c . p . = $ 100 profit % = 30 % .
Answer: c
Problem: if n = 2 ^ 0.15 and n ^ b = 8 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 20 , d ) 5 / 3 , e ) 80 / 3
Rationale: "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 3 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 3 b = 20 answer : c"
Answer: c
Problem: last year sandy saved 10 % of her annual salary . this year , she made 10 % more money than last year , and she saved 6 % of her salary . the amount saved this year was what percent of the amount she saved last year ?
Options: a ) 66 % , b ) 80 % , c ) 112 % , d ) 136 % , e ) 148 %
Rationale: "let last year ' s salary be x . last year , sandy save 0.1 x this year , sandy saved 0.06 * 1.1 x = 0.066 x 0.066 x / 0.1 x = 0.66 = 66 % the answer is a ."
Answer: a
Problem: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40000 , what is the value at the end of 2 years ?
Options: a ) 3277 , b ) 2977 , c ) 22500 , d ) 6077 , e ) 17112
Rationale: explanation : 40,000 * ( 3 / 4 ) ^ 2 answer : c
Answer: c
Problem: 5 years ago , paula was 3 times as old as karl . in 6 years , paula will be twice as old as karl . what is the sum of their ages now ?
Options: a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58
Rationale: p - 5 = 3 ( k - 5 ) and so p = 3 k - 10 p + 6 = 2 ( k + 6 ) ( 3 k - 10 ) + 6 = 2 k + 12 k = 16 p = 38 p + k = 54 the answer is d .
Answer: d
Problem: one fourth of a solution that was 8 % sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 74 % , b ) 52 % , c ) 40 % , d ) 18 % , e ) 8.5 %
Rationale: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.08 + 1 / 4 * x = 1 * 0.16 - - > x = 0.4 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.08 + 25 * x = 100 * 0.16 - - > x = 0.4 . answer : c ."
Answer: c
Problem: a and b invests rs . 2000 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 3 : 5 , b ) 3 : 4 , c ) 9 : 2 , d ) 9 : 9 , e ) 3 : 1
Rationale: "( 2 * 6 + 4 * 6 ) : ( 4 * 12 ) 36 : 48 = > 3 : 4 answer : b"
Answer: b
Problem: two trains of equal lengths take 8 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 22 , b ) 12 , c ) 77 , d ) 10 , e ) 21
Rationale: "speed of the first train = 120 / 8 = 15 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 15 + 8 = 23 m / sec . required time = ( 120 + 120 ) / 23 = 10 sec . answer : d"
Answer: d
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 5 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 5 * x hence , a 1 + a 2 + . . + a 20 + n = 25 x so , the fraction asked = 5 x / 25 x = 1 / 5 answer c"
Answer: c
Problem: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 27 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 13.5 minutes , b ) 27 minutes , c ) 35 minutes , d ) 54 minutes , e ) 81 minutes
Rationale: "danny ' s time is 27 minutes . the time to reach halfway is 13.5 minutes . steve ' s time is 54 minutes . the time to reach halfway is 27 minutes . the time difference is 27 - 13.5 = 13.5 minutes the answer is a ."
Answer: a
Problem: mr . loyd wants to fence his square shaped land of 120 sqft each side . if a pole is laid every 12 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "if each side is 120 feet . . then total perimeter is 120 * 4 = 480 poles every 12 feet hence no of poles = 480 / 12 = 40 answer : c"
Answer: c
Problem: a number exceeds by 40 from its 3 / 8 part . then the number is ?
Options: a ) a ) 32 , b ) b ) 24 , c ) c ) 64 , d ) d ) 40 , e ) e ) 45
Rationale: "x – 3 / 8 x = 40 x = 64 answer : c"
Answer: c
Problem: amar takes as much time in running 22 meters as a car takes in covering 58 meters . what will be the distance covered by amar during the time the car covers 2.6 km ?
Options: a ) 700 m , b ) 978 m , c ) 970 m , d ) 986 m , e ) 640 m
Rationale: "distance covered by amar = 22 / 58 ( 2.6 km ) = 11 / 29 ( 2600 ) = 986 m answer : d"
Answer: d
Problem: a 340 - liter solution of kola is made from 88 % water , 5 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 11 % .
Rationale: "denominator : 340 + 10 + 3.2 + 6.8 = 360 numerator : 340 ( 1 - . 88 - . 05 ) + 3.2 340 ( 0.07 ) + 3.2 23.8 + 3.2 27 ratio : 27 / 360 = 3 / 40 answer : b"
Answer: b
Problem: the average age of 28 students in a group is 12 years . when teacher â € ™ s age is included to it , the average increases by one . what is the teacher â € ™ s age in years ?
Options: a ) 31 , b ) 36 , c ) 41 , d ) 51 , e ) none
Rationale: "sol . age of the teacher = ( 29 ã — 13 â € “ 28 ã — 12 ) years = 41 years . answer c"
Answer: c
Problem: a rectangular tiled patio is composed of 60 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 60 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 8
Rationale: "r * c = 60 and ( r + 4 ) ( c - 2 ) = 60 - - > r = 8 and c = 7 . answer : e ."
Answer: e
Problem: when the perimeter of a regular polygon is divided by 5 , the length of a side is 25 . what is the name of the polygon ? what is the perimeter ?
Options: a ) 125
b ) 126
c ) 127
d ) 128
e ) 129
Rationale: regular polygon . a polygon with equal sides and equal sides . divided by 5 to get the length of a side . it is the pentagon since it has 5 sides . so p = 5 × s to get the perimeter , just multiply a side by 5 . since 25 × 5 = 125 , the perimeter is 125 . answer a
Answer: a
Problem: a vessel of capacity 60 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 23.89 , b ) 72.9 , c ) 38.3 , d ) 43.35 , e ) 79.3
Rationale: explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 60 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 60 - 9 ) / 60 ] ^ 2 ( 60 ) = 43.35 litres . answer : option d
Answer: d
Problem: an empty wooden vessel weighs 8 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .
Options: a ) 3 / 7 , b ) 5 / 9 , c ) 1 / 24 , d ) 4 / 9 , e ) 2 / 5
Rationale: "an empty wooden vessel weighs 8 % of its total weight when filled with paint : vessel = 0.08 ( vessel + paint ) ; 8 v = v + p ( so the weight of completely filled vessel is 8 v ) p = 7 v ( so the weight of the paint when the vessels is completely filled is 7 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 8 v ; p ' = 3 v ( so the weight of the paint when the vessels is partially filled is 3 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 3 v / 7 v = 3 / 7 . answer : a ."
Answer: a
Problem: in a government institute 20 nos . staffs are employed . in a festival season their boss give festival allowance to all . he says his accountant to calculate for 30 days @ 100 . also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash . he had given rs . 65000 / - to the accountant . how much amount will taken from petty cash ?
Options: a ) a ) 1000 , b ) b ) 3000 , c ) c ) 3500 , d ) d ) 2500 , e ) e ) 2250
Rationale: for 20 staffs : 300 * 100 * 20 = 60000 for driver and cleaning staff : 300 * 100 * 2 = 6000 from petty cash : 1000 answer is a
Answer: a
Problem: if $ 5,000 is invested in an account that earns 4 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.04 / 2 ) ^ 2 = 5404 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 4 / 100 ) = 5400 difference = 5404 - 5400 = 4 $ a"
Answer: a
Problem: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 7 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) rs 1200 , b ) rs 1500 , c ) rs 1600 , d ) rs 1900 , e ) rs 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 7 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2100 . hence , ( r - p ) = ( 2100 - 900 ) = 1200 answer : a"
Answer: a
Problem: in a company of 10 employees , 5 employees earn $ 30,000 , 3 employees earn $ 40,000 , and the 2 highest - paid employees earn the same amount . if the average annual salary for the 10 employees is $ 65,000 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 190,000 , b ) $ 170,000 , c ) $ 150,000 , d ) $ 130,000 , e ) $ 110,000
Rationale: "5 * 30,000 + 3 * 40,000 + 2 x = 10 * 65,000 2 x = 650,000 - 150,000 - 120,000 2 x = 380,000 x = 190,000 the answer is a ."
Answer: a
Problem: a man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "m = 45 s = 1.5 ds = 6 us = 3 as = ( 2 * 6 * 3 ) / 9 = 4 answer : a"
Answer: a
Problem: if a sum of money doubles itself in 25 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 13 , d ) 13.5 , e ) 4
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 25 ) = 4 option e"
Answer: e
Problem: a company produces 50000 bottles of water everyday . if a case can hold 25 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 9000
Rationale: "number of bottles that can be held in a case = 25 number of cases required to hold 50000 bottles = 50000 / 25 = 2000 cases . so the answer is a = 2000"
Answer: a
Problem: a small pool filled only with water will require an additional 700 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 700 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 2125
Rationale: "since pumping in additional 700 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 700 = 0.8 * { total } - - > { total } = 2,125 . answer : e ."
Answer: e
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 4356 , the number of the member is the group is :
Options: a ) 57 , b ) 66 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 43.56 x 100 ) paise = 4356 paise . number of members = square root of 4356 = 66 . answer : option b"
Answer: b
Problem: the difference of two numbers is 2 and the difference of their squares is 12 . the sum of the number is
Options: a ) 6 , b ) 8 , c ) 10 , d ) 22 , e ) 24
Rationale: "explanation : let the numbers be a , b ; ⇒ a - b = 2 and a 2 − b 2 = 12 a + b = a 2 − b 2 / a − b = 12 / 2 = 6 correct option : a"
Answer: a
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 25 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 305 , e ) 312
Rationale: "to maximize the distance that suv could be driven on 25 gallons of gasoline , we need consider only highway driving . max distance = 25 * 12.2 = 305 answer d"
Answer: d
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 120 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 8 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 120 rs . 5 m + 5 m + 5 m - - - - - 120 rs . 15 m - - - - - - 120 rs . = > 1 m = 8 rs . answer : e"
Answer: e
Problem: 3 / 5 of all married couples have more than one child . 1 / 4 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?
Options: a ) 1 / 5 , b ) b . 1 / 4 , c ) 7 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .
Rationale: "plug in simple numbers . take 100 couples for example . 3 / 5 of 100 couples have more than one child = 60 couples . 1 / 4 of 100 couples have more than 3 kids = 25 couples . this implies that 25 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples , which equals 40 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 60 - 25 = 35 . fraction will be 35 / 100 = 7 / 20 . option c"
Answer: c
Problem: a and b are two partially filled buckets of water . if 5 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 4 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 11 , b ) 52 / 5 , c ) 17 , d ) 21 , e ) 23
Rationale: "let a contains a , b contains b liters so , ( a - 5 ) / ( b + 5 ) = 1 / 3 . . . . . . . ( 1 ) again , ( b - 4 ) / ( a + 4 ) = 1 / 2 . . . . . . . . . . ( 2 ) from ( 1 ) ( 2 ) we find a = 52 / 5 ans : ( b )"
Answer: b
Problem: a company pays 12.5 % dividend to its investors . if an investor buys rs . 60 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 66 , c ) 30 , d ) 19 , e ) 01
Rationale: explanation : dividend on 1 share = ( 12.5 * 60 ) / 100 = rs . 7.5 rs . 25 is income on an investment of rs . 100 rs . 7.5 is income on an investment of rs . ( 7.5 * 100 ) / 25 = rs . 30 answer : c
Answer: c
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,500 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,500 , e ) 48,500
Rationale: "median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.5 so , answer is d ."
Answer: d
Problem: what is the 10 digit to the right of the decimal point , in the decimal expansion of ( 1 / 2 ) ^ 10 ?
Options: a ) 9 , b ) 4 , c ) 2 , d ) 1 , e ) 5
Rationale: step 1 convert fraction to decimal with two decimal places 1 / 2 = 0.50 then convert to scientific number = 5 * 10 ^ - 1 step 2 multiply 5 ^ 10 by 10 ^ - 10 step 3 5 has the sequence 5 , 25 , 125 answer is e
Answer: e
Problem: find the curved surface area , if the radius of a cone is 35 m and slant height is 30 m ?
Options: a ) 1100 , b ) 2200 , c ) 3300 , d ) 4400 , e ) 5500
Rationale: "cone curved surface area = ï € rl 22 / 7 ã — 35 ã — 30 = 110 ã — 30 = 3300 m ( power 2 ) answer is c ."
Answer: c
Problem: the sum of two numbers is 20 and the sum of their squares is 140 . find the product of the two numbers .
Options: a ) 130 , b ) 140 , c ) 120 , d ) 145 , e ) 150
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 20 a ^ 2 + b ^ 2 = 140 so , 20 ^ 2 = 140 + 2 ab 2 ab = 400 - 140 2 ab = 260 ab = 130 ans a
Answer: a
Problem: a man have 8 t - shirt and some pant . he can dress in 72 ways . then tell me the no . of pant that man have .
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: let he have x pant . by fundamental principle total no . of ways in which he can dress = 8 x 8 x = 72 x = 9 pants answer b
Answer: b
Problem: on average , machine a will produce a completed item once every 4 minutes , and machine b will produce a completed item once every 5 minutes . the number of items machine a produces in a 24 - hour period is approximately what percent greater than the number of items machine b would produce in that same period ?
Options: a ) 25 % , b ) 15 % , c ) 45 % , d ) 33 % , e ) 55 %
Rationale: machine a : 1 item in 4 minutes - - > 1 / 4 items in 1 minute ; machine b : 1 item in 5 minutes - - > 1 / 5 items in 1 minute . in the same time period , machine a produces ( 1 / 4 - 1 / 5 ) / ( 1 / 5 ) * 100 = ~ 25 % more items than machine b . answer : a .
Answer: a
Problem: what is the divisor ? the dividend is 76 , the remainder is 8 , the quotient is 4
Options: a ) 32 , b ) 48 , c ) 67 , d ) 17 , e ) 26
Rationale: divisor = dividend - remainder divided by the quotient divisor = 76 - 8 divided by 4 divisor = 68 / 4 divisor = 17
Answer: d
Problem: in a certain corporation , there are 300 male employees and 150 female employees . it is known that 30 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 3 / 10 , d ) 8 / 15 , e ) 11 / 30
Rationale: "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.3 * 300 / 450 = 90 / 450 = 1 / 5 the sum of the probabilities is 8 / 15 the answer is d ."
Answer: d
Problem: at what rate percent per annum will a sum of money double in 6 years .
Options: a ) 12.5 % , b ) 13.5 % , c ) 11.5 % , d ) 14.5 % , e ) 16.6 %
Rationale: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 6 ) ] % = 16.6 % per annum . answer : e"
Answer: e
Problem: if 8 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 48 , e ) 60
Rationale: "let the capacity of the tank = c ( 3 / 4 ) c + 8 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 8 = > ( 3 / 20 ) c = 8 = > c = ( 8 * 20 ) / 3 = 53.33 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 8 = 39.99 + 8 = 47.99 = 48 answer d"
Answer: d
Problem: a certain company ’ s profit in 1996 was 15 percent greater than its profit in 1995 , and its profit in 1997 was 20 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 33 % , d ) 35 % , e ) 38 %
Rationale: "soln : - profit in 1995 - 100 profit in 1996 - 115 % increase profit in 1997 in comparison to 1995 = 15 + 115 * 20 % = 38 % answer : e"
Answer: e
Problem: what percent of 250 is 45 ?
Options: a ) 0.25 % , b ) 18 % , c ) 25 % , d ) 40 % , e ) 250 %
Rationale: "250 * x / 100 = 45 x = 45 * 10 / 25 x = 18 ans : b"
Answer: b
Problem: i chose a number and divide it by 2 . then i subtracted 100 from the result and got 4 . what was the number i chose ?
Options: a ) 200 , b ) 208 , c ) 400 , d ) 500 , e ) 100
Rationale: "let x be the number i chose , then x / 2 − 100 = 4 x / 2 = 104 x = 208 answer is b ."
Answer: b
Problem: the perimeter of an isosceles right triangle is 12 + 12 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 5
b ) 6
c ) 7
d ) 8.485
e ) 8
Rationale: side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 12 + 12 sqrt 2 or , a . ( 2 + sqrt 2 ) = 12 ( 1 + sqrt 2 ) , a = 12 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 12 * 2.414 / 3.414 = then hypotenuse = 8.485 d
Answer: d
Problem: what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 12 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "denote | x - 3 | as y : y ^ 2 + y = 12 - - > y = - 4 or y = 3 . discard the first solution since y = | x - 3 | , so it ' s an absolute value and thus can not be negative . y = | x - 3 | = 3 - - > x = 6 or x = - 1 . the sum = 5 . answer : a ."
Answer: a
Problem: a certain protective additive increases from 50 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 20 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 60 − 50 / 50 ∗ 100 = 20 answer : e ."
Answer: e
Problem: given that 268 * 74 = 19832 , find the values of 2.68 * 0.74 .
Options: a ) 1.9328 , b ) 1.9832 , c ) 1.9823 , d ) 1.9382 , e ) none of them
Rationale: sum of decimal places = ( 2 + 2 ) = 4 2.68 * 0.74 = 1.9832 . answer is b .
Answer: b
Problem: the probability of two events a and b are 0.25 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 ) = . 25 + . 40 - . 15 = . 50 but the probability of neither a nor b = 1 - . 50 = 0.50 answer : c"
Answer: c
Problem: a pump can fill a tank with a water in 2 hours . because of a leak , it took 3 and 1 / 3 hours to fill the tank . the leak can drain all the water of the full tank in how many hours ?
Options: a ) 5 hrs , b ) 7 hrs , c ) 12 hrs , d ) 14 hrs , e ) 16 hrs
Rationale: "the rate of the pump + leak = 3 / 10 1 / 2 - leak ' s rate = 3 / 10 leak ' s rate = 1 / 5 the leak will empty the tank in 5 hours . the answer is a ."
Answer: a
Problem: if henry were to add 9 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
Options: a ) 25 , b ) 40 , c ) 64 , d ) 72 , e ) 96
Rationale: "7 / 8 x - 3 / 4 x = 9 galls 1 / 8 * x = 9 gallons x = 72 gallons answer d"
Answer: d
Problem: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many w hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is w equal to 1 / 3 ( as the work is completed in w = 3 hours ) solving these 2 equations we can find b as 12 so , d"
Answer: d
Problem: the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 30 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 63 % , c ) 64.8 % , d ) 70 % , e ) 72 %
Rationale: "let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 10 % discount = 810 price in day 3 after 30 % discount = 567 so , price in day 3 as percentage of the sale price on day 1 will be = 567 / 900 * 100 = > 63 % answer will definitely be ( b )"
Answer: b
Problem: the price of a book is increased from $ 300 to $ 330 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 35 % , e ) 45 %
Rationale: explanation : change in the price = rs 330 – rs 300 = rs 30 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 30 / 300 ) * 100 = 10 % a
Answer: a
Problem: a sum of 14,800 amounts to 19,800 in 3 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 12 % , b ) 11 % , c ) 16 % , d ) 15 % , e ) 18 %
Rationale: "b 11 % s . i . = ( 19800 - 14800 ) = 5000 . rate = ( 100 x 5000 ) / ( 14800 x 3 ) % = 11 %"
Answer: b
Problem: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 360 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 8 , b ) 8.5 , c ) 9 , d ) 9.5 , e ) 10
Rationale: "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 360 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 it takes a total of eight hours to cover the 360 mile distance . answer : a"
Answer: a
Problem: in the figure given below , abc and cde are two identical semi - circles of radius 2 units . b and d are the mid points of the arc abc and cde respectively . what is the area of the shaded region ?
Options: a ) 4 π - 1
b ) 3 π - 1
c ) 2 π - 4
d ) ½ ( 3 π - 1 )
e ) 2 π - 2
Rationale: solution p and q are the centers of the two semicircles . draw bp perpendicular to ac . bp is radius to the semi - circle . so are ap and pc . therefore , bp = ap = pc = 2 units . in semicircle abc , area of the shaded portion is the difference between the area of half the semicircle pbc and the area of the triangle pbc . triangle pbc is a right triangle because pb is perpendicular to pc . pb and pc are radii to the circle and are equal . so , triangle pbc is an isosceles triangle . therefore , triangle pbc is a right isosceles triangle . area of half the semicircle - area of region pbc area of the semicircle abc = ½ area of the circle of radius 2 . so , area of half the semicircle , pbc = ¼ area of the circle of radius 2 . area of half the semicircle , pbc = ¼ * π * 22 area of half the semicircle , pbc = π sq units area of right isosceles triangle pbc area of right triangle pbc = ½ pc * pb area of triangle pbc = ½ * 2 * 2 = 2 sq units area of shaded region area of shaded region in one of the semi circles abc = ( π - 2 ) sq units therefore , area of the overall shaded region = 2 ( π - 2 ) sq units choice c
Answer: c
Problem: from the sale of sleeping bags , a retailer made a gross profit of 16 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 24.13 , d ) 25.0 , e ) 31.36
Rationale: "cost price * 1.16 = selling price - - > cost price * 1.16 = $ 28 - - > cost price = $ 24.13 . answer : c ."
Answer: c
Problem: a number is doubled and 5 is added . if the resultant is trebled , it becomes 129 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 19 , e ) 99
Rationale: explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 129 6 x + 15 = 129 6 x = 114 x = 19 answer : d
Answer: d
Problem: the average temperature for tuesday , wednesday and thursday was 42 ° c . the average temperature for wednesday , thursday and friday was 44 ° c . if the temperature on friday be 43 ° c , what was the temperature on tuesday ?
Options: a ) 39 ° c , b ) 44 ° c , c ) 37 ° c , d ) 42 ° c , e ) none of these
Rationale: "explanation : t + w + t = 42 × 3 = 126 ° c w + t + f = 44 × 3 = 132 ° c also , temperature on friday = 43 ° c temperature on tuesday = 126 + 43 - 132 = 37 ° c answer : option c"
Answer: c
Problem: 72519 x 9999 = ?
Options: a ) 725117481 , b ) 674217481 , c ) 685126481 , d ) 696217481 , e ) none of them
Rationale: "= 7259 x 9999 = 7259 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 answer is a"
Answer: a
Problem: on a certain date , pat invested $ 5,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 20,000 , in how many years total will the total value of the investment plus interest increase to $ 40,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "5,000 ( 1 + x ) ^ 10 = 20,000 ( 1 + x ) ^ 10 = 4 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 5000 ( 1 + x ) ^ n = 40,000 ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Problem: if a , b , and c are positive real numbers such that a ( b + c ) = 152 , b ( c + a ) = 162 , and c ( a + b ) = 170 , then abc is
Options: a ) a ) 672 , b ) b ) 688 , c ) c ) 704 , d ) d ) 720 , e ) e ) 750
Rationale: ab + bc = 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) bc + ba = 162 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) ac + ab = 170 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : ac + cb = 162 + 8 ac + cb = bc + ba + 8 ac = ba + 8 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 ac = 160 ac = 80 abc has to be multiple of 80 , only 720 fits in answer = d
Answer: d
Problem: s is a set of 50 consecutive multiples of 2 . if the smallest number in s is 56 , then the greatest number in s is
Options: a ) 198 , b ) 154 , c ) 199 , d ) 102 , e ) 105
Rationale: "last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 50 consecutive multiples of 2 . if the smallest number in s is 56 , then the greatest number in s is first term = 56 ; total terms = 50 ; difference = 2 56 + ( 49 ) 2 = 154 ans b"
Answer: b
Problem: the total number of digit used in numbering the pages of a book having 366 pages , is :
Options: a ) 732 , b ) 990 , c ) 1098 , d ) 1305 , e ) none of these
Rationale: solution total number of digits = ( no . of digits in 1 - digits page nos . + no . of digits in 2 - digits page nos . + no . of digits i 3 - digits page nos . ) = ( 1 * 9 + 2 * 90 + 3 * 267 ) = ( 9 + 180 + 801 ) = 990 . answer b
Answer: b
Problem: 5.511 / 10.02 =
Options: a ) 0.35 , b ) 0.55 , c ) 0.3509 , d ) 0.351 , e ) 0.3527
Rationale: "5.511 / 10.02 5511 / 1002 = 5.5 move the comma two places to the left as we have 2 decimal places from the divisor : 0.55 . answer : b"
Answer: b
Problem: running at the same constant rate , 6 identical machines can produce a total of 240 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1,800 , c ) 1,600 , d ) 10,800 , e ) 64,800
Rationale: "6 machines produce 240 bottles per minute ; 1 machine produces 240 / 6 = 40 bottles per minute ; 10 machines produce 40 * 10 = 400 bottles per minute ; in 4 minutes 10 machines produce 400 * 4 = 1,600 bottles . answer : c ."
Answer: c
Problem: there are 5 boxes in a cargo . the weight of the 1 st box is 200 kg , the weight of the 2 nd box is 20 % higher than the third box , whose weight is 25 % higher than the 1 st box weight . the 4 th box which weighs 350 kg is 30 % lighter than the 5 th box . find the difference in average weight of the 4 heaviest boxes and the 4 lightest boxes .
Options: a ) 22 , b ) 75 , c ) 25 , d ) 70 , e ) 11
Rationale: weight of 1 st box = 200 weight of 3 rd box = ( 125 / 100 ) * 200 = 250 weight of 2 nd box = ( 120 / 100 ) * 250 = 300 weight of 4 th box = 350 weight of 5 th box = ( 10 / 7 ) * 350 = 500 average of 4 highest weighted boxes = ( 500 + 350 + 300 + 250 ) / 4 = 350 average of 4 lightest boxes = ( 350 + 300 + 250 + 200 ) / 4 = 275 therefore difference = 350 - 275 = 75 answer : b
Answer: b
Problem: veena ranks 73 rd from the top in a class of 198 . what is her rank from the bottom if 22 students have failed the examination ?
Options: a ) 88 , b ) 104 , c ) 110 , d ) 90 , e ) 93
Rationale: "total student = 198 failed = 22 paasd student = 198 - 22 = 176 from bottom her rank is = 176 - 73 + 1 = 104 answer : b"
Answer: b
Problem: if each side of a square is increased by 20 % , find the percentage change in its area ?
Options: a ) 40 % , b ) 42 % , c ) 46 % , d ) 44 % , e ) 38 %
Rationale: "let each side of the square be a , then area = a x a new side = 120 a / 100 = 6 a / 5 new area = ( 6 a x 6 a ) / ( 5 x 5 ) = ( 36 a ² / 25 ) increased area = = ( 36 a ² / 25 ) - a ² increase % = [ ( 11 a ² / 25 ) x ( 1 / a ² ) x 100 ] % = 44 % answer : d"
Answer: d
Problem: by selling 20 pencils for a rupee a man loses 30 % . how many for a rupee should he sell in order to gain 30 % ?
Options: a ) 8.56 , b ) 10.75 , c ) 14.5 , d ) 16.5 , e ) 11.4
Rationale: "70 % - - - 20 130 % - - - ? 70 / 130 * 20 = 10.75 answer : b"
Answer: b
Problem: how many positive integers less than 100 are neither multiples of 2 or 3 ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: "1 ) multiples of 2 till 100 = 100 / 2 = 50 2 ) multiples of 3 till 100 = 100 / 3 = 33.33 = 33 add the two 50 + 33 = 83 ; subtract common terms that are multiple of both 2 and 3 . . lcm of 2 and 3 = 6 multiples of 6 till 100 = 100 / 6 = 16.66 = 16 so total multiples of 2 and 3 = 83 - 16 = 67 100 - 67 = 33 answer : d"
Answer: d
Problem: an article is bought for rs . 675 and sold for rs . 775 , find the gain percent ?
Options: a ) 73 % , b ) 14.8 % , c ) 33 1 / 3 % , d ) 93 1 / 3 % , e ) 33 1 / 3 %
Rationale: "explanation : 675 - - - - 100 100 - - - - ? = > 14.8 % answer : b"
Answer: b
Problem: a man buys 60 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 7.6 % , b ) 7.7 % , c ) 29.13 % , d ) 33.6 % , e ) 37.82 %
Rationale: explanation : let marked price be re . 1 each c . p . of 60 pens = rs . 46 s . p . of 60 pens = 99 % of rs . 60 = rs . 59.4 profit % = ( profit / c . p . ) x 100 profit % = ( 13.4 / 46 ) x 100 = 29.13 % answer : c
Answer: c
Problem: a sells a bicycle to b and makes a profit of 25 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 144
Rationale: "explanation : let cp be 100 a sells at 25 % profit so sp = 125 b sells at 25 % profit = 125 x ( 1 + 25 / 100 ) = 156.25 cp sp 100 - - - 156.25 x - - - 225 cp = 225 x 100 / 156.25 = 144 answer : e"
Answer: e
Problem: what is the area of a regular hexagon with sides 1 in . long ?
Options: a ) 1.59 square inch , b ) 2.59 square inch , c ) 3.59 square inch , d ) 4.59 square inch , e ) 2.69 square inch
Rationale: "a regular hexagon of side 1 inch can be divided in to 6 equilateral triangle of side 1 inch . area of each triangle = ( root 3 / 4 ) * side ^ 2 = ( root 3 / 4 ) area of 6 triangles = 6 * ( root 3 / 4 ) = 1.5 root 3 = 2.59 square inch answer : b"
Answer: b
Problem: ratio between rahul and deepak is 4 : 2 , after 10 years rahul age will be 26 years . what is deepak present age
Options: a ) 14 , b ) 15 , c ) 12 , d ) 22 , e ) 8
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 10 = 26 = > x = 4 so deepak age is = 2 ( 4 ) = 8 answer : option e"
Answer: e
Problem: two trains running in opposite directions cross a man standing on the platform in 37 seconds and 27 seconds respectively and they cross each other in 29 seconds . the ratio of their speeds is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 8 , d ) 3 : 25 , e ) 1 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 37 x meters , and length of the second train = 27 y meters . ( 37 x + 27 y ) / ( x + y ) = 29 = = > 37 x + 27 y = 29 x + 29 y = = > 8 x = 2 y = = > x / y = 2 / 8 = 1 / 4 answer : option e"
Answer: e
Problem: what is the rate percent when the simple interest on rs . 800 amount to rs . 160 in 5 years ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 2 % , e ) 4 %
Rationale: "160 = ( 800 * 5 * r ) / 100 r = 4 % answer : e"
Answer: e
Problem: if 2 + 2 / x = 3 - 3 / x , then x =
Options: a ) - 5 , b ) 2 / 3 , c ) 1 , d ) 3 / 2 , e ) 5
Rationale: "we ' re given the equation 2 + 2 / x = 3 - 3 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we have to multiple 2 of the numbers to give them that denominator . . . 2 x / x + 2 / x = 3 x / x - 3 / x we can then eliminate that denominator , which gives us . . . . 2 x + 2 = 3 x - 3 5 = x final answer : e"
Answer: e
Problem: how many factors of 2475 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 17 , d ) 6 , e ) 7
Rationale: "prime factors of 330 are 2 ^ 1,3 ^ 2,5 ^ 2 and 11 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3 , 5,11 ) = ( 2 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 18 since we need odd divisors other than 1 = > 18 - 1 = 17 odd divisors c is the answer"
Answer: c
Problem: harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 2 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 ) 1 / 3 , b ) 2 / 5 , c ) 1 / 4 , d ) 1 / 2 , e ) 4 / 7
Rationale: "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 2 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 2 x = 8 x august tips as a fraction of total tips = 2 x / 8 x = 1 / 4 . so c"
Answer: c
Problem: a plant manager must assign 12 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 3 new workers . how many different ways can she assign the new workers ?
Options: a ) 2430 , b ) 2640 , c ) 3300 , d ) 4860 , e ) 5400
Rationale: "whatever : my take selecting team of 3 out of 12 to assign to the shifts = 12 c 3 = 220 ways . now 3 out of 12 means total of 4 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 4 * 3 * 2 * 1 = 24 here alt and alt are the same : so 24 / 2 = 12 ways . total ways of selecting = ( selecting 3 out of 12 ) * arranging those teams in shifts = 220 * 24 = 2640 ans : b"
Answer: b
Problem: a and b invests rs . 5000 and rs . 6000 in a business . after 6 months , a withdraws two - fifth of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 3 : 5 , b ) 7 : 8 , c ) 5 : 6 , d ) 3 : 4 , e ) 7 : 9
Rationale: "a : b ( 5000 * 6 ) + ( 3000 * 6 ) : ( 6000 * 8 ) + ( 4000 * 4 ) 48000 : 64000 3 : 4 answer : d"
Answer: d
Problem: in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 150 more than the correct answer . find the number .
Options: a ) 125 , b ) 288 , c ) 384 , d ) 400 , e ) 500
Rationale: "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 150 25 * x / 48 = 150 x = 288 answer b"
Answer: b
Problem: a , b and c enter into a partnership by investing $ 7000 , $ 11000 and $ 18000 respectively . at the end of 8 months , b receives $ 880 as his share . find the share of a .
Options: a ) $ 320 , b ) $ 440 , c ) $ 560 , d ) $ 670 , e ) $ 780
Rationale: "the ratio of capital of a , b and c = 7000 : 11000 : 18000 = 7 : 11 : 18 a ' s share = ( 7 / 11 ) * 880 = $ 560 the answer is c ."
Answer: c
Problem: bill downloads the movierevenge of the avengersto his computer in 2.5 hours , using a download manager that downloads from 3 sources marked a , b and c . each source provides download at a constant rate , but the rates of different sources are not necessarily identical . if the movie was downloaded from sources a and c alone , it would take 4 hours to complete the download . the next day , source b is available , but the other sources are inactive . how long will it take to download the trailer of the movie , a file that is 10 times smaller , from source b alone ?
Options: a ) 40 minutes , b ) 15 minutes , c ) 12 minutes , d ) 10 minutes , e ) 3 minutes
Rationale: let the movie size be 400 u . given , a + c = 4 hrs . a + c = 100 u / hr and a + b + c = 2.5 hrs or 400 / 2.5 = 160 u / hr b alone = 160 - 100 = 60 u / hr trailer = 40 times smaller or 400 / 10 = 40 u b will take 40 / 60 hrs or 40 minutes . ans a
Answer: a
Problem: a bowl of fruit contains 14 apples and 21 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 15 , c ) 14 , d ) 17 , e ) 20
Rationale: "number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 21 - x ) = 35 - x 14 / ( 35 - x ) = 7 / 10 = > 20 = 35 - x = > x = 15 answer b"
Answer: b
Problem: the present worth of rs . 2310 due 2 years hence , the rate of interest being 15 % per annum , is :
Options: a ) 1689 , b ) 1680 , c ) 1682 , d ) 1681 , e ) 1686
Rationale: "p . w . = rs . 100 x 2310 = rs . 1680 . 100 + 15 x 5 2 answer : b"
Answer: b
Problem: after decreasing 24 % in the price of an article costs rs . 684 . find the actual cost of an article ?
Options: a ) 218 , b ) 777 , c ) 900 , d ) 2688 , e ) 1991
Rationale: "cp * ( 76 / 100 ) = 684 cp = 9 * 100 = > cp = 900 answer : c"
Answer: c
Problem: a man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream . the ratio of the speed of the boat in still water and stream is
Options: a ) 3 : 1 , b ) 1 : 3 , c ) 2 : 4 , d ) 4 : 2 , e ) none of these
Rationale: "explanation : let speed downstream = x kmph then speed upstream = 2 x kmph so ratio will be , ( 2 x + x ) / 2 : ( 2 x - x ) / 2 = > 3 x / 2 : x / 2 = > 3 : 1 option a"
Answer: a
Problem: ritesh and co . generated revenue of rs . 1,600 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 12.5 % , b ) 19.53 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: explanation : given , ritesh and co . generated revenue of rs . 1,600 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1600 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1600 . = > 12,800 . hence , the total revenue by end of 2007 is rs . 12,800 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 12800 ) × 100 . = > 19.53 % . answer : b
Answer: b
Problem: the average ( arithmetic mean ) of the integers from 100 to 400 , inclusive , is how much greater than the average of the integers from 50 to 250 , inclusive ?
Options: a ) 100 , b ) 175 , c ) 200 , d ) 125 , e ) 300
Rationale: for an ap the mean or average of series is average of first and last term . so , average of numbers between 100 to 400 , inclusive = ( 100 + 400 ) / 2 = 250 average of numbers between 50 to 250 , inclusive = ( 50 + 250 ) / 2 = 150 difference = 250 - 150 = 100 answer is a
Answer: a