regisss/math_qa huggingface dataset:
Problem: andrew purchased 6 kg of grapes at the rate of 74 per kg and 9 kg of mangoes at the rate of 59 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 975 , c ) 980 , d ) 1020 , e ) 1080
Rationale: cost of 6 kg grapes = 74 × 6 = 444 . cost of 9 kg of mangoes = 59 × 9 = 531 . total cost he has to pay = 444 + 531 = 975 b
Answer: b
Problem: the ratio of the incomes of uma and bala is 4 : 3 and the ratio of their expenditure is 3 : 2 . if at the end of the year , each saves $ 5000 then the income of uma is ?
Options: a ) $ 24000 , b ) $ 23000 , c ) $ 22000 , d ) $ 21000 , e ) $ 20000
Rationale: "let the income of uma and bala be $ 4 x and $ 3 x let their expenditures be $ 3 y and $ 2 y 4 x - 3 y = 5000 - - - - - - - 1 ) 3 x - 2 y = 5000 - - - - - - - 2 ) from 1 ) and 2 ) x = 5000 uma ' s income = 4 x = 4 * 5000 = $ 20000 answer is e"
Answer: e
Problem: 3 / 4 of 1 / 2 of 2 / 5 of 5040 = ?
Options: a ) 392 , b ) 229 , c ) 756 , d ) 493 , e ) 540
Rationale: c 756 ? = 5040 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 756
Answer: c
Problem: there are 17 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 156 , b ) 167 , c ) 157 , d ) 342 , e ) 380
Rationale: "the total number of stations = 19 from 19 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 19 p ₂ ways . ² ⁰ p ₂ = 19 * 18 = 342 . answer : d"
Answer: d
Problem: there are 18 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 800 , b ) 380 , c ) 360 , d ) 478 , e ) 566
Rationale: "the total number of stations = 20 from 20 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 20 p 2 ways . 20 p 2 = 20 * 19 = 380 answer : b"
Answer: b
Problem: tickets numbered 1 to 30 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?
Options: a ) 2 / 15 , b ) 7 / 15 , c ) 10 / 30 , d ) 7 / 30 , e ) 8 / 30
Rationale: "here , the sample space s = ( 1 , 2 , 3 , 4 , 5 , . . . , 29 , 30 ) . let e = the event of getting a multiple of 3 or 5 . e = ( 3 , 6 , 9 , 12 , 15 , 18 , 5 , 10 , 20 , 21 , 24 , 25 , 27 , 30 ) p ( e ) = n ( e ) / n ( s ) = 14 / 30 = 7 / 15 answer : b"
Answer: b
Problem: a 160 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 96 kmph , b ) 94 kmph , c ) 92 kmph , d ) 86 kmph , e ) 76 kmph
Rationale: s = 160 / 6 * 18 / 5 = 96 kmph answer : a
Answer: a
Problem: an alloy of copper and zinc contains copper and zinc in the ratio 6 : 4 . another alloy of copper and zinc contains copper and zinc in the ratio 3 : 7 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 12 : 1 , b ) 1 : 2 , c ) 4 : 1 , d ) 2 : 5 , e ) 2 : 6
Rationale: "let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 6 x / 10 , and fraction of zinc in alloy _ 1 = 4 x / 10 similarly , fraction of copper in alloy _ 2 = 3 y / 10 , and fraction of zinc in alloy _ 2 = 7 y / 10 . mixing them , we get copper = 6 x / 10 + 3 y / 10 ; zinc = 4 x / 10 + 7 y / 10 so , 6 x + 3 y = 4 x + 7 y - > 2 x = 4 y - > x / y = 2 / 4 = 1 / 2 so , they must be mixed in the ratio 1 : 2 answer : b"
Answer: b
Problem: a tank contains 7,500 gallons of a solution that is 6 percent sodium chloride by volume . if 2,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 5.18 % , b ) 6.18 % , c ) 7.18 % , d ) 8.18 % , e ) . 7 %
Rationale: "we start with 7,500 gallons of a solution that is 6 % sodium chloride by volume . this means that there are 0.06 x 7,500 = 450 gallons of sodium chloride . when 2,000 gallons of water evaporate we are left with 5,500 gallons of solution . from here we can determine what percent of the 5,500 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 450 / 5,500 ) x 100 = ? 0.081 x 100 = ? = 8.18 % answer is d ."
Answer: d
Problem: the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 16 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 16 = 404 hence , new average = 404 ⁄ 10 = 40.4 answer b"
Answer: b
Problem: rs . 705 is divided amongst a , b , c so that 3 times a ' s share , 5 times b ' s share and 4 times c ' s share are all equal . find b ' s share ?
Options: a ) 177 , b ) 150 , c ) 180 , d ) 716 , e ) 616
Rationale: a + b + c = 705 3 a = 5 b = 4 c = x a : b : c = 1 / 3 : 1 / 5 : 1 / 4 = 20 : 12 : 15 12 / 47 * 705 = rs . 180 answer : c
Answer: c
Problem: the sale price sarees listed for rs . 175 after successive discount is 20 % and 5 % is ?
Options: a ) 187 , b ) 133 , c ) 142 , d ) 178 , e ) 175
Rationale: "175 * ( 80 / 100 ) * ( 95 / 100 ) = 133 answer : b"
Answer: b
Problem: the average salary of all the workers in a workshop is rs . 9500 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 12
Rationale: let the total number of workers be x . then , 9500 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = > 3500 x = 42000 = x = 12 . answer : e
Answer: e
Problem: solve x 2 – 3 x – 4 = 0 .
Options: a ) 1,4 , b ) - 1,4 , c ) 2,3 , d ) 2 , - 3 , e ) 3,4
Rationale: "this one factors easily : x 2 – 3 x – 4 = 0 ( x + 1 ) ( x – 4 ) = 0 x + 1 = 0 or x – 4 = 0 x = – 1 or x = 4 the solution is x = – 1 , 4 answer b - 1,4"
Answer: b
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 2 / 5 % his yearly income diminishes by rs . 61.50 . his capital is
Options: a ) 223.78 , b ) 37.78 , c ) 246.0 , d ) 278.88 , e ) 102.5
Rationale: "explanation : capital = rs . x , then 3 / 5 x = 61.5 x = 102.50 answer : e ) rs . 102.50"
Answer: e
Problem: a sum of money lent at compound interest for 2 years at 20 % per annum would fetch rs . 482 more , if the interest was payable half yearly than if it was payable annually . the sum is
Options: a ) 200000 , b ) 20000 , c ) 200029 , d ) 288778 , e ) 277789
Rationale: explanation : let sum = rs . x c . i . when compounded half yearly = c . i . when compounded annually = = > x = 20000 answer : b ) 20000
Answer: b
Problem: a monkey start climbing up a tree 20 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 17 hrs it wil be 17 ft . bt since the height of the tree is 20 ft , so if the monkey hops up the tree in the next hr i . e 18 th hr then it reaches at the top of the tree . hence it takes 18 hrs for monkey to reach at the top answer : b
Answer: b
Problem: 1 / 0.06 is equal to
Options: a ) 25.5 , b ) 16.7 , c ) 25 , d ) . 25 , e ) none of these
Rationale: "explanation : 1 / 0.06 = ( 1 * 100 ) / 6 = 100 / 6 = 16.7 option b"
Answer: b
Problem: rs 3600 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 4000 , b ) s 2800 , c ) s 1800 , d ) s 3500 , e ) s 3100
Rationale: "explanation : average rate = ( 144 / 3600 ) * 100 = 4 ratio = 1 : 1 so , first part = ( 1 / 2 ) * 3600 = rs 1800 . answer : c"
Answer: c
Problem: without stoppages , a train travels certain distance with an average speed of 200 km / h , and with stoppages , it covers the same distance with an average speed of 160 km / h . how many minutes per hour the train stops ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "due to stoppages , it covers 40 km less . time taken to cover 40 km = 40 â  „ 200 h = 1 â  „ 5 h = 1 â  „ 5 ã — 60 min = 12 min answer e"
Answer: e
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 56 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320.8 $ , b ) 387.8 $ , c ) 420.8 $ , d ) 457.8 $ , e ) 480.8 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 56 ) = 457.8 hence answer will be ( d )"
Answer: d
Problem: the price of an item is discounted 2 percent on day 1 of a sale . on day 2 , the item is discounted another 12 percent , and on day 3 , it is discounted an additional 25 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 66 % , b ) 67.5 % , c ) 69 % , d ) 70 % , e ) 72 %
Rationale: "let initial price be 1000 price in day 1 after 2 % discount = 980 price in day 2 after 12 % discount = 862.4 price in day 3 after 25 % discount = 646.8 so , price in day 3 as percentage of the sale price on day 1 will be = 646.8 / 980 * 100 = > 66 % answer will definitely be ( a )"
Answer: a
Problem: find the smallest number of four digits exactly divisible by 4 , 5,7 and 8 .
Options: a ) 1150 , b ) 1160 , c ) 1140 , d ) 1152 , e ) 1145
Rationale: "smallest number of four digits is 1000 . required number must be divisible by l . c . m . of 4,5 , 7,8 i . e 280 , on dividing 1000 by 280 , we get 120 as remainder . therefore , required number = 1000 + ( 280 â € “ 120 ) = 1160 . answer is b ."
Answer: b
Problem: a sum fetched a total simple interest of rs . 2700 at the rate of 6 p . c . p . a . in 3 years . what is the sum ?
Options: a ) 25000 , b ) 20000 , c ) 18000 , d ) 14000 , e ) 15000
Rationale: "sol . principal = rs . [ 100 * 2700 / 6 * 3 ] = rs . [ 270000 / 18 ] = rs . 15000 . answer e"
Answer: e
Problem: if 20 men can build a water fountain 56 metres long in 21 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 10 m , b ) 14 m , c ) 17 m , d ) 19 m , e ) 20 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 21 : 3 : : 56 : x therefore ( 20 x 21 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 420 = 14 hence , the required length is 14 m . answer : b"
Answer: b
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 5 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 1 , b ) 2 , c ) 10 , d ) 8 , e ) 16
Rationale: "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 5 ( pir ^ 2 ) pir ^ 2 = 10 pir r = 10 answer : c"
Answer: c
Problem: the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 3 . if the sum of the first and the last number is 13 . what is the last numbers ?
Options: a ) 4 , b ) 2 , c ) 6 , d ) 7 , e ) 8
Rationale: a + b + c = 18 b + c + d = 9 a + d = 13 a – d = 9 a + d = 13 2 d = 4 d = 2 answer : b
Answer: b
Problem: a classroom has equal number of boys and girls . 8 girls left to play kho - kho , leaving twice as many boys as girls in the classroom . what was the total number of girls and boys present initially ?
Options: a ) 16 , b ) 24 , c ) 32 , d ) 48 , e ) 54
Rationale: after 8 girls left remaining 8 girls now boys 16 are twice as many as remaining girls . initially boys = 16 and girls = 16 . answer : c
Answer: c
Problem: a person ' s present age is two - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . what is the present age of the mother ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "let present age of the mother = 5 x then , present age of the person = 2 x 5 x + 8 = 2 ( 2 x + 8 ) 5 x + 8 = 4 x + 16 x = 8 present age of the mother = 5 x = 40 answer is d ."
Answer: d
Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "given : positive integer n is a perfect square and a perfect cube - - > n is of a form of n = x 6 for some positive integer x - - > 0 < x ^ 6 < 10 ^ 3 - - > 0 < x ^ 2 < 10 - - > x can be 1 , 2 or 3 hence nn can be 1 ^ 6 , 2 ^ 6 or 3 ^ 6 . answer : b ."
Answer: b
Problem: the speed of a boat in still water is 50 kmph and the speed of the current is 20 kmph . find the speed and upstream ?
Options: a ) 30 kmph , b ) 40 kmph , c ) 78 kmph , d ) 15 kmph , e ) 23 kmph
Rationale: speed downstream = 50 + 20 = 70 kmph speed upstream = 50 - 20 = 30 kmph answer : a
Answer: a
Problem: if 5 x = 6 y and xy ≠ 0 , what is the ratio of 1 / 5 * x to 1 / 8 * y ?
Options: a ) 48 / 25 , b ) 36 / 25 , c ) 6 / 5 , d ) 5 / 6 , e ) 25 / 36
Rationale: "5 x = 6 y = > x / y = 6 / 5 1 / 5 * x to 1 / 8 * y = x / y * 8 / 5 = ( 6 / 5 ) * ( 8 / 5 ) = 48 / 25 ans : a"
Answer: a
Problem: when a number is divided by 6 & then multiply by 12 the answer is 10 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.6 , d ) 5.7 , e ) 6.5
Rationale: "if $ x $ is the number , x / 6 * 12 = 10 = > 2 x = 10 = > x = 5 b"
Answer: b
Problem: a company that ships boxes to a total of 13 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )
Options: a ) 6 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "back - solving is the best way to solve this problem . you basically need 13 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b"
Answer: b
Problem: a and b start from house at 10 am . they travel on the mg road at 20 kmph and 40 kmph . there is a junction t on their path . a turns left at t junction at 12 : 00 noon , b reaches t earlier , and turns right . both of them continue to travel till 2 pm . what is the distance between a and b at 2 pm
Options: a ) 160 km , b ) 170 km , c ) 180 km , d ) 190 km , e ) 150 km
Rationale: at 12 a will travel = 20 * 2 = 40 km b will travel this 40 km in 40 / 40 = 1 hr i . e . by 11 am . after t junction for a - distance travelled = 2 * 20 = 40 km for b distance travelled = 40 * 3 = 120 so distance between a & b is = 120 + 40 = 160 km answer : a
Answer: a
Problem: the circulation for magazine p in 1971 was 4 times the average ( arithmetic mean ) yearly circulation for magazine p for the years 1972 - 1980 . what is the ratio of the circulation in 1971 to the total circulation during 1971 - 1980 for magazine p ?
Options: a ) 4 / 7 , b ) 5 / 7 , c ) 3 / 7 , d ) 2 / 7 , e ) 1 / 7
Rationale: there are 9 years from 1972 - 1980 , inclusive . let ' s say the average circulation every year between 1972 - 1980 inclusive is x . so the total circulation is 9 x from 1972 - 1980 , inclusive . in 1971 , the circulation is 4 x . so total circulation for 1971 - 1980 is 4 x + 9 x = 13 x . ratio of circulation in 1971 to total circulation during 1971 - 1980 is 4 x to 14 x or 4 / 14 = 2 / 7 answer : d
Answer: d
Problem: the regular price per can of a certain brand of soda is $ 0.30 . if the regular price per can is discounted 15 percent when the soda is purchased in 24 - can cases , what is the price of 72 cans of this brand of soda purchased in 24 - can cases ?
Options: a ) $ 16.32 , b ) $ 18.36 , c ) $ 21.60 , d ) $ 24.48 , e ) $ 28.80
Rationale: "the discounted price of one can of soda is ( 0.85 ) ( $ 0.30 ) , or $ 0.255 . therefore , the price of 72 cans of soda at the discounted price would be ( 72 ) ( $ 0.255 ) = 18.36 answer : b ."
Answer: b
Problem: a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 9 / 16 . how many marbles are in the bag ?
Options: a ) 48 , b ) 24 , c ) 60 , d ) 72 , e ) 84
Rationale: "ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 9 / 16 - - > ( x - 12 ) ^ 2 = 16 / 25 x ^ 2 a square rooting u have x - 12 / x = 3 / 4 or 4 x - 48 = 3 x or x = 48"
Answer: a
Problem: the average marks of a class of 26 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 53.1
Rationale: sum of the marks for the class of 26 students = 26 * 40 = 1040 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 76 students = 1040 + 3000 = 4040 average marks of all the students = 4040 / 76 = 53.15 answer : e
Answer: e
Problem: a train 125 m long passes a man , running at 6 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 51 , b ) 50 , c ) 88 , d ) 65 , e ) 22
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 6 ) km / hr . x - 6 = 45 = = > x = 51 km / hr . answer : a"
Answer: a
Problem: tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many l minutes it takes john to reach the station ?
Options: a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min
Rationale: since the question states “ after 15 minutes ” , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john ’ s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , l 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c .
Answer: c
Problem: pipe a can fill a tank in 8 hours . due to a leak at the bottom , it takes 12 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 5 , b ) 24 , c ) 78 , d ) 90 , e ) 54
Rationale: "let the leak can empty the full tank in x hours 1 / 8 - 1 / x = 1 / 12 = > 1 / x = 1 / 8 - 1 / 12 = ( 3 - 2 ) / 24 = 1 / 24 = > x = 24 . answer : b"
Answer: b
Problem: three 8 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 38 , b ) 1 / 48 , c ) 1 / 56 , d ) 1 / 64 , e ) 1 / 68
Rationale: "it all 3 numbers have to be same basically we want triplets . 111 , 222 , 333 , 444 , 555 , 666 , 777 and 888 . those are eight in number . further the three dice can fall in 8 * 8 * 8 = 512 ways . hence the probability is 8 / 512 = 1 / 64 answer : d"
Answer: d
Problem: an escalator is descending at constant speed . a walks down and takes 50 steps to reach the bottom . b runs down and takes 90 steps in the same time as a takes 10 steps . how many steps are visible when the escalator is not operating ?
Options: a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: lets suppose that a walks down 1 step / min and escalator moves n steps / min it is given that a takes 50 steps to reach the bottom in the same time escalator would have covered 50 n steps so total steps on escalator is 50 + 50 n . again it is given that b takes 90 steps to reach the bottom and time taken by him for this is equal to time taken by a to cover 10 steps i . e 10 minutes . so in this 10 min escalator would have covered 10 n steps . so total steps on escalatro is 90 + 10 n again equating 50 + 50 n = 90 + 10 n we get n = 1 hence total no . of steps on escalator is 100 . answer : c
Answer: c
Problem: how many kg of sugar must be added to 30 kg of 2 % solution of sugar and water to increase it to a 10 % solution ?
Options: a ) 2.6 kg , b ) 4 kg , c ) 3.4 kg , d ) 1.8 kg , e ) none of these
Rationale: explanation : solution : amount of sugar in 30 kg solution = ( 2 / 100 * 30 ) kg = 0.6 kg . let x kg of sugar be added . then , ( 0.6 + x ) / ( 30 + x ) = 10 / 100 60 + 100 x = 300 + 10 x x = 240 / 90 = 8 / 3 = 2.6 answer : a
Answer: a
Problem: each of the integers from 1 to 18 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even
Options: a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 3
Rationale: out of the 18 integers : 9 are odd and 9 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 9 odd numbers first 2 . 10 th number will be the first even number so we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 10 . ( d )
Answer: d
Problem: suppose f ( x ) is an odd function for which f ( x + 2 ) = f ( x ) for all x , and f ( x ) = x 2 for x 2 ( 0 , 1 ) . compute f ( - 3 / 2 ) + f ( 1 ) .
Options: a ) - 1 , b ) - 1 / 2 , c ) - 1 / 4 , d ) 1 / 4 , e ) 1 / 2
Rationale: because f is periodic , we know that f ( - 3 / 2 ) = f ( 1 / 2 ) = ( 1 / 2 ) 2 = 1 = 4 . because f is odd , we know that f ( 1 ) = - f ( / 1 ) , but because f is periodic , f ( 1 ) = f ( - 1 ) . therefore , f ( 1 ) = 0 and the answer is 1 = 4 . correct answer d
Answer: d
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1980 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 9 % , d ) 10 % , e ) 45 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 1980 100 r + 120 r = 1980 r = 9 % answer : c"
Answer: c
Problem: sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 06 : 00 and starts climbing at a constant pace . ken starts climbing only at 08 : 00 , when sari is already 600 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
Options: a ) 13 : 00 , b ) 11 : 15 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30
Rationale: "both sari and ken climb in the same direction . speed of sari = 600 / 2 = 300 meters / hr ( since she covers 700 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 600 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 600 + 50 ) / ( 500 - 300 ) = 3.25 hrs starting from 8 : 00 , in 5 hrs , the time will be 11 : 15 answer ( b )"
Answer: b
Problem: if x > 0 , x / 50 + x / 5 is what percent of x ?
Options: a ) 6 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 50 + 100 / 5 = 2 + 20 = 25 25 is 25 % of 100 = b"
Answer: b
Problem: in what time will a railway train 60 m long moving at the rate of 72 kmph pass a telegraph post on its way ?
Options: a ) 8 sec , b ) 3 sec , c ) 2 sec , d ) 6 sec , e ) 9 sec
Rationale: "t = 60 / 72 * 18 / 5 = 3 sec answer : b"
Answer: b
Problem: a can do a piece of work in 18 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
Options: a ) 5 days , b ) 6 days , c ) 7.5 days , d ) 8.5 days , e ) 9 days
Rationale: "explanation : b ' s 5 days work = 1 / 10 ∗ 5 = 1 / 2 remaining work = 1 − 1 / 2 = 1 / 2 a can finish work = 18 ∗ 1 / 2 = 9 days option e"
Answer: e
Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 36000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 20 : 9 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 3
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 36000 × 9 = 45 × 12 : 36 × 9 = 15 × 12 : 9 × 9 = 20 : 9 answer is a ."
Answer: a
Problem: a car travels first 160 km at 75 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 71.17 , e ) 77.42
Rationale: car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 160 / 80 total distance traveled = 160 + 160 = 2 × 160 total time taken = 160 / 75 + 160 / 80 average speed = total distance traveled / total time taken = 320 / ( 160 / 75 + 160 / 80 ) = 77.42 km / hr answer : e
Answer: e
Problem: if a – 8 = b , then determine the value of | a - b | - | b - a | .
Options: a ) 16 , b ) 0 , c ) 4 , d ) 2 , e ) 1
Rationale: sol . ( b ) | a - b | = | 8 | = 8 = > | b - a | = | - 8 | = 8 = > | a - b | - | b - a | = 8 - 8 = 0 . answer b
Answer: b
Problem: the measure of the side of a square is multiplied by 5 . if x represents the perimeter of the original square , what is the value of the new perimeter ?
Options: a ) 3 x
b ) 4 x
c ) 5 x
d ) 12 x
e ) 27 x
Rationale: original perimeter = x hence original side = x / 4 new side = 5 x / 4 new perimeter = 4 * 5 x / 4 = 5 x correct option : c
Answer: c
Problem: the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 18 . find the sum :
Options: a ) 4500 , b ) 7500 , c ) 5000 , d ) 7200 , e ) none of these
Rationale: "sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 18 , the sum = 400 × 18 = 7200 answer d"
Answer: d
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter w of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) w = 7 * 3 = 21 . c"
Answer: c
Problem: a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 6 hours , then the distance covered at 40 kmph is
Options: a ) 220 km , b ) 120 km , c ) 100 km , d ) 140 km , e ) none of these
Rationale: "let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 6 or , x / 40 + ( 250 - x ) / 60 = 6 or , ( 3 x + 500 - 2 x ) / / 120 = 6 or 500 + x = 720 x = 220 answer : a"
Answer: a
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 180 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 43.2 sec , d ) 40 sec , e ) none of these
Rationale: "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 180 = 540 meter time taken to cross the platform = 540 / ( 25 / 2 ) = 540 ã — 2 / 25 = 43.2 seconds answer : c"
Answer: c
Problem: if the length of the longest chord of a certain circle is 22 , what is the radius of that certain circle ?
Options: a ) 11 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 22 = 2 * 11 so radius of the circle = 11 correct answer - a"
Answer: a
Problem: company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 20.00 each , what was company c ’ s gross profit ?
Options: a ) $ 7,250 , b ) $ 8,500 , c ) $ 8,100 , d ) $ 8,250 , e ) $ 8,600
Rationale: "cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 20 = $ 10000 profit : 10000 - 1900 = $ 8100 option c is correct"
Answer: c
Problem: if y is 70 % greater than x , than x is what % less than y ?
Options: a ) 18.7 , b ) 25.5 , c ) 33.3 , d ) 41.2 , e ) 54.4
Rationale: y = 1.7 x x = y / 1.7 = 10 y / 17 x is 7 / 17 less which is about 41.2 % less than y . the answer is d .
Answer: d
Problem: in a room filled with 7 people , 3 people have exactly 1 sibling in the room and 4 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 13 / 21
Rationale: there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssds ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssdssibl ∈ gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 4 people who have exactly 2 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 2 people out of 7 is 7 c 2 = 21 first sibling pair - - - - ( a and b ) - - selecting 2 people - - 2 c 2 = 1 second sibling pair ( c and d ) - - selecting 2 people - - 2 c 2 = 1 third sibling pair ( e f g ) - - selecting 2 out of 4 - - 4 c 2 = 6 total = 1 + 1 + 6 = 8 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 2 people who are siblings = 8 / 21 ( 21 is 7 c 2 ) = 1 - 8 / 21 = 13 / 21 ans e
Answer: e
Problem: mohit sold an article for $ 27000 . 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 ) 22500 , c ) 15000 , 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 = 27000 - 10 / 100 ( 27000 ) = 27000 - 2700 = $ 22500 = > 1.08 x = 22500 = > x = 22500 b"
Answer: b
Problem: if a farmer wants to plough a farm field on time , he must plough 260 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 312 , b ) 490 , c ) 720 , d ) 435 , e ) 679
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 260 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 260 x = 85 ( x + 2 ) + 40 175 x = 210 x = 1.2 so the farmer planned to have the work done in 6 days , and the area of the farm field is 260 ( 1.2 ) = 312 hectares correct answer a"
Answer: a
Problem: on my sister ' s 15 th birthday , she was 159 cm in height , having grown 6 % since the year before . how tall was she the previous year ?
Options: a ) 150 cm , b ) 160 cm , c ) 170 cm , d ) 140 cm , e ) 150 cm
Rationale: explanation : given that height on 15 th birthday = 159 cm and growth = 6 % let the previous year height = x then height on 15 th birthday = x × ( 100 + 6 ) / 100 = x × 106 / 100 ⇒ 159 = x × 106 / 100 ⇒ x = 159 × 100 / 106 = 1.5 × 100 = 150 cm answer : option a
Answer: a
Problem: jim â € ™ s taxi service charges an initial fee of $ 2.35 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.50 , e ) $ 5.40
Rationale: "let the fixed charge of jim â € ™ s taxi service = 2.35 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.35 + ( 3.6 / . 4 ) * . 35 = 2.35 + 9 * . 35 = 5.5 $ answer d"
Answer: d
Problem: a special municipal payroll tax charges not tax on a payroll less than $ 200,000 and only 0.2 % on a company ’ s payroll above $ 200,000 . if belfried industries paid $ 400 in this special municipal payroll tax , then they must have had a payroll of
Options: a ) $ 180,000 , b ) $ 400,000 , c ) $ 220,000 , d ) $ 402,000 , e ) $ 2 , 200,000
Rationale: "answer : b , ( with different approach ) : the 400 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 400 therefore x = 200,000 total = 200,000 + x = 400,000"
Answer: b
Problem: the speed of a boat in still water in 20 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 9.6 , b ) 10.2 , c ) 9.2 , d ) 10.4 , e ) 9.0
Rationale: "speed downstream = ( 20 + 3 ) = 23 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 23 = 9.20 km answer is c ."
Answer: c
Problem: what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 42 ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 6 , e ) 2
Rationale: "denote | x - 3 | as y : y ^ 2 + y = 42 - - > y = - 7 or y = 6 . discard the first solution since y = | x - 3 | , so it ' s an absolute value and thus can not be negative . y = | x - 3 | = 6 - - > x = 9 or x = - 4 . the sum = 5 . answer : c ."
Answer: c
Problem: what is remainder of the division ( 1225 * 1227 * 1229 ) / 12 ?
Options: a ) 1 , b ) 0 , c ) 3 , d ) 2 , e ) 4
Rationale: "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : c"
Answer: c
Problem: the sum of three consecutive multiples of 3 is 99 . what is the largest number ?
Options: a ) 36 , b ) 33 , c ) 30 , d ) 27 , e ) 24
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 99 9 x = 90 x = 10 largest number = 3 x + 6 = 36 answer : a"
Answer: a
Problem: what number should replace the question mark ? 2 , 16 , 4 , 14 , 6 , 12 , - - - ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: answer : a 2 , 16 , 4 , 14 , 6 , 12 , 8 ? there are two alternate sequences : + 2 and - 2 .
Answer: a
Problem: a garrison of 400 men had a provision for 31 days . after 28 days 280 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 45 days , c ) 10 days , d ) 16 days , e ) 18 days
Rationale: "400 - - - 31 400 - - - 3 120 - - - ? 400 * 3 = 120 * x = > x = 10 days . answer : c"
Answer: c
Problem: a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 62 now , the son age 5 years back was
Options: a ) 14 , b ) 17 , c ) 11 , d ) 19 , e ) 26
Rationale: "let the son ' s present age be x years . then , ( 62 - x ) = x x = 31 . son ' s age 5 years back = ( 31 - 5 ) = 26 years answer : e"
Answer: e
Problem: calculate the average of all the numbers between 7 and 49 which are divisible by 6 .
Options: a ) 20 , b ) 18 , c ) 19 , d ) 15 , e ) 30
Rationale: "explanation : numbers divisible by 6 are 12 , 18,24 , 30,36 , 42,48 , average = ( 12 + 18 + 24 + 30 + 36 + 42 + 48 , ) / 7 = 210 / 7 = 30 answer : e"
Answer: e
Problem: a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 35 more than that received by b , find the total amount shared by a , b and c .
Options: a ) $ 1360 , b ) $ 1250 , c ) $ 1260 , d ) $ 1270 , e ) $ 1280
Rationale: "a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 35 a = 35 + b ( 1 ) = = = > c = 105 + 3 b - b = 2 b + 105 = = > 2 b - c = - 105 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 35 = 2.5 b - 35 = = > 2.5 b - c = 35 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 140 b = $ 280 a = $ 315 c = 945 - 280 = $ 665 total amount = 315 + 280 + 665 = $ 1260 answer : c"
Answer: c
Problem: a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 45 kmph , b ) 25 kmph , c ) 30 kmph , d ) 50 kmph , e ) none of these
Rationale: "explanation : speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) x ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be ' s ' km / hr . then , relative speed = ( s - 5 ) km / hr . s - 5 = 45 = > s = 50 km / hr . answer is d"
Answer: d
Problem: the number which exceeds 16 % of it by 21 is :
Options: a ) 25 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 21 x - 16 / 100 x = 21 x - 4 / 25 x = 21 21 / 25 x = 21 x = ( 21 x 25 / 21 ) = 25 answer a"
Answer: a
Problem: excluding stoppages , the speed of a bus is 60 kmph and including stoppages , it is 50 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 10 min , b ) 15 min , c ) 12 min , d ) 8 min , e ) 16 min
Rationale: "due to stoppages , it covers 10 km less . time taken to cover 10 km = ( 10 / 60 x 60 ) min = 10 min answer : a"
Answer: a
Problem: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4960 , r will receive
Options: a ) 600 , b ) 700 , c ) 800 , d ) 960 , e ) none of these
Rationale: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4960 * ( 6 / 31 ) = 160 * 6 = 960 . answer : option d"
Answer: d
Problem: an isosceles triangle those sides are 13 cm , 13 cm , 10 cm long inscribed in a circle . find the radius of the circle
Options: a ) 8 cm
b ) 9 cm
c ) 10 cm
d ) 11 cm
e ) 7 cm
Rationale: a , b , c are sides of triangle , ad is the median , ad ^ 2 = ab ^ 2 - bd ^ 2 then ad = 12 , the centriod median divides into 2 : 1 ratio so 12 will be divide into 2 : 1 ratio so 8 is radius . so ans is 8 cm answer : a
Answer: a
Problem: n is an 80 - digit positive integer ( in the decimal scale ) . all digits except the 44 th digit ( from the left ) are 2 . if n is divisible by 13 , find the 26 th digit ?
Options: a ) 5 , b ) 6 , c ) 1 , d ) 2 , e ) 3
Rationale: detailed solution to begin with , the question should read ` ` find the 44 th digit ' ' . any number of the form abcabc is a multiple of 1001 . 1001 is 7 * 11 * 13 . so , any number of the form abcabc is a multiple of 13 . so , a number comprising 42 2 ' s would be a multiple of 13 , so would a number comprising 36 2 ' s . so , in effect , we are left with a two digit number 2 a , where a is the 44 th digit . 26 is a multiple of 13 , so the 44 th digit should be 6 . correct answer b
Answer: b
Problem: 60 boys can complete a work in 40 days . how many men need to complete twice the work in 20 days
Options: a ) 160 , b ) 170 , c ) 180 , d ) 190 , e ) 240
Rationale: "one man can complete the work in 40 * 60 = 2400 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 2400 m = 240 workers answer : e"
Answer: e
Problem: an outlet pipe empties a tank which is full in 8 hours . if the inlet pipe is kept open , which lets water in at the rate of 8 litres / min then outlet pipe would take 4 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 200 litres , c ) 12800 litres , d ) 11520 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 8 * 60 = 480 liters / hour ; net outflow rate when both pipes operate would be x - 480 liters / hour . capacity of the tank = x * 8 hours = ( x - 480 ) * ( 8 + 4 ) hours 8 x = ( x - 480 ) * 12 - - > x = 1440 - - > capacity = 8 x = 11520 liters . answer : d ."
Answer: d
Problem: how should we mix two rice packets to get one 1 kg packet priced at rs 8 when the prices of 1 kg packets of the two types are rs 7.1 and rs 9.2 .
Options: a ) 4 : 3 , b ) 4 : 7 , c ) 4 : 9 , d ) 4 : 2 , e ) 4 : 1
Rationale: explanation : no explanation is available for this question ! answer : a
Answer: a
Problem: car a runs at the speed of 35 km / hr & reaches its destination in 9 hr . car b runs at the speed of 43 km / h & reaches its destination in 10 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 65 : 69 , b ) 56 : 45 , c ) 89 : 71 , d ) 68 : 23 , e ) 63 : 86
Rationale: "sol . distance travelled by car a = 35 × 9 = 315 km distance travelled by car b = 43 × 10 = 430 km ratio = 315 / 430 = 63 : 86 e"
Answer: e
Problem: a and b ’ s salaries together amount to rs . 3,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is a ’ s salary ?
Options: a ) 2777 , b ) 2250 , c ) 2789 , d ) 2776 , e ) 2881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 3000 4 b = 3000 = > b = 750 a = 2250 answer b"
Answer: b
Problem: the average weight of 3 packets a , b and c is 84 kg . another packet d added into the group and the average now becomes 80 kg . if another packet e , whose weight is 3 kg more than that of d , replaces a then the average weight of b , c , d and e becomes 79 kg . the weight of a is :
Options: a ) 70 kg , b ) 72 kg , c ) 75 kg , d ) 80 kg , e ) none of these
Rationale: explanation : a + b + c = ( 84 x 3 ) = 252 kg , a + b + c + d = ( 80 x 4 ) = 320 kg . d = ( 320 - 252 ) = 68 , e = ( 68 + 3 ) = 7 l . b + c + d + e = ( 79 x 4 ) = 316 . ( a + b + c + d ) - ( b + c + d + e ) = ( 320 - 316 ) kg = 4 kg . a - e = 4 = a = ( 4 + e ) = 75 kg answer : c
Answer: c
Problem: the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 60 kmph its consumption is 1 litre per hour . if each litre costs $ 30 and other expenses per hous is $ 20 , then what would be the minimum expenditure required to cover a distance of 600 km ?
Options: a ) 500 , b ) 450 , c ) 600 , d ) 650 , e ) 750
Rationale: 60 kmph consumption is 1 lt / hr so 600 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 30 so 10 lt costs $ 300 extra expenses for 1 hr - $ 20 10 hrs - $ 200 total expense - $ 300 + $ 200 = $ 500 answer : a
Answer: a
Problem: if the average of 10 consecutive integers is 19.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 24 , e ) 25
Rationale: "the average falls between the 5 th and 6 th integers , integer 5 = 19 , integer 6 = 20 . counting up to the tenth integer we get 24 . answer : d"
Answer: d
Problem: on the first day of her vacation , louisa traveled 100 miles . on the second day , traveling at the same average speed , she traveled 175 miles . if the 100 - mile trip took 3 hours less than the 175 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 27 , b ) 28 , c ) 25 , d ) 30 , e ) 35
Rationale: "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 100 / t = 175 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 100 / 4 = 25 answer : c"
Answer: c
Problem: at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 28 liters of forest green to change it to verdant green ?
Options: a ) 28 / 3 , b ) 13 / 6 , c ) 3 , d ) 4 , e ) 14 / 3
Rationale: "28 liter of forset green have 16 liter of blue and 12 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 16 / ( 12 + x ) = ¾ 36 + 3 x = 64 = > x = 28 / 3 answer : a"
Answer: a
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 minutes , then what is the area of the park ( in sq . m ) ?
Options: a ) 153500 , b ) 153650 , c ) 153600 , d ) 153700 , e ) 153750
Rationale: "let length = 3 x km , breadth = 2 x km distance travelled by the man at the speed of 12 km / hr in 8 minutes = 2 ( 3 x + 2 x ) = 10 x therefore , 12 × 860 = 10 xx = 425 km = 160 m area = 3 x × 2 x = 6 x 2 = 6 × 1602 = 153600 m 2 answer is c ."
Answer: c
Problem: in a office work is distribute between p persons . if 1 / 5 members are absent then work increased for each person is ?
Options: a ) 13.28 % , b ) 14.28 % , c ) 15.28 % , d ) 16.28 % , e ) 25 %
Rationale: "let total % of work is 100 % total person = p 1 / 5 person are absent of total person . so absent person is 1 / 5 p ie p / 5 . left person is , p - p / 5 = 4 p / 5 . p person do the work 100 % 1 person do the work 100 * p % 4 p / 5 person do the work ( 100 * p * 5 ) / 4 p % = 125 % work increased for each person is = ( 125 - 100 ) % = 25 % answer : e"
Answer: e
Problem: what could be the range of a set consisting of odd multiples of 5 ?
Options: a ) 21 , b ) 24 , c ) 35 , d ) 62 , e ) 60
Rationale: "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 5 * ( 2 n + 1 ) where n is any positive integer . range = 5 * ( 2 m + 1 ) - 5 * ( 2 n + 1 ) = 5 * 2 * ( m - n ) = 10 * ( m - n ) . m , n - any positive integers the answer must be divisible by 10 , which is only 60 . the correct answer is e ."
Answer: e