regisss/math_qa huggingface dataset:
Problem: a certain industrial loom weaves 0.127 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.127 : 15 : : 1 : x = > 0.127 * x = 15 = > x = 15 / 0.127 = > x = 118 answer : e"
Answer: e
Problem: the average marks of a class of 35 students is 45 and that of another class of 55 students is 65 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 57 , e ) 52.9
Rationale: "sum of the marks for the class of 35 students = 35 * 45 = 1575 sum of the marks for the class of 55 students = 55 * 65 = 3575 sum of the marks for the class of 90 students = 1575 + 3575 = 5150 average marks of all the students = 5150 / 90 = 57 . answer : d"
Answer: d
Problem: a and b together have $ 100 . if 3 / 10 of a ' s amount is equal to 1 / 5 of b ' s amount , how much amount does b have ?
Options: a ) $ 60 , b ) $ 55 , c ) $ 42 , d ) $ 31 , e ) $ 100
Rationale: "3 / 10 a = 1 / 5 b a = 1 / 5 * 10 / 3 b a = 2 / 3 b a / b = 2 / 3 a : b = 2 : 3 b ' s share = 100 * 3 / 5 = $ 60 answer is a"
Answer: a
Problem: two cars start from the opposite places of a main road , 150 km apart . first car runs for 30 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 60 , d ) 28 , e ) 21
Rationale: answer : c ) 60 km
Answer: c
Problem: if the given two numbers are respectively 6 % and 30 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 30 % , e ) none of these
Rationale: here , l = 6 and m = 30 therefore , first number = l / m x 100 % of second number = 6 / 30 x 100 % of second number = 20 % of second number answer : a
Answer: a
Problem: mary can do a piece of work in 11 days . rosy is 10 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "ratio of times taken by mary and rosy = 110 : 100 = 11 : 10 suppose rosy takes x days to do the work . 11 : 10 : : 11 : x = > x = 10 days . hence , rosy takes 10 days to complete the work . answer : a"
Answer: a
Problem: in a certain game of dice , the player ’ s score is determined as a sum of three throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if jim plays this game against 24 other players , what is the probability of the minimum score that will guarantee jim some monetary payoff ?
Options: a ) 1 / 216 , b ) 1 / 221 , c ) 1 / 212 , d ) 1 / 84 , e ) 1 / 42
Rationale: "toguaranteethat jim will get some monetary payoff he must score the maximum score of 6 + 6 + 6 = 18 , because if he gets even one less than that so 17 , someone can get 18 and jim will get nothing . p ( 18 ) = 1 / 6 ^ 3 = 1 / 216 . answer : a ."
Answer: a
Problem: 24 oz of juice p and 25 oz of juice v are mixed to make smothies m and y . the ratio of p to v in smothie m is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie m ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: the ratio of p to v in smothie m is 4 is to 1 and that in y is 1 is to 5 . p 1 + p 2 = 24 v 1 + v 2 = 25 p 1 = 4 v 1 p 2 = v 2 / 5 4 v 1 + v 2 / 5 = 24 v 1 + v 2 = 25 4 v 2 - v 2 / 5 = 76 19 v 2 / 5 = 76 = > v 2 = 20 = > v 1 = 5 = > p 1 = 20 answer - d
Answer: d
Problem: a volume of 10940 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812 , b ) 8231 , c ) 2734 , d ) 2735 , e ) 4254
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10940 l can be kept in ( 10940 / 4 ) hemispheres ans . 2735 answer : d"
Answer: d
Problem: a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 80 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 87 , b ) 279 , c ) 80 , d ) 278 , e ) 379
Rationale: "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 80 - 40 ) = 1 hours so , the two trains meet at 11 a . m . the two trains meet 1 * 80 = 80 km away from mumbai . answer : c"
Answer: c
Problem: 0 , 1 , 4 , 15 , 64 , ____
Options: a ) 225 , b ) 325 , c ) 125 , d ) 145 , e ) none
Rationale: "0 , 1,4 , 15,64 . . . . . 0 * 1 + 1 = 1 1 * 2 + 2 = 4 4 * 3 + 3 = 15 15 * 4 + 4 = 64 64 * 5 + 5 = 325 answer : b"
Answer: b
Problem: virginia , adrienne , and dennis have taught history for a combined total of 93 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 32 , c ) 40 , d ) 41 , e ) 44
Rationale: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 93 = > 3 d = 93 + 27 = 120 = > d = 40 answer c"
Answer: c
Problem: if the simple interest on a certain sum of money for 5 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 4 % , b ) 7 % , c ) 6 % , d ) 4 % , e ) 3 %
Rationale: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 5 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 5 ) = 20 / 5 = 4 % answer : option d"
Answer: d
Problem: how many six - digit numbers that do not contain the digits 5 or 8 are there ?
Options: a ) 483224 , b ) 156444 , c ) 229376 , d ) 816416 , e ) 316544
Rationale: "we can have 7 digits ( 1 , 2,3 , 4,6 , 7,9 ) for the first place ( hundred thousand ' s place ) . and similarly 8 digits for ten thousands , thousands , hundred ' s , tenth ' s and unit digit . ( 0,1 , 2,3 , 4,6 , 7,9 ) so in total 7 * 8 * 8 * 8 * 8 * 8 = 229376 hence c"
Answer: c
Problem: simplify : 200 x 200 - 150 x 150
Options: a ) 761200 , b ) 761400 , c ) 761800 , d ) 17500 , e ) none of them
Rationale: "( 200 ) ^ 2 - ( 150 ) ^ 2 = ( 200 + 150 ) ( 200 - 150 ) = 350 x 50 = 17500 . answer is d"
Answer: d
Problem: a batsman in his 17 th innings makes a score of 80 and their by increasing his average by 3 . what is his average after the 17 thinnings ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: "16 x + 80 = 17 ( x + 3 ) x = 27 + 3 = 30 answer : c"
Answer: c
Problem: a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 10 % so that the customer could not buy the required amount of the product . the customer managed to buy only 90 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?
Options: a ) 5 % , b ) 4 % , c ) 3 % , d ) 2 % , e ) 1 %
Rationale: "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.9 ( 1.1 x ) = 0.99 x . the difference is 1 % . the answer is e ."
Answer: e
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 30 million in sales of and then $ 9 million in royalties on the next $ 120 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 30 million in sales to the next $ 120 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 25 % , d ) 52 % , e ) 56 %
Rationale: "( 9 / 120 ) / ( 3 / 30 ) = 3 / 4 = 75 % it means that 9 / 120 represents only 75 % . therefore a decrease of 25 % . answer c"
Answer: c
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 126 km / hr ?
Options: a ) 2.5 , b ) 2.9 , c ) 2.4 , d ) 2.85 , e ) 2.1
Rationale: "speed = 126 * 5 / 18 = 35 m / sec time taken = 100 / 35 = 2.85 sec . answer : d"
Answer: d
Problem: youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 8 minutes more to walk to work than to ride his bike to work , then x equals ?
Options: a ) 4 , b ) 7 , c ) 12 , d ) 15 , e ) 20
Rationale: "please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 480 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 480 - - - - > 40 x = 480 - - > x = 12 . option c"
Answer: c
Problem: there are two names given johnson and jones . if one letter is picked from both simultaneously at random , then find the probability that the letter is same ?
Options: a ) 24 / 35 , b ) 17 / 35 , c ) 8 / 25 , d ) 6 / 35 , e ) 1 / 25
Rationale: this question can also be solved by using ' brute force ' - you just have to ' map out ' the possibilities . the namejohnsonhas 7 letters and the namejoneshas 5 letters , so there are ( 7 ) ( 5 ) = 35 possible pairings of letters that can occur . of those 35 , the pairings that include the same letter both times are : j and j 1 st o and o 1 st n and n s and s 2 nd o and o 2 nd n and n total : 6 so the probability that the two randomly selected letters will match is 6 / 35 . d
Answer: d
Problem: the expression ( 11.98 × 11.98 + 11.98 × x + 0.02 × 0.02 ) will be a perfect square for x equal to
Options: a ) 0.02 , b ) 0.2 , c ) 0.04 , d ) 0.4 , e ) 4
Rationale: "solution given expression = ( 11.98 ) 2 + ( 0.02 ) 2 + 11.98 × x . for the given express to be a perfect square , we must have 11.98 × x = 2 × 11.98 × 0.02 or x = 0.04 . answer c"
Answer: c
Problem: when a merchant imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 101.50 , what was the total value of the item ?
Options: a ) $ 1,850 , b ) $ 2,450 , c ) $ 2,750 , d ) $ 3,150 , e ) $ 3,450
Rationale: "let x be the value in excess of $ 1,000 . 0.07 x = 101.5 x = $ 1,450 the total value was $ 1,450 + $ 1,000 = $ 2,450 . the answer is b ."
Answer: b
Problem: a and b go around a circular track of length 300 m on a cycle at speeds of 18 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 198 sec , c ) 60 sec , d ) 665 sec , e ) 276 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 300 / ( 90 * 5 / 18 ) , 300 / ( 54 * 5 / 18 ) } = lcm ( 12 , 20 ) = 60 sec . answer : c"
Answer: c
Problem: the unit digit in the product 1457 * 7863 * 4575 * 9719 is ?
Options: a ) 5 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "unit digit in the given product = unit digit in 7 * 3 * 5 * 9 = 5 answer is a"
Answer: a
Problem: tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 72000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 10000 , c ) 25000 , d ) 34000 , e ) 40000
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 72000 = 40000 e"
Answer: e
Problem: the average height of 35 boys in a class was calculated as 180 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) .
Options: a ) 178.89 cm , b ) 178.29 cm , c ) 178.79 cm , d ) 177.89 cm , e ) 178.69 cm
Rationale: calculated average height of 35 boys = 180 cm . wrong total height of 35 boys = 180 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm = 180 * 35 cm - 166 cm + 106 cm / 35 = 180 cm - 60 / 35 cm = 180 cm - 1.71 cm = 178.29 cm . answer : b
Answer: b
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 70 sq . cm . find the length of the rectangle .
Options: a ) 12 cm , b ) 14 cm , c ) 16 cm , d ) 18 cm , e ) 20 cm
Rationale: "explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 70 = > 5 x - 25 = 70 = > x = 18 . length of the rectangle = 18 cm . answer : option d"
Answer: d
Problem: a + 2 b = 6 , ab = 4 2 / a + 1 / b = ?
Options: a ) 3 / 2 , b ) 5 / 2 , c ) 7 / 2 , d ) 9 / 2 , e ) 11 / 2
Rationale: 2 / 2 + 1 / 2 = 1 + 1 / 2 = 3 / 2 answer : a
Answer: a
Problem: a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 20 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 15 % , b ) 18 % , c ) 20 % , d ) 25 % , e ) 26 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.2 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 20 % income the savings increased by 100 % . or s = . 2 i or s = 20 % of income c is the answer"
Answer: c
Problem: a fair 2 sided coin is flipped 6 times . what is the probability that tails will be the result at least twice , but not more than 5 times ?
Options: a ) 5 / 8 , b ) 3 / 4 , c ) 7 / 8 , d ) 57 / 64 , e ) 15 / 16
Rationale: it would be easier to calculate the probability of opposite event and subtract it from 1 . opposite event : 0 tail , 1 tail , 6 tails . probability of getting no tails : 1 / 2 ^ 6 = 1 / 64 probability of getting 1 tail : 6 c 1 ∗ 1 / 2 ^ 6 = 6 / 64 , we must multiply by 6 c 1 or by 6 as tail can occur for any flip from 6 , hence in 6 ways ; probability of getting 6 tails : 1 / 2 ^ 6 = 1 / 6 ^ 4 p = 1 − ( 1 / 64 + 6 / 64 + 1 / 64 ) = 56 / 64 = 7 / 8 answer : c .
Answer: c
Problem: a , b and c started a business with a total investment of rs . 90000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find b ' s share .
Options: a ) rs . 2592 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 90000 = > x + ( x - 3000 ) + ( x + 3000 ) = 90000 = > 3 x = 90000 = > x = 30000 hence , a ' s investment = rs . 33000 b ' s investment = rs . 27000 c ' s investment = rs . 30000 ratio of the capitals of a , b and c = 33000 : 27000 : 30000 = 11 : 9 : 10 a ' s share = rs . [ ( 9 / 30 ) ã — 8640 ] = rs . 2592 answer : option a"
Answer: a
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 4 litres a minute . when the tank is full , the inlet is opened and due to the leak the tank is empty in 8 hours . the capacity of the tank ( in litres ) is
Options: a ) 5780 litres , b ) 5770 litres , c ) 5760 litres , d ) 5750 litres , e ) 5740 litres
Rationale: "explanation : work done by the inlet in 1 hour = 1 / 6 − 1 / 8 = 1 / 24 work done by inlet in 1 min = 1 / 24 ∗ 1 / 60 = 1 / 1440 = > volume of 1 / 1440 part = 4 liters volume of whole = ( 1440 * 4 ) litres = 5760 litres . option c"
Answer: c
Problem: how many digits will be there to the right of the decimal point in the product of 95 and . 02554 ?
Options: a ) 6 , b ) 7 , c ) 4 , d ) 5 , e ) 8
Rationale: product of 95 and . 02554 is 2.4263 . therefore number of digits to right of decimal point is 4 answer is c .
Answer: c
Problem: the average of first 9 odd numbers is ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "sum of 9 odd no . = 90 average = 81 / 9 = 9 answer : e"
Answer: e
Problem: dacid obtained 86 , 85 , 92 , 87 and 95 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 67 , b ) 26 , c ) 89 , d ) 26 , e ) 75
Rationale: "average = ( 86 + 85 + 92 + 87 + 95 ) / 5 = 445 / 5 = 89 . answer : c"
Answer: c
Problem: david and andrew can finish the work 12 days if they work together . they worked together for 8 days and then andrew left . david finished the remaining work in another 8 days . in how many days david alone can finish the work ?
Options: a ) 30 days , b ) 60 days , c ) 70 days , d ) 80 days , e ) 24 days
Rationale: amount of work done by david and andrew in 1 day = 1 / 12 amount of work done by david and andrew in 8 days = 8 ã — ( 1 / 12 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 david completes 1 / 3 work in 8 days amount of work david can do in 1 day = ( 1 / 3 ) / 8 = 1 / 24 = > david can complete the work in 24 days answer : e
Answer: e
Problem: a firm is comprised of partners and associates in a ratio of 2 : 63 . if 45 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 9 of the increase in 45 associates . the ratio changed from 18 : 567 to 18 : 612 . thus the number of partners is 18 . the answer is d ."
Answer: d
Problem: a , b and c started a partnership business by investing rs . 27000 , rs . 72000 , rs . 81000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 80000 , d ) 90000 , e ) 50000
Rationale: a : b : c = 27000 : 72000 : 81000 = 3 : 8 : 9 let total profit = p then p × 9 / 20 = 36000 p = ( 36000 × 20 ) / 9 = 80000 answer is c .
Answer: c
Problem: a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 30,000 , c receives :
Options: a ) s . 7,000 , b ) s . 7,200 , c ) s . 7,400 , d ) s . 7,700 , e ) s . 7,800
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 30000 x 12 / 50 ) = rs . 7,200 . b"
Answer: b
Problem: a pair of articles was bought for $ 50 at a discount of 20 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 31.25 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 80 % of x = 25 x = 25 * 100 / 80 = $ 31.25 answer is b"
Answer: b
Problem: what percentage of numbers from 1 to 60 have 1 or 9 in the unit ' s digit ?
Options: a ) 12 , b ) 14.11 , c ) 18.33 , d ) 20 , e ) 21
Rationale: "clearly , the numbers which have 1 or 9 in the unit ' s digit , have squares that end in the digit 1 . such numbers from 1 to 60 are 1 , 9 , 11 , 19 , 21 , 29 , 31 , 39 , 41 , 49 , 51 , 59 number of such number = 11 answer : c"
Answer: c
Problem: shop offered 32 % offer for every shirt , smith bought a shirt at rs . 650 . and what was the shop ' s original selling price ?
Options: a ) 955 , b ) 550 , c ) 600 , d ) 700 , e ) 750
Rationale: "sp * ( 68 / 100 ) = 650 sp = 9.55 * 100 = > cp = 955 answer : a"
Answer: a
Problem: each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 96 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 25 , c ) 92 , d ) 96 , e ) 98
Rationale: out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 96 % water and 4 % of non - water , so now 1 pound of non - water composes 4 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.04 = 25 pounds . answer : b .
Answer: b
Problem: a certain elevator has a safe weight limit of 2,500 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 150 pounds and the average weight of the others being 160 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 16
Rationale: "lets assume there are 2 x people . half of them have average weight of 150 and other half has 160 . maximum weight is = 2500 so 150 * x + 160 * x = 2500 = > 310 x = 2500 = > x is approximately equal to 8 . so total people is 2 * 8 = 16 answer e ."
Answer: e
Problem: two trains start from p and q respectively and travel towards each other at a speed of 50 km / hr and 40 km / hr respectively . by the time they meet , the first train has traveled 100 km more than the second . the distance between p and q is ?
Options: a ) 900 km , b ) 300 km , c ) 700 km , d ) 800 km , e ) 100 km
Rationale: a 900 km at the time of meeting , let the distance traveled by the second train be x km . then , distance covered by the first train is ( x + 100 ) km . x / 40 = ( x + 100 ) / 50 50 x = 40 x + 4000 = > x = 400 so , distance between p and q = ( x + x + 100 ) km = 900 km .
Answer: a
Problem: if grapes are 92 % water and raisins are 20 % water , then how many kilograms did a quantity of raisins , which currently weighs 5 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 50 , b ) 54 , c ) 55 , d ) 56 , e ) 60
Rationale: "let x be the original weight . the weight of the grape pulp was 0.08 x . since the grape pulp is 80 % of the raisins , 0.08 x = 0.8 ( 5 ) . then x = 50 kg . the answer is a ."
Answer: a
Problem: a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 70 , how many questions did student a answer correctly ?
Options: a ) 55 , b ) 90 , c ) 73 , d ) 82 , e ) 91
Rationale: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 70 ( subtracting twice of incorrect from correct ) 3 x = 270 x = 90 answer : b"
Answer: b
Problem: there are 8 executives , including the ceo and cfo , that are asked to form a small team of 4 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
Rationale: "the total number of ways to form a team of 4 is 8 c 4 = 70 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 6 c 2 = 15 . the number of ways to form an acceptable team is 70 - 15 = 55 . the answer is b ."
Answer: b
Problem: redo ’ s manufacturing costs for sets of horseshoes include a $ 10,000 initial outlay , and $ 20 per set . they can sell the sets $ 50 . if profit is revenue from sales minus manufacturing costs , and the company producessells 500 sets of horseshoes , what was their profit ?
Options: a ) $ 4500 , b ) $ 3500 , c ) $ 5500 , d ) $ 5000 , e ) $ 6300
Rationale: total manufacturing cost = 10000 + 500 * 20 = 20000 total selling cost = 500 * 50 = 25000 profit = 25000 - 20000 = 5000 answer : d
Answer: d
Problem: a 300 meter long train crosses a pla ƞ orm in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the pla ƞ orm .
Options: a ) 310 meter , b ) 335 meter , c ) 345 meter , d ) 350 meter , e ) none of these
Rationale: explanation : speed = distance / ɵ me = 300 / 18 = 50 / 3 m / sec let the length of the pla ƞ orm be x meters then distance = speed ∗ timex + 300 = 503 ∗ 39 = > 3 ( x + 300 ) = 1950 = > x = 350 meters answer : d
Answer: d
Problem: what is the smallest positive integer x such that ( x + 1 ) ^ 2 is divisible by 28 , 98 , 242 , and 308 ?
Options: a ) 153 , b ) 308 , c ) 121 , d ) 96 , e ) 511
Rationale: "28 = 2 * 2 * 7 98 = 2 * 7 * 7 242 = 2 * 11 * 11 308 = 2 * 2 * 7 * 11 so ( x + 1 ) ^ 2 = 2 * 2 * 7 * 7 * 11 * 11 , which means ( x + 1 ) = 2 * 7 * 11 = 154 , which means x = 153 , which is option a"
Answer: a
Problem: 18 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 190 , b ) 153 , c ) 210 , d ) 220 , e ) 230
Rationale: "1 st person will shake hand with 17 people 2 nd person will shake hand with 16 people 3 rd person will shake hand with 15 people . . . . . . total no . of handshakes = 17 + . . . + 3 + 2 + 1 = 17 * ( 17 + 1 ) / 2 = 153 or , if there are n persons then no . of shakehands = nc 2 = 18 c 2 = 153 answer : b"
Answer: b
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 700 grams per kg , what is his percent ?
Options: a ) 42.8 % , b ) 25 % , c ) 55 % , d ) 28 % , e ) 55 %
Rationale: "700 - - - 300 100 - - - ? = > 42.8 % answer : a"
Answer: a
Problem: ? x 120 = 173 x 240
Options: a ) 545 , b ) 685 , c ) 865 , d ) 495 , e ) 346
Rationale: let y x 120 = 173 x 240 then y = ( 173 x 240 ) / 120 = 346 . answer : e
Answer: e
Problem: in a soap company a soap is manufactured with 11 parts . for making one soap you will get 1 part as scrap . at the end of the day you have 251 such scraps . from that how many soaps can be manufactured ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: using 251 scraps we make = 22 soaps . ( i . e . , 11 * 22 = 242 ) remaining scraps = 9 . again , 22 soaps produce = 22 scraps . so , now we have 22 + 9 = 31 scraps remaining . using 31 scraps we make 2 soaps and 2 scraps remaining . ( i . e . , 2 * 11 = 22 ) again , that 2 soaps produce = 2 scraps . and already we have 9 scraps . total 9 + 2 = 11 sscraps . by using 11 scraps , we make 1 soap . so , total = 22 + 2 + 1 = 25 soaps we produce . answer : b
Answer: b
Problem: a sum of rs . 2665 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1888 , b ) 1640 , c ) 2768 , d ) 2976 , e ) 2691
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2665 - x ) * 3 * 5 ) / 100 24 x / 100 = 39975 / 100 - 15 x / 100 39 x = 39975 = > x = 1025 second sum = 2665 – 1025 = 1640 answer : b"
Answer: b
Problem: in a survey of parents , exactly 3 / 4 of the mothers and 9 / 10 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 27 % , b ) 21 % , c ) 19 % , d ) 18 % , e ) 16 %
Rationale: "let the total number of parents = 100 number of women = 40 number of men = 60 number of mothers who held full time jobs = 3 / 4 * 40 = 30 number of fathers who held full time jobs = 9 / 10 * 60 = 54 total number of parents who held full time jobs = 84 total number of parents who did not hold jobs = 100 - 84 = 16 alternatively , percentage of women = 40 % percentage of women who did not hold full time jobs = ( 1 - 3 / 4 ) * 100 % = 25 % of all mothers did not have full time jobs 25 % of 40 % - - > 10 % of the total parents percentage of men = 60 % percentage of men who held full time jobs = ( 1 - 9 / 10 ) * 100 % = 10 % of all fathers did not have full time jobs 10 % of 60 % - - > 6 % of the total parents therefore , percentage of parents who did not hold full time jobs = 10 + 6 = 16 % answer e - 16 %"
Answer: e
Problem: a garrison of 1850 men has provisions for 28 days . at the end of 12 days , a reinforcement arrives , and it is now found that the provisions will last only for 10 days more . what is the reinforcement ?
Options: a ) 1850 , b ) 2960 , c ) 3000 , d ) 1110 , e ) 1712
Rationale: "1850 - - - - 28 1850 - - - - 16 x - - - - - 10 x * 10 = 1850 * 16 x = 2960 1850 - - - - - - - 1110 answer : d"
Answer: d
Problem: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 240 . find the sum ?
Options: a ) 7000 , b ) 7029 , c ) 2778 , d ) 2800 , e ) 2000
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 240 = > 36 x / 100 - 24 x / 100 = 240 = > 12 x / 100 = 240 = > x = 2000 . answer : e"
Answer: e
Problem: a train 150 m long is running at a speed of 62 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 10 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
Rationale: "answer : b . speed of the train relative to man = ( 62 - 8 ) kmph = ( 54 * 5 / 18 ) m / sec = 15 m / sec time taken by the train to cross the man = time taken by it to cover 150 m at 15 m / sec = 150 * 1 / 15 sec = 10 sec"
Answer: b
Problem: the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 588 sq meters , then what is the width ( in meters ) of the rectangular plot ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "area = l * w = 3 w ^ 2 = 588 w ^ 2 = 196 w = 14 the answer is a ."
Answer: a
Problem: the radius of a cone is 10 m , height 21 m . the volume of the cone is :
Options: a ) 2200
b ) 1100
c ) 5500
d ) 3300
e ) 1050
Rationale: 1 / 3 π rh = 1 / 3 × 22 / 7 × 100 × 21 = 2200 m ( power 3 ) answer is a .
Answer: a
Problem: jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 5 hours . how long would it take taimour to paint the fence alone ?
Options: a ) 6 hours , b ) 8 hours , c ) 15 hours , d ) 24 hours , e ) 32 hours
Rationale: "i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 5 = > 1 / 15 working alone taimour can do the job in 1 = 1 / 15 * hours = > 15 answer c"
Answer: c
Problem: a group of boy scouts and girls scouts is going on a rafting trip . 45 % of the scouts arrived with signed permission slips . if 60 % of the scouts were boy scouts and 25 % of the boy scouts arrived with signed permission slips , then what percentage of the scouts were girl scouts who arrived with signed permission slips ?
Options: a ) 20 , b ) 21 , c ) 25 , d ) 28 , e ) 30
Rationale: "we do n ' t know how many scouts went on the trip , so let ' s assume 100 scouts went on the trip 60 % were boy scouts so 60 % of 100 = 60 were boy scouts 25 % of the boy scouts brought their permission slips signed , so . 25 * 60 = 15 boy scouts had signed slips 60 - 15 = 45 boy scouts did not 45 % of all the scouts had signed slips , so . 45 * 100 = 45 in total had signed slips thus 45 - 15 = 30 girl scouts had signed slips thus the percentage of scouts who were girl scouts arriving with signed permission slips is 30 / 100 = . 30 = 30 % e"
Answer: e
Problem: two dice are thrown simultaneously . what is the probability of getting two numbers whose product is even ?
Options: a ) 1 / 2 , b ) 3 / 8 , c ) 3 / 4 , d ) 5 / 16 , e ) 9 / 16
Rationale: "in a simultaneous throw of two dice , we have n ( s ) = ( 6 x 6 ) = 36 . then , e = { ( 1 , 2 ) , ( 1 , 4 ) , ( 1 , 6 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 2 , 6 ) , ( 3 , 2 ) , ( 3 , 4 ) , ( 3 , 6 ) , ( 4 , 1 ) , ( 4 , 2 ) , ( 4 , 3 ) , ( 4 , 4 ) , ( 4 , 5 ) , ( 4 , 6 ) , ( 5 , 2 ) , ( 5 , 4 ) , ( 5 , 6 ) , ( 6 , 1 ) , ( 6 , 2 ) , ( 6 , 3 ) , ( 6 , 4 ) , ( 6 , 5 ) , ( 6 , 6 ) } n ( e ) = 27 . p ( e ) = n ( e ) / n ( s ) = 27 / 36 = 3 / 4 . answer : c ."
Answer: c
Problem: when sold at a 40 % discount , a sweater nets the merchant a 20 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 80 % , e ) 100 %
Rationale: "et the marked up price = 100 . . selling price = 100 - 40 % of 100 = 60 . . profit = 20 % . . therefore the wholesale purchase cost = x . . . . 1.2 x = 60 or x = 50 . . . marked price was 100 so 50 over 50 . . . so answer is 100 % . . answer : e"
Answer: e
Problem: a man can row upstream at 15 kmph and downstream at 25 kmph , and then find the speed of the man in still water ?
Options: a ) 27 , b ) 29 , c ) 30 , d ) 20 , e ) 24
Rationale: "us = 15 ds = 25 m = ( 15 + 25 ) / 2 = 20 answer : d"
Answer: d
Problem: workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.60 lacs . how many workers were they ?
Options: a ) 220 , b ) 230 , c ) 1200 , d ) 560 , e ) 590
Rationale: "n * 50 = ( 360000 - 300000 ) = 60000 n = 60000 / 50 = 1200 c"
Answer: c
Problem: evaluate : 983 x 207 - 983 x 107
Options: a ) 93700 , b ) 97300 , c ) 93800 , d ) 98300 , e ) none of them
Rationale: "983 x 207 - 983 x 107 = 983 x ( 207 - 107 ) = 983 x 100 = 98300 . answer is d ."
Answer: d
Problem: find value of x : 3 x ^ 2 + 5 x + 2 = 0
Options: a ) - 1 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "a = 3 , b = 5 , c = 2 x 1,2 = ( - 5 ± √ ( 52 - 4 × 3 × 2 ) ) / ( 2 × 3 ) = ( - 5 ± √ ( 25 - 24 ) ) / 6 = ( - 5 ± 1 ) / 6 x 1 = ( - 5 + 1 ) / 6 = - 4 / 6 = - 2 / 3 x 2 = ( - 5 - 1 ) / 6 = - 6 / 6 = - 1 a"
Answer: a
Problem: the probability that a computer company will get a computer hardware contract is 3 / 4 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 4 / 5 , what is the probability that it will get both the contracts ?
Options: a ) 4 / 11 , b ) 5 / 12 , c ) 6 / 17 , d ) 7 / 20 , e ) 11 / 30
Rationale: "let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 3 / 4 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 4 / 5 = ( 3 / 4 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 7 / 20 . hence , the required probability is 7 / 20 . the answer is d ."
Answer: d
Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exectly twice in 3 consecutive flips ?
Options: a ) 0.375 , b ) 0.25 , c ) 0.325 , d ) 0.5 , e ) 0.666
Rationale: "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 th thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : a"
Answer: a
Problem: if the average ( arithmetic mean ) of 10 consecutive odd integers is 154 , then the least of these integers is
Options: a ) a ) 51 , b ) b ) 58 , c ) c ) 145 , d ) d ) 190 , e ) e ) 210
Rationale: "a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 154 . there are 10 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 5 th and 6 th numbers in the set ) . this means that numbers 5 and 6 in this set are 153 and 155 . because we know that number 5 is 153 , we know that the smallest number is 4 odd numbers below this , which means that it is 4 * 2 = 8 below this ( every odd number is every other number ) . therefore 153 - 8 = 145 , answer choice c"
Answer: c
Problem: the average weight of a class is x pounds . when a new student weighing 100 pounds joins the class , the average decreases by 1 pound . in a few months the student ’ s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds . none of the other students ’ weights changed . what is the value of x ?
Options: a ) 85 , b ) 86 , c ) 88 , d ) 90 , e ) 92
Rationale: "when the student weighs 80 pounds the average weight is x - 1 pounds ; when the student weighs 110 pounds the average weight is x + 4 pounds . so , the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of ( x + 4 ) - ( x - 1 ) = 5 pounds , which means that there are 30 / 5 = 6 students ( including the new one ) . so , initially there were 5 student . total weight = 5 x + 80 = 6 ( x - 1 ) - - > x = 92 pounds . answer : e ."
Answer: e
Problem: each of 3 investments has a 20 % of becoming worthless within a year of purchase , independently of what happens to the other two investments . if simone invests an equal sum v in each of these 3 investments on january 1 , the approximate chance that by the end of the year , she loses no more than 1 / 3 of her original investment is
Options: a ) 90 % , b ) 80 % , c ) 70 % , d ) 60 % , e ) 40 %
Rationale: the problem asks for the approximate chance that no more than 1 / 3 of the original investment is lost . we can apply the “ 1 – x ” technique : what ’ s the chance that more than 1 / 3 of the original investment is lost ? there are two outcomes we have to separately measure : ( a ) all 3 investments become worthless . ( b ) 2 of the 3 investments become worthless , while 1 doesn ’ t . outcome ( a ) : the probability is ( 0.2 ) ( 0.2 ) ( 0.2 ) = 0.008 , or a little less than 1 % . outcome ( b ) : call the investments x , y , and z . the probability that x retains value , while y and z become worthless , is ( 0.8 ) ( 0.2 ) ( 0.2 ) = 0.032 . now , we have to do the same thing for the specific scenarios in which y retains value ( while x and z don ’ t ) and in which z retains value ( while x and y don ’ t ) . each of those scenarios results in the same math : 0.032 . thus , we can simply multiply 0.032 by 3 to get 0.096 , or a little less than 10 % . the sum of these two probabilities is 0.008 + 0.096 = 0.104 , or a little more than 10 % . finally , subtracting from 100 % and rounding , we find that the probability we were looking for is approximately 90 % . the correct answer is a . this problem illustrates the power of diversification in financial investments . all else being equal , it ’ s less risky to hold a third of your money in three uncorrelated ( independent ) but otherwise equivalent investments than to put all your eggs in one of the baskets . that said , be wary of historical correlations ! housing price changes in different us cities were not so correlated — and then they became highly correlated during the recent housing crisis ( they all fell together ) , fatally undermining spreadsheet models that assumed that these price changes were independent .
Answer: a
Problem: a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 75000 rs , what is the value of buzness ?
Options: a ) 150000 , b ) 160000 , c ) 170000 , d ) 190000 , e ) 250000
Rationale: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 75000 - > x = 150000 answer : a"
Answer: a
Problem: on a certain day , joey , the ice - cream seller sold his ice creams to 4 different kids in a manner that each of the kids purchased half of the remaining ice creams and half ice - cream more . if we tell you that the fourth kid bought just a single ice cream , can you find out how many ice creams were sold by joey that day ?
Options: a ) 15 , b ) 20 , c ) 22 , d ) 12 , e ) 8
Rationale: a joey sold 15 ice creams that day . the fourth kid bought a single ice cream . therefore , we have the following equation : total - ( total / 2 + 1 / 2 ) = 1 solving it , we get the total as 3 . let ' s work this method till we reach the first kid . the first kid bought 15 / 2 + 1 / 2 = 8 ( leaving 7 ) the second kid bought 7 / 2 + 1 / 2 = 4 ( leaving 3 ) the third kid bought 3 / 2 + 1 / 2 = 2 ( leaving 1 ) the fourth kid bought 1 / 2 + 1 / 2 = 1 adding all of them together , we get 8 + 4 + 2 + 1 = 15 .
Answer: a
Problem: the population of a town is 7900 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9750 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7900 ã — 100 / 90 ã — 100 / 90 = 9753 a )"
Answer: a
Problem: a 160 meter long train crosses a man standing on the platform in 12 sec . what is the speed of the train ?
Options: a ) 48 kmph , b ) 54 kmph , c ) 92 kmph , d ) 86 kmph , e ) 76 kmph
Rationale: "s = 160 / 12 * 18 / 5 = 48 kmph answer : a"
Answer: a
Problem: 9 log 9 ( 5 ) = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 5 ) = 5 correct answer d"
Answer: d
Problem: the unit digit in the product ( 124 * 812 * 816 * 467 ) is :
Options: a ) 2 , b ) 7 , c ) 6 , d ) 8 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 4 * 2 * 6 * 7 ) = 6 answer : c"
Answer: c
Problem: if a truck is traveling at a constant rate of 72 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )
Options: a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 48
Rationale: "speed = 72 km / hr = > 72,000 m / hr in one minute = > 72000 / 60 = 1200 meters in one sec = > 1200 / 60 = 20 meters time = total distance need to be covered / avg . speed = > 600 / 20 = 30 and hence the answer : c"
Answer: c
Problem: the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 40 less . what was the total cost cost of the vacation ?
Options: a ) $ 200 , b ) $ 300 , c ) $ 480 , d ) $ 500 , e ) $ 600
Rationale: "c for cost . p price per person . c = 3 * p c = 4 * p - 160 substituting the value of p from the first equation onto the second we get p = 160 . plugging in the value of p in the first equation , we get c = 480 . which leads us to answer choice c"
Answer: c
Problem: a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 150 pounds of the mixture ?
Options: a ) 107 , b ) 84 , c ) 40 , d ) 28 , e ) 20
Rationale: "almonds : walnuts = 5 : 2 total mixture has 7 parts in a 150 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 150 = 107 pounds answer ( a )"
Answer: a
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2340 , what will be c ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 520 , c ) $ 1080 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 2340 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 2340 will be 4 : 3 : 2 . hence , c ' s share will be 2 * 2340 / 9 = 520 . correct choice is ( b )"
Answer: b
Problem: in the coordinate plane , points ( x , 1 ) and ( 5 , y ) are on line k . if line k passes through the origin and has slope 1 / 5 , then what are the values of x and y respectively ?
Options: a ) 4 and 1 , b ) 1 and 5 , c ) 5 and 1 , d ) 3 and 5 , e ) 5 and 3
Rationale: "line k passes through the origin and has slope 1 / 5 means that its equation is y = 1 / 5 * x . thus : ( x , 1 ) = ( 5 , 1 ) and ( 5 , y ) = ( 5,1 ) - - > x = 5 and y = 1 answer : c"
Answer: c
Problem: one fourth of a solution that was 13 % salt 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 salt by weight ?
Options: a ) 25 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.13 + 25 * x = 100 * 0.16 - - > x = 0.25 . answer : a ."
Answer: a
Problem: if daily wages of a man is double to that of a woman , how many men should work for 25 days to earn rs . 14400 ? given that wages for 40 women for 30 days are rs . 21600 .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: explanation : wages of 1 woman for 1 day = 21600 / 40 × 30 wages of 1 man for 1 day = 21600 × 2 / 40 × 30 wages of 1 man for 25 days = 21600 × 2 × 25 / 40 × 30 number of men = 14400 / ( 21600 × 2 × 25 / 40 × 30 ) = 144 / ( 216 × 50 / 40 × 30 ) = 144 / 9 = 16 answer : option c
Answer: c
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 7 / 9
Rationale: "it has two vertices on sides , which do not make a diagonal but a side . . so remaining 3 vertices make diagonals . . . only the opposite vertex will make largest diagonal and other two smaller ones . . so prob = 2 / ( 2 + 1 ) = 2 / 3 answer : d"
Answer: d
Problem: what is the compound interest on rs : 30,000 for 4 months at the rate of 5 % per annum
Options: a ) 501.13 , b ) 502.13 , c ) 503.13 , d ) 504.13 , e ) 505.13
Rationale: it is monthly compound rate = 5 / 12 % per month 30000 * ( 1 + 5 / 1200 ) ^ 4 - 30000 = 503.13 answer : c
Answer: c
Problem: the speed of a car is 90 km in the first hour and 40 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 88 , d ) 65 , e ) 15
Rationale: "s = ( 90 + 40 ) / 2 = 65 kmph answer : d"
Answer: d
Problem: how many trailing zeroes does 53 ! + 54 ! have ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: 53 ! + 54 ! = 53 ! + 54 * 53 ! = 53 ! ( 1 + 54 ) = 53 ! * 55 number of trailing 0 s in 53 ! = number of 5 s in the expansion of 53 ! = 10 + 2 = 12 there is 1 more 5 in 55 . hence , total number of trailing 0 s = 12 + 1 = 13 answer ( b ) . in most cases , when we are adding multiple terms , all of which have trailing 0 s , the sum will have as many trailing 0 s as that in the lowest term . example : 20 + 2300 + 34210000 = 34212320 - > one 0 because lowest term 20 has one 0 . this case has an exception because of an additional 5 in 55 . answer is b
Answer: b
Problem: an empty fuel tank with a capacity of 208 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 82 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 208 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 208 - a gallons of fuel b is 0.16 ( 208 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 208 - a ) = 30 - - > a = 82 . answer : c ."
Answer: c
Problem: 5020 − ( 502 ÷ 100.4 ) = ?
Options: a ) 15 , b ) 20 , c ) 5015 , d ) 25 , e ) 35
Rationale: "explanation : = 5020 − ( 502 / 1004 × 10 ) = 5020 − 5 = 5015 option c"
Answer: c