regisss/math_qa huggingface dataset:
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 62,500 , how much profit did the business make ?
Options: a ) $ 100,000 , b ) $ 125,000 , c ) $ 150,000 , d ) $ 200,000 , e ) $ 250,000
Rationale: "majority owner + two partners = 0.25 * p + 2 * ( 0.25 ) * ( 0.75 ) * p = 0.25 * p + ( 0.5 ) * ( 0.75 ) * p = 0.25 * p + ( 0.375 ) * p = ( 0.625 ) * p this equals $ 62,500 . ( 0.625 ) * p = 62,500 - - - - - divide both sides by 625 ( 0.001 ) * p = 100 - - - - - - multiply by 1000 p = 100,000 answer = a"
Answer: a
Problem: when a random experiment is conducted , the probability that event a occurs is 1 / 5 . if the random experiment is conducted 4 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 16 / 625 , b ) 56 / 625 , c ) 96 / 625 , d ) 126 / 625 , e ) 156 / 625
Rationale: "one case is : 1 / 5 * 1 / 5 * 4 / 5 * 4 / 5 = 16 / 625 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 16 / 625 ) = 96 / 625 the answer is c ."
Answer: c
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.9 km respectively . the time taken by the slower train to cross the faster train in seconds is :
Options: a ) 28 sec , b ) 36 sec , c ) 48 sec , d ) 52 sec , e ) 56 sec
Rationale: "relative speed = ( 60 + 90 ) km / hr = 150 x 5 / 18 = 120 / 3 m / sec distance covered = ( 1.10 + 0.9 ) km = 2 km = 2000 m . required time = 2000 x 3 / 125 = 48 sec . answer : c ."
Answer: c
Problem: a 6 - liter solution is 30 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 1.8 , b ) 2.1 , c ) 2.4 , d ) 2.7 , e ) 3.0
Rationale: "let x be the amount of pure alcohol required . 0.3 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.8 x = 2.4 liters the answer is c ."
Answer: c
Problem: find the average of all the numbers between 17 and 32 which are divisible by 3 .
Options: a ) 15 , b ) 18 , c ) 20 , d ) 26 , e ) none
Rationale: "sol . average = ( 21 + 24 + 27 + 30 / 4 ) = 102 / 4 = 25.5 answer d"
Answer: d
Problem: a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 4 km / hr . find the time taken by the boat to go 72 km downstream ?
Options: a ) 2 hours , b ) 4 hours 12 minutes , c ) 4 hours , d ) 5 hours , e ) none
Rationale: "solution speed downstream = ( 13 + 4 ) km / hr = 17 km / hr . time taken to travel 72 km downstream = ( 72 / 17 ) hrs = 4 hrs 12 minutes . answer b"
Answer: b
Problem: if you add all the numbers on your mobile phone , what is the answer ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 100 , e ) 60
Rationale: 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 are in your mobile phone . therefore 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 answer is a
Answer: a
Problem: what is the sum of the integers from - 190 to 192 inclusive ?
Options: a ) 0 , b ) 5 , c ) 383 , d ) 875 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = 190 + 192 / 2 = 1 number of items ( n ) = b - a + 1 = 192 - ( - 190 ) + 1 = 192 + 191 = 383 . sum = average * n = 1 * 383 = 383 . answer is c"
Answer: c
Problem: if $ 650 is deposited into a savings account at an annual interest rate of 5 % that compounds monthly , what is the value of the investment after 7 years ?
Options: a ) $ 750.00 , b ) $ 823.50 , c ) $ 973.25 , d ) $ 921.75 , e ) $ 110.00
Rationale: using ci formula : a = p ( 1 + r / n ) ^ n * t a = 650 ( 1 + 5 / 7 ) ^ 5 * 7 a = 921.75 option : d
Answer: d
Problem: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 15 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 26 % , e ) 34 %
Rationale: since 15 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.85 = 0.22 ; { % of customers who sample candy } = 0.259 answer : d .
Answer: d
Problem: the jogging track in a sports complex is 561 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 5.28 min , c ) 4.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: clearly , the two will meet when they are 561 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 561 m apart , they take ( 100 / 825 * 561 / 1000 ) hrs = ( 561 / 8250 * 60 ) min = 4.08 min . answer : c
Answer: c
Problem: at a small company , 76 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?
Options: a ) 13 / 19 , b ) 1 / 3 , c ) 9 / 20 , d ) 7 / 10 , e ) 5 / 7
Rationale: "lets take total employees are 100 . given that , total women = 76 and total married = 60 . total men = 100 - 76 = 24 and single men = 2 / 3 * 24 = 16 . married men = total men - single men = 24 - 16 = 8 . married women = total married - married men = 60 - 8 = 52 . fraction of women are married = married women / total women = 52 / 76 = 13 / 19 . ans a"
Answer: a
Problem: a shopkeeper sells 20 % of his stock at 25 % profit ans sells the remaining at a loss of 5 % . he incurred an overall profit of rs . 400 . find the total worth of the stock ?
Options: a ) 25500 , b ) 25000 , c ) 40500 , d ) 20000 , e ) 40000
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 5 / 4 = 5 x / 20 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 152 x / 200 total sp = 50 x / 200 + 152 x / 200 = 202 x / 200 overall profit = 152 x / 200 - x = 2 x / 200 x / 50 = 400 = > x = 40000 answer : e"
Answer: e
Problem: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 340 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 13 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 385 million february sales last year = 340 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 385 million and the old value = 340 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 385 – 340 ) / 340 ] x 100 65 / 340 x 100 ≈ 13 % . the answer is e ."
Answer: e
Problem: each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 36 have long fur , 27 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?
Options: a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6
Rationale: "no of dogs = 45 long fur = 36 brown = 27 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 36 + 27 - both both = 26 answer a"
Answer: a
Problem: an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 10000 people who applied for the army and 98 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "step ( 1 ) 4000 accepted . step ( 2 ) another 40 % of 40000 = 1600 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 1600 = 800 step ( 4 ) 50 % of 800 = 400 step ( 5 ) 50 % of 400 = 200 . . . here we are done with total 5 steps 70 % of 200 = 140 and last step of accepting 70 % of 140 = 98 ( our target ) total 7 steps required . ans d"
Answer: d
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 55 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1980 km , c ) 2000 km , d ) 2500 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 55 = 30 x = 1980 km answer is b"
Answer: b
Problem: a certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 25 − 20 / 20 ∗ 100 = 25 answer : a ."
Answer: a
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 13 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 15 % , c ) 105 / 8 % , d ) 11 % , e ) 12 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 13 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 15 % ( option b ) answer : b"
Answer: b
Problem: the monthly rent of a shop of dimension 20 feet × 15 feet is rs . 3600 . what is the annual rent per square foot of the shop ?
Options: a ) 43 , b ) 144 , c ) 68 , d ) 87 , e ) 92
Rationale: "sol . monthly rent per square feet = 3600 / ( 20 * 15 ) = 12 & annual rent per square feet = 12 * 12 = 144 answer : b"
Answer: b
Problem: liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 40 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )
Options: a ) 50 mph , b ) 45 mph , c ) 48 mph , d ) 52 mph , e ) 60 mph
Rationale: let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 40 where s is the speed and 30 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 40 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 60 mph therefore answer is e
Answer: e
Problem: an article costing rs . 160 is sold at 20 % discount on a mark - up price . what is the selling price after discount ?
Options: a ) 106 , b ) 116 , c ) 128 , d ) 136 , e ) 146
Rationale: 160 * 80 / 100 = 128 answer : c
Answer: c
Problem: 75 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 160 , b ) 264 , c ) 360 , d ) 354 , e ) 400
Rationale: 75 x / 100 - x / 3 = 110 5 x / 12 = 110 x = 264 answer : b
Answer: b
Problem: there are 8 stores in town that had a total of 21 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 8 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "8 people visited 2 stores each for 16 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 21 - 16 - 3 = 2 , which is the maximum that one person could have visited . the answer is a ."
Answer: a
Problem: indu gave bindu rs . 2500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2500 = d ( 100 / 4 ) 2 d = 4 answer : d"
Answer: d
Problem: 7 people average age is 30 . youngest person age is 7 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 49 = 161 so average age would be 161 / 7 = 23 answer : a"
Answer: a
Problem: how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 35 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 20 , b ) 15 , c ) 40 , d ) 50 , e ) 25
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 35 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - salt avg ) / ( salt avg - salt 1 ) = ( 50 - 40 ) / ( 40 - 35 ) = 2 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 20 lbs . answer ( a )"
Answer: a
Problem: a factory that employs 1000 assembly line workers pays each of these workers $ 5 per hour for the first 40 hours worked during a week and 1 ½ times that rate for hours worked in excess of 40 . what was the total payroll for the assembly - line workers for a week in which 30 percent of them worked 10 hours , 50 percent worked 40 hours , and the rest worked 50 hours ?
Options: a ) $ 180,000 , b ) $ 185,000 , c ) $ 170,000 , d ) $ 200,000 , e ) $ 205,000
Rationale: 30 % of 1000 = 300 worked for 20 hours payment @ 5 / hr total payment = 300 * 10 * 5 = 15000 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 15000 + 100000 + 40000 + 15000 = 170000 hence , answer is c
Answer: c
Problem: along a yard 273 metres long , 14 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 18 , b ) 19 , c ) 10 , d ) 21 , e ) 12
Rationale: "explanation : 14 trees have 13 gaps between them , required distance ( 273 / 13 ) = 21 option d"
Answer: d
Problem: a sum of money deposited at c . i . amounts to rs . 2442 in 2 years and to rs . 2926 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 20 , c ) 28 , d ) 24 , e ) 82
Rationale: "explanation : 2420 - - - 484 100 - - - ? = > 20 % answer : option b"
Answer: b
Problem: a ratio between two numbers is 8 : 9 and their l . c . m . is 432 . the first number is
Options: a ) 60 , b ) 45 , c ) 50 , d ) 48 , e ) none
Rationale: sol . let the required numbers be 8 x and 9 x . then , their l . c . m . is 72 x . ∴ 72 x = 432 ⇔ x = 6 . hence , the first number is 48 . answer d
Answer: d
Problem: jim needs $ 1000 to buy a new flat - screen tv . since he has only $ 7 , he borrows the remaining balance from his sister mary . the loan will be repaid in 3 annual installments at an interest rate of 10 % , compounded annually . the formula for calculating the monthly payment p is p = ( l x c x r ) / ( c – 1 ) where l = amount of the loan , r = annual interest rate , and c = compounding factor = ( 1 + r ) ^ n where n = number of annual payments . how much does jim have to pay mary at the end of each of the next 3 years ( rounded to the nearest penny ) ?
Options: a ) $ 357.67 , b ) $ 375.85 , c ) $ 387.40 , d ) $ 399.30 , e ) $ 433.33
Rationale: l = 993 r = 0.1 c = 1.1 ^ 3 = 1.331 insert all of these in the formula and we get p = 993 * 1.331 * 0.1 / 0.331 in order to resolve above without a calc , we need to find the approx value of 0.1331 / 0.331 ~ 0.4 ~ ~ 993 * 0.4 ~ 397 answer d
Answer: d
Problem: there is a 35 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 35 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 10
Rationale: "only the prime numbers greater than 10 and less than 35 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , and 31 . the total is 7 . the answer is d ."
Answer: d
Problem: a circular well with a diameter of 2 metres , is dug to a depth of 14 metres . what is the volume of the earth dug out ?
Options: a ) 32 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none
Rationale: "sol . volume = π r 2 h = ( 22 / 7 x 1 x 1 x 14 ) m 3 = 44 m 3 . answer d"
Answer: d
Problem: a searchlight on top of the watchtower makes 4 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 5 / 6 , b ) 4 / 5 , c ) 3 / 4 , d ) 2 / 3 , e ) 1 / 2
Rationale: the searchlight completes one revolution every 15 seconds . the probability that the man ' s area will be lit up is 5 / 15 = 1 / 3 . the probability that he will stay in the dark is 1 - 1 / 3 = 2 / 3 the answer is d .
Answer: d
Problem: how many integers are between 7 and 120 / 9 , inclusive ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 9 , e ) 10
Rationale: "120 / 9 = 13 . xx we are not concerned about the exact value of 120 / 9 as we just need the integers . the different integers between 7 and 120 / 9 would be 7 , 8 , 9 , 10 , 11 , 12,13 total number of integers = 7 option c"
Answer: c
Problem: the two lines y = x and x = - 5 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 7.5 , b ) 10 , c ) 12.5 , d ) 15 , e ) 17.5
Rationale: "the point of intersection is ( - 5 , - 5 ) . the triangle has a base of length 5 and a height of 5 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 5 * 5 = 12.5 the answer is c ."
Answer: c
Problem: in a 100 - mile trip , the first 30 miles were completed at 60 mph . if the average speed for the whole trip was 40 mph , what was the average speed in the last 70 miles ?
Options: a ) 30 mph , b ) 32 mph , c ) 35 mph , d ) 37 mph , e ) 38 mph
Rationale: the time to complete the first 30 miles was ( 30 miles / 60 mph ) = ( 1 / 2 ) hours . the time to complete the whole trip was ( 100 miles / 40 mph ) = ( 5 / 2 ) hours . the time to complete the last 70 miles was ( 5 / 2 ) - ( 1 / 2 ) = ( 2 ) hours . the average speed in the last 70 miles was ( 70 miles / 2 hours ) = 35 mph . the answer is c .
Answer: c
Problem: diana took out a charge account at the general store and agreed to pay 6 % simple annual interest . if she charges $ 60 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 62.40 , b ) $ 62.80 , c ) $ 63.20 , d ) $ 63.60 , e ) $ 64.00
Rationale: "1.06 * $ 60 = $ 63.60 the answer is d ."
Answer: d
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 13000 , then the share of b is ?
Options: a ) 6000 , b ) 12000 , c ) 18000 , d ) 24009 , e ) 24002
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 13000 share of b = 6 / 13 ( 13000 ) = rs . 6000 answer : a"
Answer: a
Problem: if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 103 , what is the value of x ?
Options: a ) 95 , b ) 97 , c ) 101 , d ) 85 , e ) 87
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 103 x = 101 answer : c"
Answer: c
Problem: divide rs . 32000 in the ratio 1 : 7 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 4000 , 28000 , d ) 12000 , 20006 , e ) 12000 , 20001
Rationale: "1 / 8 * 32000 = 4000 7 / 8 * 32000 = 28000 answer : c"
Answer: c
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 10 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.1 * 80 90 x - 80 = 8 90 x = 88 x = 88 / 90 = 44 / 45 = 0.977 x is slightly under 0.977 = 0.98 answer : c"
Answer: c
Problem: a rectangle having length 140 cm and width 40 cm . if the length of the rectangle is increased by thirty percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 17.64 % , b ) 33.33 % , c ) 40 % , d ) 75 % , e ) none of these
Rationale: explanation : solution : ( 30 / ( 140 + 30 ) * 100 ) % = 17.64 % answer : a
Answer: a
Problem: which number can we add to 722425 to get a number exactly divisible by 456 ?
Options: a ) 312 , b ) 335 , c ) 347 , d ) 361 , e ) 383
Rationale: "722425 / 456 = 1584 with a remainder of 121 . we need to add 456 - 121 = 335 the answer is b ."
Answer: b
Problem: a man is walking at the rate of 8 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 2000 meters , e ) none of these
Rationale: explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 8 â ˆ — 5 / 18 = 20 / 9 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 20 / 9 â ˆ — 900 = 2000 meter option d
Answer: d
Problem: a certain company reported that the revenue on sales increased 15 % from 2000 to 2003 , and increased 30 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 13 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 115 and and in 2005 130 , so from 2003 to 2005 it increased by ( 130 - 115 ) / 115 = 15 / 115 = 13 % . answer : e ."
Answer: e
Problem: p and q invested in a business . the profit earned was divided in the ratio 2 : 3 . if p invested rs 40000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 40000 , d ) 20000 , e ) 60000
Rationale: let the amount invested by q = q 40000 : q = 2 : 3 ⇒ 40000 × 3 = 2 q ⇒ q = ( 40000 × 3 ) / 2 = 60000 answer is e .
Answer: e
Problem: in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 3 : 1 . in the subsequent n games , the ratio of the team ´ s wins to losses was 1 : 4 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: "m = 4 / 9 of total games n = 5 / 9 of total games wins = 3 / 4 * 4 / 9 + 1 / 5 * 5 / 9 = 3 / 9 + 1 / 9 = 4 / 9 losses = 1 - 4 / 9 = 5 / 9 the ratio of wins to losses is 4 : 5 . the answer is d ."
Answer: d
Problem: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 65 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950
Rationale: "0.1 x = 0.08 ( 2000 - x ) + 65 0.18 x = 225 x = 1250 then the amount invested at 8 % is $ 2000 - $ 1250 = $ 750 the answer is c ."
Answer: c
Problem: ramu bought an old car for rs . 36000 . he spent rs . 15000 on repairs and sold it for rs . 62900 . what is his profit percent ?
Options: a ) 16 % , b ) 17 % , c ) 18 % , d ) 58 % , e ) 23 %
Rationale: total cp = rs . 36000 + rs . 15000 = rs . 51000 and sp = rs . 62900 profit ( % ) = ( 62900 - 51000 ) / 51000 * 100 = 23 % answer : e
Answer: e
Problem: the sum of the ages of 4 children born at the intervals of 4 years each is 48 years . what is the age of the youngest child ?
Options: a ) 2 years , b ) 4 years , c ) 6 years , d ) 8 years , e ) 10 years
Rationale: "let the ages of the children be x , ( x + 4 ) , ( x + 4 ) and ( x + 12 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 48 4 x = 24 = > x = 6 . age of youngest child = x = 6 years . answer : c"
Answer: c
Problem: the two lines y = x and x = - 7 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length of a cube whose surface area is equal to 6 z ?
Options: a ) 16 , b ) 8 √ 2 , c ) 8 , d ) 7 / √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 7 , - 7 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 7 × 7 ) = 49 / 2 ; so z = 49 / 2 . the next step requires us to find the length of a side of a cube that has a face area equal to 49 / 2 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 49 / 2 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 49 / 2 . clearly s = √ 49 / 2 = 7 / √ 2 , oranswer choice ( d ) ."
Answer: d
Problem: find the smallest four - digit number which is a multiple of 112
Options: a ) 137 , b ) 112 , c ) 287 , d ) 121 , e ) 191
Rationale: "explanation : the smallest four digit number is 1000 . if 1000 is divided by 112 , the remainder is 104 . 112 - 104 = 8 , if 8 is added to 1000 , it will become the smallest four digit number and a multiple of 112 . answer : b"
Answer: b
Problem: a goods train runs at a speed of 72 kmph and crosses a 270 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 250 m , c ) 260 m , d ) 270 m , e ) 240 m
Rationale: "s = 270 + x / t 72 * 5 / 18 = 270 + x / 26 x = 250 answer : b"
Answer: b
Problem: alex takes a loan of $ 4,000 to buy a used truck at the rate of 6 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 680 , b ) 700 , c ) 240 , d ) 620 , e ) 260
Rationale: "from the details given in the problem principle = p = $ 4,000 and r = 6 % or 0.06 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 4,000 x 1 x 0.06 = 240.00 annual interest to be paid = $ 240 answer : c"
Answer: c
Problem: if 145 % of j is equal to 25 % of k , 160 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 40 % of m is equal to what percent of 200 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 35 , d ) 700 , e ) 3500
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 40 % of 350 , comes out to be 140 . . . . 200 % of 10 is 20 . . . . ( 140 * 100 ) / 20 = 700 . . . . ans : d"
Answer: d
Problem: ron cycles his way up on a hill side and back . he takes the exact same route both ways . on the trip out he cycles an average speed of 5 miles per hour . on the trip back , downhill cycling at an average speed of 100 miles per hour , he is quick to return back . what is his approximate average speed for the round trip in miles per hour ?
Options: a ) 8 , b ) 9.52 , c ) 10 , d ) 11.7 , e ) 20
Rationale: average speed = total distance / total time here distance to hill top and back is same as he takes the same route . d = 5 t 1 and d = 100 t 2 therefore , t 1 = d / 5 and t 2 = d / 100 t 1 + t 2 = 21 d / 100 therefore , average speed = 2 d / 21 d / 100 = 2 d * 100 / 21 d answer is 9.52 since , the options are far away we need not solve till the decimal points so correct answer is option b
Answer: b
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability q that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability q = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Problem: how many 3 digit positive integers q exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e .
Answer: e
Problem: a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the addition between the maximum and minimum possible values of ' a - b ' ?
Options: a ) 0 , b ) 12 , c ) 24 , d ) 26 , e ) 18
Rationale: "possible values of a and b can be 5,4 ; 4,5 and 1,20 ; 20,1 maximum possible value for a - b is 20 - 1 = 19 minimum possible value for a - b is 1 - 20 = - 19 19 - 19 = 0 ans is a"
Answer: a
Problem: alice , benjamin , and carol each try independently to win a carnival game . if their individual probabilities for success are 1 / 5 , 3 / 8 , and 2 / 7 , respectively , what is the probability that exactly two of the 3 players will win but one will lose ?
Options: a ) 3 / 140 , b ) 1 / 28 , c ) 3 / 56 , d ) 3 / 35 , e ) 7 / 40
Rationale: p = p ( a wins , b wins , c loses ) + p ( a wins , b loses , c wins ) + p ( a loses , b wins , c wins ) = 1 / 5 * 3 / 8 * 5 / 7 + 1 / 5 * 5 / 8 * 2 / 7 + 4 / 5 * 3 / 8 * 2 / 7 = 7 / 40 . answer : e .
Answer: e
Problem: a person takes 10 minutes more to cover a certain distance by decreasing his speed by 20 % . what is the time taken to cover the distance at his original speed ?
Options: a ) 50 minutes , b ) 20 minutes , c ) 40 minutes , d ) 60 minutes , e ) 80 minutes
Rationale: let the distance and original speed be d km and k kmph respectively . d / 0.8 k - d / k = 10 / 60 = > 5 d / 4 k - d / k = 1 / 6 = > ( 5 d - 4 d ) / 4 k = 1 / 6 = > d = 4 / 6 k = 2 / 3 k time taken to cover the distance at original speed = d / k = 2 / 3 hours = 40 minutes . answer : c
Answer: c
Problem: victor gets 92 % marks in examinations . if these are 184 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 200 , d ) 288 , e ) 271
Rationale: "let the maximum marks be m then 92 % of m = 184 ⇒ 92 / 100 × m = 184 ⇒ m = ( 184 × 100 ) / 92 ⇒ m = 18400 / 92 ⇒ m = 200 therefore , maximum marks in the examinations are 200 . answer : c"
Answer: c
Problem: by selling 8 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ?
Options: a ) 8 , b ) 9 , c ) 2 , d ) 6 , e ) 4
Rationale: "40 % - - - 8 160 % - - - ? 40 / 160 * 12 = 2 answer : c"
Answer: c
Problem: a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 3.5 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )
Options: a ) 5 , 500,000 , b ) 3 , 200,000 , c ) 55,000 , d ) 28,000 , e ) 280
Rationale: "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 3.5 gms in 400,000 cm ^ 3 , x = 3.5 * 400,000 = 1 , 400,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 1 , 400,000 + 1 , 800,000 = 3 , 200,000 answer : b"
Answer: b
Problem: for any integer k > 1 , the term “ length of an integer ” refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 × 2 × 2 × 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 1000 , what is the maximum possible sum of the length of x and the length of y ?
Options: a ) 5 , b ) 6 , c ) 15 , d ) 16 , e ) 18
Rationale: basically the length of an integer is the sum of the powers of its prime factors . for example the length of 24 is 4 because 24 = 2 ^ 3 * 3 ^ 1 - - > 3 + 1 = 4 . given : x + 3 y < 1,000 . now , to maximize the length of x or y ( to maximize the sum of the powers of their primes ) we should minimize their prime bases . minimum prime base is 2 : so if x = 2 ^ 9 = 512 then its length is 9 - - > 512 + 3 y < 1,000 - - > y < 162.7 - - > maximum length of y can be 7 as 2 ^ 7 = 128 - - > 9 + 7 = 16 . answer : d .
Answer: d
Problem: there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total t of the book ?
Options: a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018
Rationale: "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) t 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."
Answer: a
Problem: a jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 18 sec , c ) 36 sec , d ) 72 sec , e ) none
Rationale: category formulae examples directions : problems based on trains . 11 . a train 280 m long , running with a speed of 63 km / hr will pass a tree in a . 15 sec . b . 16 sec . c . 18 sec . d . 20 sec . solution speed = ( 63 x 5 / 18 ) m / sec = 35 / 2 msec time taken = ( 280 x 2 / 35 ) m / sec = 16 sec . 12 . a train running at the speed of 60 km / hr crosses a pole in 9 seconds . what is ihe length of the train ? a . 120 metres b . 180 metres c . 324 metres d . none of these solution 13 . a jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ? a . 3.6 sec b . 18 sec c . 36 sec d . 72 sec solution speed of train relative to jogger = ( 45 - 9 ) km / hr = 36 km / hr = ( 36 x 5 / 18 ) m / sec = 10 m / sec distance covered = ( 240 + 120 ) m = 360 m time taken = ( 360 / 10 ) sec = 36 sec . answer c
Answer: c
Problem: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 100 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 500 , e ) 840
Rationale: "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 100 geese survived the first year : 1 / 5 * ( total ) = 100 - - > ( total ) = 500 . answer : d ."
Answer: d
Problem: a shopkeeper sold an article for rs 2524.36 . approximately what was his profit percent if the cost price of the article was rs 2400
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "explanation : gain % = ( 125.36 * 100 / 2400 ) = 5.2 % = 5 % approx option b"
Answer: b
Problem: at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 30 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 28 , c ) 40 , d ) 68 , e ) 70
Rationale: "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 30 are males , so remaining 90 - 30 = 60 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 60 , 100 % = 60 * 100 / 60 = 100 . ans 40 % of 100 = 40 c"
Answer: c
Problem: how many multiples of 5 are there between 1 and 36 , exclusive ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "7 multiples of 5 between 1 and 36 exclusive . from 5 * 1 upto 5 * 7 , ( 1,2 , 3,4 , . . . , 7 ) . hence , 7 multiples ! correct option is d"
Answer: d
Problem: a cave is going to explode . a family is trapped inside that cave . the only way to get outside is a narrow tunnel . but the tunnel is weak and thus only two people can go at one time . also , everybody is afraid of going alone . the father takes one minute to go through till the end , the mother takes two , the son takes 4 and the daughter takes 5 . the cave and tunnel will explode in 12 minutes . can they make it to the other end in that time frame ? ps : keep in mind that when two people are moving , the total time taken will be as per the slower one .
Options: a ) 10 minutes , b ) 12 minutes , c ) 18 minutes , d ) 19 minutes , e ) 16 minutes
Rationale: b 12 minutes explanation : yes , surely they can all make it out of the cave . first , father and mother will go . time taken = 2 minutes . father comes back . time taken = 2 + 1 = 3 minutes . both children go . time taken = 3 + 5 = 8 minutes . mother comes back . time taken = 8 + 2 = 10 minutes . mother and father go . time taken = 10 + 2 = 12 minutes . thus in 12 minutes , all of them will be out of the cave through the tunnel .
Answer: b
Problem: a bag contains 10 balls numbered from 0 to 9 . the balls are such that the person picking a ball out of the bag is equally likely to pick anyone of them . a person picked a ball and replaced it in the bag after noting its number . he repeated this process 2 more times . what is the probability that the ball picked first is numbered higher than the ball picked second and the ball picked second is numbered higher than the ball picked third ?
Options: a ) 72 / 100 , b ) 3 / 25 , c ) 4 / 5 , d ) 1 / 6 , e ) 1 / 9
Rationale: explanation : let , the number of the ball picked first = a , second = b and third = c and these three numbers a , b and c are distinct . three distinct ball can be picked in ( 10 × 9 × 8 ) ways . the order of a , b and c can be as follows : - ( i ) a > b > c . ( ii ) a > c > b . ( iii ) b > c > a . ( iv ) b > a > c . ( v ) c > a > b . ( vi ) c > b > a . they will occur equal number of times . so , the number of ways in which ( a > b > c ) are : - = > 1 / 6 x 10 x 9 x 8 . = > 120 . hence , the required probability is : - = > 120 / ( 10 x 10 x 10 ) . = > 3 / 25 . answer : b
Answer: b
Problem: what sum of money will produce rs . 70 as simple interest in 3 years at 3 1 / 2 percent ?
Options: a ) 263 , b ) 500 , c ) 367 , d ) 368 , e ) 666.7
Rationale: "70 = ( p * 3 * 7 / 2 ) / 100 p = 666.7 answer : e"
Answer: e
Problem: a person x working alone can complete a work in 5 days . a person y completes the same amount of work in 20 days , and a person z when working alone can complete the same amount of work in 30 days . all 3 people work together for 2 days but then x and y leave . how many more days does z need to complete the work after x and y leave ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: the fraction of work completed in two days is 2 / 5 + 2 / 20 + 2 / 30 = 17 / 30 the fraction of work remaining is 1 - 17 / 30 = 13 / 30 the number of days required for z is 13 days . the answer is a .
Answer: a
Problem: a train 100 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 ) 46 , b ) 50 , c ) 40 , d ) 36 , e ) 41
Rationale: "speed of the train relative to man = 100 / 10 m / sec = 10 m / sec . = 10 x 18 / 5 km / hr = 36 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 36 = 41 km / hr . answer : e"
Answer: e
Problem: in what time will a train 200 meters long completely pass an electric pole , if it travels at a speed of 80 kmph .
Options: a ) 7 , b ) 9 , c ) 5 , d ) 10 , e ) 3
Rationale: sol . speed = [ 80 x 5 / 18 ] m / sec = 22.2 m / sec . time taken = ( 200 / 22.2 ) sec = 9 sec . answer b
Answer: b
Problem: a company organzied a help desk . there have been done 24 hrs work on software , 17 hrs on help user nd 40 % on other services . find the total no . of hrs have been worked on that day ?
Options: a ) 68 , b ) 69 , c ) 70 , d ) 67 , e ) 76
Rationale: let total no of hrs = x they have done 24 + 17 = 41 40 % of x is 40 / 100 = 2 / 5 x = 41 + 2 x / 5 x = 68.3 answer : a
Answer: a
Problem: the true discount on a bill of rs . 2360 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 425 , c ) rs . 412 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2360 td = rs . 360 pw = f - td = 2360 - 360 = rs . 2000 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2000 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2360 for unexpired time = 360 / 2000 × 2360 = 0.18 × 2160 = rs . 425 answer : option b"
Answer: b
Problem: a and b go around a circular track of length 600 m on a cycle at speeds of 18 kmph and 48 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 176 sec , c ) 360 sec , d ) 187 sec , e ) 189 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 { 600 / ( 18 * 5 / 18 ) , 600 / ( 48 * 5 / 18 ) } = 360 sec . answer : c"
Answer: c
Problem: o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 8.3 ) + e ( – 8.7 ) + o ( – 7.3 ) + e ( 6.6 ) is :
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "o ( 8.3 ) + e ( – 8.7 ) + o ( – 7.3 ) + e ( 6.6 ) = 9 + ( - 8 ) + ( - 9 ) + 6 = - 2 the answer is a ."
Answer: a
Problem: 15 litres of mixture contains 20 % alcohol and the rest water . if 2 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 23 % , c ) 18.3 % , d ) 17.64 % , e ) 21.23 %
Rationale: "alcohol in the 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 2 = 17 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 17 = 17.64 % answer is d"
Answer: d
Problem: two pipes p and q can fill a cistern in 10 and 15 minutes respectively . both are opened together , but at the end of 2 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "let x be the total time it takes for the cistern to fill . 2 / 10 + x / 15 = 1 x / 15 = 4 / 5 x = 12 after the first pipe is turned off , it takes 10 more minutes to fill the cistern . the answer is e ."
Answer: e
Problem: there are 16 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 750 , b ) 900 , c ) 1050 , d ) 1200 , e ) 1350
Rationale: the number of ways to choose two teams is 16 c 2 = 16 * 15 / 2 = 120 the total number of games in the season is 10 * 120 = 1200 . the answer is d .
Answer: d
Problem: in an examination , the percentage of students qualified to the number of students appeared from school a is 70 % . in school b , the number of students appeared is 20 % more than the students appeared from school a and the number of students qualified from school b is 50 % more than the students qualified from school a . what is the percentage of students qualified to the number of students appeared from school b ?
Options: a ) 30 % , b ) 70 % , c ) 80 % , d ) 87.5 % , e ) none
Rationale: solution let number of students appeared from school a = 100 . then , number of students qualified from school a = 70 . number of students appeared from school b = 120 . number of students qualified from school b = [ 150 / 100 x 70 ] = 105 . required percentage = [ 105 / 120 x 100 ] % = 87.5 % answer d
Answer: d
Problem: a man sitting in a train which is travelling at 20 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 72 kmph . , d ) 92 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 20 ) kmph = 92 kmph . answer d"
Answer: d
Problem: the area of one square is x ^ 2 + 6 x + 9 and the area of another square is 4 x ^ 2 − 20 x + 25 . if the sum of the perimeters of both squares is 52 , what is the value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the areas are ( x + 3 ) ^ 2 and ( 2 x - 5 ) ^ 2 . the lengths of the sides are x + 3 and 2 x - 5 . if we add the two perimeters : 4 ( x + 3 ) + 4 ( 2 x - 5 ) = 52 12 x = 60 x = 5 the answer is c ."
Answer: c
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 130 m long ?
Options: a ) 39.2 sec , b ) 35 sec , c ) 44 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 + 130 = 490 meter time taken to cross the platform = 490 / ( 25 / 2 ) = 490 ã — 2 / 25 = 39.2 seconds answer : a"
Answer: a
Problem: two trains are traveling from point a to point b such that the speed of first train is 65 kmph and the speed of 2 train is 29 kmph . where is the distance b / w a and b such that the slower train reached 5 hrs late compared to the faster ?
Options: a ) 3 , b ) 65 , c ) 9 , d ) 5 , e ) 31
Rationale: answer : b
Answer: b