regisss/math_qa huggingface dataset:
Problem: the present worth of rs . 845 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 150.50 , b ) rs . 154.75 , c ) rs . 781.25 , d ) rs . 158 , e ) none
Rationale: "solution present worth = rs . [ 845 / ( 1 + 4 / 100 ) ² ] = rs . ( 845 x 25 / 26 x 25 / 26 ) = rs . 781.25 answer c"
Answer: c
Problem: on the first of the year , james invested x dollars at proudstar bank in an account that yields 4 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 22.04 % , b ) 26.12 % , c ) 28 % , d ) 16.25 % , e ) 30 %
Rationale: per quarter , interest = 4 % so for a year , interest = 16 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 16.25 % answer = 16.25 % = answer : d
Answer: d
Problem: if a store owner increases a product ’ s price by 20 percent and then increases this price by another 15 percent , what percent of the original price is the total price increase ?
Options: a ) 20 % , b ) 35 % , c ) 38 % , d ) 65 % , e ) 135 %
Rationale: let the initial price be 100 1 st increase = 20 % the price now is 120 2 nd increase of 15 % on 120 = 18 final price = 138 , total increase = 38 % answer : c
Answer: c
Problem: if 5 students are made to sit in a row , then 6 do n ' t have seats . if 12 students are made to sit in a row , then 3 rows are empty . how many students have to sit a row such that each row has equal number of students and all students are seated ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: let there be a rows . then 5 a + 6 = 12 ( a - 3 ) [ equating the number of students ] = > a = 6 and total number of students = 36 therefore 6 students much sit in each row such that each row has an equal number of students and all students are seated . option ( e )
Answer: e
Problem: a pupil ' s marks were wrongly entered as 85 instead of 33 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 30 , b ) 104 , c ) 20 , d ) 25 , e ) 26
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 33 ) = > x / 2 = 52 = > x = 104 . answer : b"
Answer: b
Problem: if the ratio of two number is 6 : 7 and lcm of the number is 450 then what is the number .
Options: a ) 11 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "product of two no = lcm * hcf 6 x * 7 x = 450 * x x = 11 answer : a"
Answer: a
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 54 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3 km , d ) 3.4 km , e ) 5 km
Rationale: "d 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 54 / 60 47 x / 60 = 54 / 60 = > x = 1.14 total distance = 3 * 1.14 = 3.4 km ."
Answer: d
Problem: jim is able to sell a hand - carved statue for $ 620 which was a 25 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 496.00 , b ) $ 512.40 , c ) $ 555.40 , d ) $ 574.90 , e ) $ 588.20
Rationale: "620 = 1.25 * x x = 620 / 1.25 = 496.00 which rounds to $ 496.00 , which is ( a ) ."
Answer: a
Problem: praveen starts business with rs . 3780 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 7500 , b ) s . 8000 , c ) s . 8500 , d ) s . 9720 , e ) s . 6000
Rationale: "let hari ’ s capital be rs . x . then , 3780 * 12 / 7 x = 2 / 3 = > 14 x = 136080 = > x = 9720 . answer : d"
Answer: d
Problem: find the greatest number that will divide 48 , 210 and 136 leaving 4 , 12 and 4 as remainders respectively
Options: a ) 19 , b ) 17 , c ) 13 , d ) 22 , e ) 21
Rationale: "explanation : answer will be hcf of ( 48 - 4 , 210 - 12 , 136 - 4 ) hcf of ( 44 , 198 , 132 ) = 22 option d"
Answer: d
Problem: a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 500 , d ) 610 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 125 + 40 33 x / 100 = 165 x = 500 answer is c"
Answer: c
Problem: the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 524 different signs . if the company used 522 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 524 signs ?
Options: a ) 46 , b ) 248 , c ) 2092 , d ) 15,128 , e ) 30,256
Rationale: # of 2 - letter codes possible from 524 different signs = 524 * 524 . # of 2 - letter codes possible from 522 different signs = 522 * 522 . the difference = 524 ^ 2 - 522 ^ 2 = ( 524 - 522 ) ( 524 + 522 ) = 2092 . answer : c .
Answer: c
Problem: a case contains c cartons . each carton contains b boxes , and each box contains 200 paper clips . how many paper clips are contained in 2 cases ?
Options: a ) 200 bc , b ) 200 b / c , c ) 400 bc , d ) 400 b / c , e ) 400 / bc
Rationale: "2 cases * c cartons / case * b boxes / carton * 200 clips / box = 400 bc paper clips the answer is c ."
Answer: c
Problem: what is the value of x ^ 2 yz − xyz ^ 2 , if x = − 2 , y = 1 , and z = 1 ?
Options: a ) 6 , b ) 24 , c ) 30 , d ) 32 , e ) 48
Rationale: 4 * 1 * 1 - ( - 2 * 1 * 1 ) = 4 + 2 = 6 ans : a
Answer: a
Problem: 2.205 divided by 0.3 gives
Options: a ) 7.35 , b ) 6.25 , c ) 8.15 , d ) 6.95 , e ) none of these
Rationale: "explanation : 2.205 / 0.3 = 22.05 / 3 = 7.35 . answer : option a"
Answer: a
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.88 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.70 , b ) $ 3.00 , c ) $ 3.30 , d ) $ 3.60 , e ) $ 3.90
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 88 4 x / 15 = 88 x = 330 = $ 3.30 the answer is c ."
Answer: c
Problem: a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 4 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage lesser than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) - 87.5 %
Rationale: "typical dosage per 15 pound of the body weight = 4 c . c typical dosage per 120 pound of the body weight = 4 * ( 120 / 15 ) = 4 * 8 = 32 c . c dosage prescribed by doctor for 120 pound patient = 18 c . c % prescribed dosage greater than the typical dosage = ( 18 - 32 / 16 ) * 100 % = ( - 14 / 16 ) * 100 % = - 87 . . 5 % answer e"
Answer: e
Problem: calculate how much time could be saved if the train would run at its usual speed , given that it ran at 2 / 3 of its own speed and got to its destination in 20 hours ?
Options: a ) 5.67 hrs , b ) 9.67 hrs , c ) 8.95 hrs , d ) 8.67 hrs , e ) 6.67 hrs
Rationale: "new speed = 2 / 3 of usual speed new time = 2 / 3 of usual time 2 / 3 of usual time = 20 hrs usual time = 20 * 2 / 3 = 13.33 hrs time saved = 22 - 13.33 = 8.67 hrs answer is d"
Answer: d
Problem: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 10 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 35 , c ) 39 , d ) 30 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 7 and 10 ( in order 3 / 7 and 5 / 10 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 10 , which is 70 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 70 people in the room . therefore there are 3 / 7 * 70 = 30 people in the room under the age of 21 . answer : d ."
Answer: d
Problem: a 5 - digit number is formed by the digits 2 , 45 , 68 ( each digit used exactly once ) . what is the probability that the number formed is divisible by 4 ?
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 4 / 5 , d ) 6 / 5 , e ) 7 / 5
Rationale: a no . is divisible by 4 if last two digit is divisible by 4 so numbers ending with 2428 , 4852 , 5664 , 6884 are divisible by 4 last two places are fixed by 2428 , 4852 , 5664 , 6884 so remaining 3 places can be filled in 3 ! ways for each total = 8 * 3 ! = 48 = n ( e ) n ( s ) = 5 c 4 = 120 p = 48 / 120 = 2 / 5 answer : a
Answer: a
Problem: if x is 20 percent more than y and y is 60 percent less than z , then x is what percent of z ?
Options: a ) 500 % , b ) 48 % , c ) 500 / 3 % , d ) 125 % , e ) 60 %
Rationale: "z = 100 ; y = 40 so x = 48 x as % of z = 48 / 100 * 100 = > 48 % answer will be ( b )"
Answer: b
Problem: the area of one square is x ^ 2 + 4 x + 4 and the area of another square is 4 x ^ 2 − 12 x + 9 . if the sum of the perimeters of both squares is 32 , what is the value of x ?
Options: a ) 0 , b ) 2 , c ) 2.5 , d ) 4.67 , e ) 3
Rationale: "spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 2 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 2 l 2 = 2 x - 3 p 1 = 4 ( x + 2 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 32 4 ( x + 2 ) + 4 ( 2 x - 3 ) = 32 . . . . . . . . . . . . . . > x = 3 answer : e"
Answer: e
Problem: from mumbai railway station , two trains a and b start simultaneously from stations 400 miles apart , and travel the same route toward each other on adjacent parallel tracks . if train a and train b travel at a constant rate of 40 miles per hour and 40 miles per hour , respectively , how many miles will train a have traveled when the trains pass each other , to the nearest mile ?
Options: a ) 112 , b ) 133 , c ) 150 , d ) 167 , e ) 180
Rationale: since we know the distance ( 400 ) and the combined rate ( 80 ) , we plug it into the formula : distance = rate * time 400 = 80 * time we can solve for the time they will meet cause we added the rate of train a and train b together . so the time will be 400 / 80 from dividing 80 on both sides to isolate time in the equation above . time will be 20 hours so now you can plug that in for train a ’ s distance . distance = rate * time distance = 40 * 20 distance = 180 according to answer choice e .
Answer: e
Problem: a batsman scored 80 runs which included 2 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 % , b ) 500 / 11 , c ) 75 % , d ) 55 % , e ) 35 %
Rationale: "explanation : number of runs made by running , = > 80 − ( 2 × 4 + 2 × 6 ) . = > 80 − 20 = > 60 hence , the required percentage is : - = > 60 / 80 * 100 = > 75 % answer : c"
Answer: c
Problem: a certain car can travel 20 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 16.67 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "let , tank capacity = t gallon used fuel = ( t - 8 ) gallons distance travelled ( @ 60 miles / hr ) = 80 miles distance travelled in 1 gallon = distance travelled in 20 mins ( @ 60 miles / hr ) = ( 60 / 60 ) * 20 = 20 miles fuel used to travel 80 miles = ( 80 / 20 ) = 4 gallon i . e . used fuel = ( t - 8 ) = 4 gallon i . e . t = 12 gallons i . e . used fuel = ( 2 / 12 ) * 100 = 16,67 % a"
Answer: a
Problem: there is a church tower 150 feet tall and another catholic tower at a distance of 350 feet from it which is 200 feet tall . there is one each bird sitting on top of both the towers . they fly at a constant speed and time to reach a grain in b / w the towers at the same time . at what distance from the church is the grain ?
Options: a ) 170 meters , b ) 160 meters , c ) 150 meters , d ) 140 meters , e ) 130 meters
Rationale: if x ft is the distance of grain from 200 ft tall tower , then 150 ^ 2 + ( 350 - x ) ^ 2 = 200 ^ 2 + x ^ 2 then x = 150 meters answer : c
Answer: c
Problem: for 1 rs 4 p interest wat will be for 5000 rs ?
Options: a ) 350 rs , b ) 450 rs , c ) 200 rs , d ) 30 rs , e ) 448 rs
Rationale: for 1 rs , 4 p interest for 5000 rs , x x = 5000 / 1 * 4 p = = > 20000 paise to express in rs , 20000 / 100 = 200 rs answer : c
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 15 seconds . find the length of the train .
Options: a ) 150 m , b ) 145 m , c ) 240 m , d ) 135 m , e ) 250 m
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 250 meter answer : e"
Answer: e
Problem: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 600 more . what was the sum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1400 , d ) rs . 1500 , e ) none of these
Rationale: "explanation : at 5 % more rate , the increase in s . i for 10 years = rs . 600 ( given ) so , at 5 % more rate , the increase in si for 1 year = 600 / 10 = rs . 60 / - i . e . rs . 60 is 5 % of the invested sum so , 1 % of the invested sum = 60 / 5 therefore , the invested sum = 60 × 100 / 5 = rs . 1200 answer : a"
Answer: a
Problem: a shop owner sells 60 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 60 m cloth ) – ( c . p . of 60 m cloth ) selling price of 50 m cloth = selling price of 60 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 50 m cloth = rs . 5000 and s . p . of 50 m cloth = rs . rs . 6000 profit % = 10 / 50 × 100 = 20 % 20 profit of 20 % was made by the merchant . a"
Answer: a
Problem: a no . when divided by 221 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 10 , e ) 12
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Problem: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 4 : 7 : 9 . if the shop carries 364 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154
Rationale: "let us assume the number of dogs , cats and bunnies to be 4 x , 7 x and 9 x total dogs and bunnies = 13 x . and we are given that 13 x = 364 . hence x = 28 . dogs = 4 x = 4 * 28 = 112 ( option d )"
Answer: d
Problem: albert invested rs . 6500 in a scheme for 2 years at compound interest rate 6.5 % p . a . how much amount will albert get on maturity of the fixed deposit ?
Options: a ) s . 8829 , b ) s . 7200 , c ) s . 7200.5 , d ) s . 4000 , e ) s . 7372.46
Rationale: amount = [ 6500 * ( 1 + 6.5 / 100 ) 2 ] = 6500 * 106.5 / 100 * 106.5 / 100 = rs . 7372.46 answer : e
Answer: e
Problem: keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 30 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
Options: a ) 47 % , b ) 59 % , c ) 71 % , d ) 83 % , e ) 95 %
Rationale: "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.3 ( 5 b + x ) = b + x 0.5 b = 0.7 x x = 0.71 b the answer is c ."
Answer: c
Problem: if the average ( arithmetic mean ) of the 4 numbers 3 , 16 , 33 , and ( n + 1 ) is 20 , then n =
Options: a ) 19 , b ) 20 , c ) 21 , d ) 27 , e ) 29
Rationale: 3 + 16 + 33 + n + 1 = 20 x 4 = 80 = > n + 53 = 80 = > n = 27 answer d
Answer: d
Problem: the mean of 50 observations is 200 . but later he found that there is decrements of 6 from each observations . what is the the updated mean is ?
Options: a ) 165 , b ) 185 , c ) 190 , d ) 198 , e ) 194
Rationale: 194 answer is e
Answer: e
Problem: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 6000 , c ) $ 6050 , d ) $ 7050 , e ) $ 8000
Rationale: "let t be the tier price , p be total price = 14000 per the given conditions : 0.12 t + 0.08 ( p - t ) = 1440 - - - - > t = 8000 . e is the correct answer ."
Answer: e
Problem: a sum fetched a total simple interest of rs . 144 at the rate of 15 p . c . p . a . in 1 year 6 months . what is the sum ?
Options: a ) 490 , b ) 850 , c ) 580 , d ) 640 , e ) 760
Rationale: "sol . principal = rs . [ 100 * 144 / 15 * ( 18 / 12 ) ] = rs . [ 14400 / 22.5 ] = rs . 640 . answer d"
Answer: d
Problem: the ` ` racing magic ' ' takes 120 seconds to circle the racing track once . the ` ` charging bull ' ' makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: time taken by racing magic to make one circle = 120 seconds = 2 mins time taken by ` ` charging bull ' ' to make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 120 seconds = 360 seconds = 6 mins time taken for them to meet at the starting point for the second time = 6 mins * 2 = 12 mins answer d
Answer: d
Problem: find the constant k so that : - x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) 11 , b ) 12 , c ) 16 , d ) 14 , e ) 15
Rationale: "- x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 10 ) x - 8 = - x 2 + 6 x - 8 - ( k + 10 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 16 : solve the above for k correct answer c"
Answer: c
Problem: 102 ã — 102 + 98 ã — 98 = ?
Options: a ) 20018 , b ) 20028 , c ) 20108 , d ) 10008 , e ) 20008
Rationale: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1022 + 982 = ( 100 + 2 ) 2 + ( 100 â ˆ ’ 2 ) 2 = 2 ( 1002 + 22 ) = 2 ( 10000 + 4 ) = 20008 . answer : option e"
Answer: e
Problem: two trains 140 m and 190 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 11.88 sec , b ) 13.8 sec , c ) 53.8 sec , d ) 10.8 sec , e ) 10.4 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 190 = 330 m . required time = 330 * 9 / 250 = 11.88 sec . answer : a :"
Answer: a
Problem: mary works in a restaurant a maximum of 70 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
Options: a ) 600 , b ) 620 , c ) 660 , d ) 320 , e ) 400
Rationale: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 50 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 50 ( 20 ) = $ 500 . the total amount is $ 160 + $ 500 = $ 660 answer c 660 ."
Answer: c
Problem: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 4 per metre approximately
Options: a ) 4457 , b ) 4567 , c ) 5943 , d ) 4547 , e ) 4675
Rationale: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 4 ) = rs . 5943 . answer : option c"
Answer: c
Problem: 49 × 49 × 49 × 49 = 7 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 16 , e ) none of these
Rationale: "49 × 49 × 49 × 49 = 7 ? or , 7 ( 2 ) × 7 ( 2 ) × 7 ( 2 ) × 7 ( 2 ) = 7 ? or 7 ( 8 ) = 7 ? or , ? = 8 answer c"
Answer: c
Problem: 30 pens and 75 pencils were purchased for 750 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 20 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 750 – 150 ) = 600 ∴ average price of a pen = 600 ⁄ 60 = 20 answer a"
Answer: a
Problem: the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 16 and 17 . the larger of the two numbers is :
Options: a ) 338 , b ) 278 , c ) 322 , d ) 231 , e ) 391
Rationale: "clearly , the numbers are ( 23 * 16 ) and ( 23 * 17 ) . larger number = ( 23 * 17 ) = 391 . answer : e"
Answer: e
Problem: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two - fifth of its present ?
Options: a ) 52.5 , b ) 62.5 , c ) 72.5 , d ) 82.5 , e ) 81.5
Rationale: explanation : let the capacity of 1 bucket = x . then , capacity of tank = 25 x . new capacity of bucket = 2 / 5 x . required no of buckets = 25 x / ( 2 x / 5 ) = 62.5 answer is b
Answer: b
Problem: the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 110 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?
Options: a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 440
Rationale: "if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 110 group # 2 = ( like understood ) = 3 / 4 ( 1 / 4 ) n = 110 n = 440 answer = ( e )"
Answer: e
Problem: a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area r covered by the two roads ?
Options: a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625
Rationale: "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads r = 1000 + 600 - 25 = 1575 answer : option c"
Answer: c
Problem: a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 21 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 25 , c ) 60 , d ) 30 , e ) 28
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 21 days whole work will be done by a in 21 * 4 / 3 = 28 days answer is e"
Answer: e
Problem: how many integers are between 6 and 74 / 5 , inclusive ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "74 / 5 = 14 . xx we are not concerned about the exact value of 74 / 5 as we just need the integers . since the values are small , we can write down the integers . the different integers between 6 and 74 / 5 would be 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13,14 total number of integers = 9 option e"
Answer: e
Problem: what is the smallest positive integer x such that 180 - x is the cube of a positive integer
Options: a ) 50 , b ) 52 , c ) 60 , d ) 55 , e ) 12
Rationale: "given 180 - x is a perfect cube so we will take 125 = 5 * 5 * 5 180 - x = 125 x = 180 - 125 = 55 correct option is d"
Answer: d
Problem: what will be the cost of building to paint which area equal to 196 sq ft , if the price per foot of building is rs . 15 ?
Options: a ) 120
b ) 240
c ) 360
d ) 380
e ) 840
Rationale: let the side of the square plot be a ft . a 2 = 196 = > a = 14 length of the fence = perimeter of the plot = 4 a = 56 ft . cost of building the fence = 56 * 15 = rs . 840 . answer : e
Answer: e
Problem: in the youth summer village there are 175 people , 100 of them are not working , 75 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 70 , b ) 75 , c ) 85 , d ) 80 , e ) 100
Rationale: "total = 175 not working = 100 having family = 75 like to sing in shower = 125 working = 175 - 100 = 75 not having family = 175 - 75 = 100 like to sing in shower = 100 largest possible number is the lowest possible among the above thus 75 b"
Answer: b
Problem: if it takes a tub 3 minutes to drain 6 / 7 of its content , how much more time will it take for the tub to be empty ?
Options: a ) 30 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 50 seconds , d ) 2 minutes , 14 seconds , e ) 4 minutes , 12 seconds
Rationale: "if 6 / 7 of tub ' s content is drained 1 / 7 th of tub still needs to be drained . if it takes 3 minutes to drain 6 / 7 th of tub it takes 3 * ( 7 / 6 ) minutes to drain the entire tub and 3 * ( 7 / 6 ) * ( 1 / 7 ) min to drain 1 / 7 th of the tub which is 6 / 5 minutes or 0.5 minutes or 30 seconds so answer is a"
Answer: a
Problem: exactly 3 sides of a certain 10 - sided die are red . what is the probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll ?
Options: a ) 0.184 , b ) 0.16 , c ) 0.18 , d ) 0.147 , e ) 0.148
Rationale: total no . of sides = 10 sides that are red = 3 probability that the die lands with red side up = 3 / 10 therefore , probability that the die does not land with red side up = 1 - 3 / 10 = 7 / 10 probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll = ( 1 st roll - non red face ) x ( 2 nd roll - non red face ) x ( 3 rd roll - red face ) = ( 7 / 10 ) x ( 7 / 10 ) x ( 3 / 10 ) = 128 / 1000 = 0.147 d
Answer: d
Problem: the average runs scored by a batsman in 25 matches is 45 . in the next 7 matches the batsman scored an average of 15 runs . find his average in all the 32 matches ?
Options: a ) 31355 , b ) 38.44 , c ) 29.55 , d ) 97.66 , e ) 45.66
Rationale: total score of the batsman in 25 matches = 1125 . total score of the batsman in the next 7 matches = 105 . total score of the batsman in the 32 matches = 1230 . average score of the batsman = 1230 / 32 = 38.44 . answer : b
Answer: b
Problem: carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 4 % . what is the approximate interest he pays annually ?
Options: a ) $ 1750 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 12000
Rationale: "an easy way too attempt this is by approximation : for the first quarter , he pays 4 % of 10,000 which is $ 400 . so for the four quarters in the year , he will approximately play 400 * 4 = 1600 over the entire year . because of compound interest it will be more than 1600 . approx . option a is correct . answer : a"
Answer: a
Problem: jack and jill work at a hospital with 7 other workers . for an internal review , 2 of the 9 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 15 , d ) 3 / 8 , e ) 1 / 36
Rationale: "1 / 9 c 2 = 1 / 36 . answer : e ."
Answer: e
Problem: a student has to obtain 50 % of the total marks to pass . he got 200 marks and failed by 20 marks . the maximum marks are ?
Options: a ) 510 , b ) 520 , c ) 530 , d ) 540 , e ) 440
Rationale: "let the maximum marks be x then , 50 % of x = 200 + 20 50 x / 100 = 220 50 x = 220 * 100 = 22000 x = 440 answer is e"
Answer: e
Problem: the cost of 3 pens and 5 pencils is rs . 150 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 450 , e ) none of these
Rationale: "explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 150 15 x + 5 x = rs . 150 x = 150 / 20 = 7.50 : . cost of 1 pen = 5 x = 5 x 7.50 = 37.50 : . cost of 12 pens , i . e . ( one dozen ) = 37.50 x 12 = rs . 450 answer : option d"
Answer: d
Problem: car dealership x , the total profit from sales increased by 8 percent over the previous years , while the number of cars sold decreased by 8 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 17.39 % , b ) 20 % , c ) 22 % , d ) 23 % , e ) 25 %
Rationale: "let profit be x and cars sold be y originally profit / car = x / y now it is 1.08 x / 0.92 y = 108 / 92 ( x / y ) increase in profit per car = ( ( 16 / 92 ) ( x / y ) ) / ( x / y ) * 100 = 17.39 % answer = a"
Answer: a
Problem: the product z of two prime numbers is between 16 and 40 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 12 but less than 30 then what is z ?
Options: a ) 21 , b ) 22 , c ) 28 , d ) 35 , e ) 39
Rationale: "the smallest possible product is 39 which is 3 * 13 . all other products are too big . the answer is e ."
Answer: e
Problem: if 4 people are selected from a group of 8 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 8 / 13 , d ) 16 / 33 , e ) 11 / 12
Rationale: "if we are to select 4 people from 8 couples without any restriction , how many ways can we make the selection ? 16 ! / 4 ! 12 ! = 1820 if we are to select 4 people from 8 couples with restriction that no married couple can both make it to the group , only a representative ? 8 ! / 4 ! 4 ! = 70 but we know that to select a person from each couple , take 2 possibilities 70 * 2 * 2 * 2 * 2 = 1120 probability = desired / all possibilities = 1120 / 1820 = 8 / 13 answer : c"
Answer: c
Problem: the tax on a commodity is diminished by 20 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 19 % , c ) 15 % , d ) 12 % , e ) 24 %
Rationale: "answer : option d 100 * 100 = 10000 80 * 110 = 8800 10000 - - - - - - - 1200 100 - - - - - - - ? = 12 %"
Answer: d
Problem: a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 72 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 55 , b ) 84 , c ) 63 , d ) 75 , e ) 70
Rationale: "let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 72 or 1 / 7 t + 1 t = 60 therefore t = 72 * 7 / 8 = 63 c"
Answer: c
Problem: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 25 % , what is the total capacity of the pool in gallons ?
Options: a ) 1875 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1625
Rationale: "300 gallons of water increases capacity by 25 % that means 25 % is 300 gallons , so 100 % would be = 300 * 100 / 25 = 1200 gallons now 1200 + 300 gallons is 80 % capacity of tank . so 100 % capacity would be = 1500 * 100 / 80 = 1875 a is the answer"
Answer: a
Problem: at 3 : 40 , the hour hand and the minute hand of a clock form an angle of
Options: a ) 160 ° , b ) 180 ° , c ) 130 ° , d ) 110 ° , e ) 150 °
Rationale: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 3 , m = 40 and minute hand is ahead of the hour hand . hence the angle = 30 ( m / 5 − h ) − m / 2 = 30 ( 40 / 5 − 3 ) − 40 / 2 = 30 ( 8 − 3 ) − 20 = 30 × 5 − 20 = 130 ° answer is c ."
Answer: c
Problem: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 20 litres of tomato juice ?
Options: a ) 2.8 liters . , b ) 2.5 liters . , c ) 8.5 liters . , d ) 2.6 liters . , e ) 2.1 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . ⇒ ⇒ 10 % ( 20 ) = 80 % ( x ) ⇒ ⇒ x = 2.5 liters . answer : b"
Answer: b
Problem: if 2 ^ 5 , 3 ^ 3 , and 14 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 26 , b ) 39 , c ) 42 , d ) 65 , e ) 168
Rationale: here 156 has three two ' s two three ' s and one 14 rest of them must be in w so w = 14 * 3 * 4 = 168 smash e
Answer: e
Problem: a and b can finish a work in 10 days while b and c can do it in 18 days . a started the work , worked for 5 days , then b worked for 10 days and the remaining work was finished by c in 15 days . in how many days could c alone have finished the whole work ?
Options: a ) 30 days , b ) 15 days , c ) 45 days , d ) 24 days , e ) none of these
Rationale: let c completes the work in x days . work done by ( a + b ) in 1 day = 1 ⁄ 10 work done by ( b + c ) in 1 day = 1 ⁄ 18 a ’ s 5 days ’ work + b ’ s 10 days ’ work + c ’ s 15 days ’ work = 1 or ( a + b ) ’ s 5 days ’ work + ( b + c ) ’ s 5 days ’ work + c ’ s 10 days ’ work = 1 or 5 ⁄ 10 + 5 ⁄ 18 + 10 ⁄ x = 1 or x = 45 days answer c
Answer: c
Problem: a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it take 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?
Options: a ) 1 : 3 , b ) 3 : 8 , c ) 6 : 3 , d ) 8 : 3 , e ) none
Rationale: "sol . let the man rate upstream be x kmph and that downstream be y kmph . then , distance coverd upstream in 8 hrs 48 min . = distance coverd downstream in 4 hrs . ⇒ [ x 8 4 / 5 ] = ( y * 4 ) ⇒ 44 / 5 x = 4 y ⇒ y = 11 / 5 x . ∴ required ratio = [ y + x / 2 ] : [ 6 x / 5 * 1 / 2 ] : [ 6 x / 5 * 1 / 2 ] = 8 / 5 : 3 / 5 = 8 : 3 . answer d"
Answer: d
Problem: if 2 ^ x + 2 ^ y = 10 ^ 0 + 90 ^ 0 , where x and y are non negative integers , what is the greatest possible value of | x â € “ y | ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: | x â € “ y | for x and y 2 ^ x + 2 ^ y = 10 ^ 0 + 90 ^ 0 a . x = y x = y = 0 1 + 1 = 1 + 1 right b . 1 x = 2 , y = 1 4 + 2 = 1 + 1 wrong c . 2 x = 3 , y = 1 8 + 2 = 1 + 1 wrong d . 3 x = 4 , y = 1 16 + 2 = 1 + 1 wrong e . 4 x = 5 , y = 1 32 + 2 = 1 + 1 wrong my answer is a .
Answer: a
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1032 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 54
Rationale: for 40 hrs = 40 * 16 = 640 excess = 1032 - 640 = 392 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 392 / 28 = 98 / 7 = 14 total hrs = 40 + 14 = 54 answer e 52
Answer: e
Problem: find the length of the wire required to go 15 times round a square field containing 69696 m 2 ?
Options: a ) 15840 , b ) 19879 , c ) 27997 , d ) 15842 , e ) 15823
Rationale: "a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : a"
Answer: a
Problem: p , q and r have rs . 7000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) rs . 3000 , b ) rs . 3600 , c ) rs . 2400 , d ) rs . 2800 , e ) none of these
Rationale: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 7000 - r ) = > 3 r = 14000 - 2 r = > 5 r = 14000 = > r = 2800 . answer : d"
Answer: d
Problem: rahul put his timepiece on the table in such a way that at 6 p . m . hour hand points to north . in which direction the minute hand will point at 9.15 p . m . ?
Options: a ) 233 , b ) 37 , c ) 27 , d ) west , e ) 271
Rationale: explanation : at 9.15 p . m . , the minute hand will point towards west . answer : d ) west
Answer: d
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 overs to reach a target of 282 runs ?
Options: a ) 6.25 , b ) 6.5 , c ) 6.75 , d ) 7.0 , e ) none of the above
Rationale: "total runs in the first 10 overs = 10 × 3.2 = 32 run rate required in the remaining 40 overs = 282 − 32 / 40 = 250 / 40 = 6.25 runs per over . answer a"
Answer: a
Problem: a and b together can complete a piece of work in 10 days . if a alone can complete the same work in 15 days , in how many days , in how many days can b alone complete that work ?
Options: a ) 10 , b ) 30 , c ) 25 , d ) 15 , e ) 45
Rationale: ( a + b ) ' s 1 day ' s work = 1 / 10 a ' s 1 day ' s work = 1 / 15 b ' s 1 days ' s work = ( 1 / 10 ) - ( 1 / 15 ) = 1 / 30 hence , b alone can complete the work in 30 days . answer is b
Answer: b
Problem: the triplicate ratio of 2 : 4 is ?
Options: a ) 1 : 64 , b ) 1 : 8 , c ) 1 : 34 , d ) 3 : 64 , e ) 5 : 64
Rationale: "2 ^ 3 : 4 ^ 3 = 8 : 64 = 1 : 8 answer : b"
Answer: b
Problem: how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 32 % iodine solution ?
Options: a ) 35 , b ) 49 , c ) 100 , d ) 102 , e ) 140
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 32 / 100 40 x + 700 = 32 x + 1120 8 x = 820 x = 102 lts correct option : d"
Answer: d
Problem: a garrison of 2000 men has provisions for 54 days . at the end of 18 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1977 , b ) 1600 , c ) 1979 , d ) 1900 , e ) 1278
Rationale: "2000 - - - - 54 2000 - - - - 36 x - - - - - 20 x * 20 = 2000 * 36 x = 3600 2000 - - - - - - - 1600 answer : b"
Answer: b
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
Options: a ) 95 kg , b ) 90 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "a 95 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 75 + 20 ) kg = 95 kg ."
Answer: a
Problem: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 109.20 , what was the total value of the item ?
Options: a ) $ 1,600 , b ) $ 1,850 , c ) $ 2,250 , d ) $ 2,440 , e ) $ 2,560
Rationale: "let x be the value of the item . 0.07 * ( x - 1000 ) = 109.20 x = 2560 the answer is e ."
Answer: e
Problem: the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 1,080 ?
Options: a ) 13 , b ) 10 , c ) 9 , d ) 7 , e ) 6
Rationale: to maximize the length of z we should minimize its prime base . the smallest prime is 2 and since 2 ^ 10 = 1,024 < 1,080 then the greatest possible length of integer z is 10 . answer : b .
Answer: b
Problem: how many multiples of 3 are less than 6500 , and also multiples of 7 ?
Options: a ) 104 , b ) 208 , c ) 310 , d ) 340 , e ) 454
Rationale: "lcm of 3 & 7 = 21 tried dividing 6500 by 21 got quotient 309.5 ' so c is answer"
Answer: c
Problem: a can finish a piece of work in 4 days . b can do it in 10 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: 2 / 4 + ( 2 + x ) / 10 = 1 = > x = 3 days answer : a
Answer: a
Problem: if the sides of a triangle are 26 cm , 24 cm and 15 cm , what is its area ?
Options: a ) 120 , b ) 772 , c ) 180 , d ) 266 , e ) 2848
Rationale: "the triangle with sides 26 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : c"
Answer: c
Problem: two trains , a and b , started simultaneously from opposite ends of a 125 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 125 - mile trip in 12 hours ; train b , traveling at a constant rate , completed the 125 - mile trip in 8 hours . how many miles had train a traveled when it met train b ?
Options: a ) 25 , b ) 37.5 , c ) 40 , d ) 45.5 , e ) 50
Rationale: as the ratio of the rates of a and b is 8 to 12 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that a would cover 8 / ( 8 + 12 ) = 8 / 20 of 125 miles : 125 * 8 / 20 = 50 miles . answer : e .
Answer: e
Problem: if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2400 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2500 , c ) 2507 , d ) 3000 , e ) 11500
Rationale: "p - 2400 = ( p * 5 * 4 ) / 100 p = 3000 answer : d"
Answer: d
Problem: out of 250 students of a college , 160 play football , 90 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: explanation : solution : n ( a ) = 160 , n ( b ) = 90 , n ( a u b ) = 250 - 50 = 200 . required number = > n ( a ^ b ) = n ( a ) + n ( b ) - n ( a u b ) = 160 + 90 - 200 = 250 - 200 = 50 . answer : c
Answer: c
Problem: what is the area a of the square with the following coordinates : ( x , y ) , ( 20 , 20 ) , ( 20 , 5 ) , ( x , 5 ) ?
Options: a ) 60 .
b ) 85 .
c ) 125 .
d ) 225 .
e ) it can not be determined from the information given
Rationale: length of one side = 15 ( 20 - 5 ) since , its a square , the area will be a = 15 ^ 2 = 225 d is the answer
Answer: d
Problem: a van takes 5 hours to cover a distance of 495 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 60 , b ) 63 , c ) 66 , d ) 69 , e ) 72
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 495 / 7.5 = 66 kph the answer is c ."
Answer: c
Problem: what is the probability of getting a queen or spade from a set of cards ?
Options: a ) 3 / 13 , b ) 4 / 13 , c ) 5 / 13 , d ) 6 / 13 , e ) 7 / 13
Rationale: "no . of spade = 13 no . of queen = 3 ( excluding queen of spade ) no . of possible outcome = 13 + 3 = 16 probability = no . of favorable outcome / total possible outcomes = 16 / 52 = 4 / 13 answer : b"
Answer: b
Problem: find the compound interest on $ 1000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 82.43 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 1020.45
Rationale: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 1000 * ( 1 + 2 / 100 ) ^ 4 = 1000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 1082.43 c . i . = 1082.43 - 1000 = $ 82.43 answer is b"
Answer: b
Problem: if n is a positive integer and n ^ 2 is divisible by 36 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "the question asks aboutthe largest positive integer that must divide n , not could divide n . since the least value of n for which n ^ 2 is a multiple of 72 is 12 then the largest positive integer that must divide n is 12 . complete solution of this question is given above . please ask if anything remains unclear . i spent a few hours on this one alone and i ' m still not clear . i chose 12 at first , but then changed to 48 . i ' m not a native speaker , so here is how i interpreted this question : the largest positive integer that must divide n = the largest positive factor of n . since n is a variable ( i . e . n is moving ) , so is its largest factor . please correct if i ' m wrong here . i know that if n = 12 , n ^ 2 = 144 = 2 * 72 ( satisfy the condition ) . when n = 12 , the largest factor of n is n itself , which is 12 . check : 12 is the largest positive number that must divide 12 - - > true however if n = 48 , n ^ 2 = 48 * 48 = 32 * 72 ( satisfy the condition too ) . when n = 48 , the largest factor of n is n itself , which is 48 . check : 48 is the largest positive number that must divide 48 - - > true so , i also notice that the keyword ismust , notcould . the question is , why is 48 notmust divide 48 , but instead onlycould divide 48 ? i ' m not clear right here . why is 12 must divide 12 ? what ' s the difference between them ? only restriction we have on positive integer n is that n ^ 2 is divisible by 72 . the least value of n for which n ^ 2 is divisible by 72 is 12 , thus nmustbe divisible by 12 ( n is in any case divisible by 12 ) . for all other values of n , for which n ^ 2 is divisible by 72 , n will still be divisible by 12 . this means that n is always divisible by 12 if n ^ 2 is divisible by 72 . now , ask yourself : if n = 6 , is n divisible by 48 ? no . so , n is not always divisible by 48 . a"
Answer: a
Problem: the population of a town is 8000 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9876 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 100 / 90 ã — 100 / 90 = 9876 a )"
Answer: a
Problem: sum of two numbers is 40 and their difference is 4 . the ratio of the numbers is
Options: a ) 10 : 3 , b ) 5 : 9 , c ) 11 : 9 , d ) 13 : 9 , e ) none of these
Rationale: "explanation : = > ( x + y ) / ( x − y ) = 40 / 4 = > ( x + y ) = 10 ( x − y ) = > 9 x = 11 y = > x / y = 11 / 9 option c"
Answer: c
Problem: a man sitting in a train which is traveling at 36 kmph observes that a goods train , traveling in opposite direction , takes 10 seconds to pass him . if the goods train is 240 m long , find its speed
Options: a ) 50 kmph , b ) 56 kmph , c ) 58 kmph , d ) 62 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 240 / 10 m / sec = ( ( 240 / 10 ) × ( 18 / 5 ) ) kmph = 86 kmph . speed of goods train = ( 86 - 36 ) kmph = 50 kmph answer : option a"
Answer: a
Problem: a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 15 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 300 meters , d ) 600 meters , e ) can not be determined
Rationale: speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 15 * 20 = 300 = length of train length of platform = 600 - 300 = 300 answer : c
Answer: c