regisss/math_qa huggingface dataset:
Problem: the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 6 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 12 , d ) 6 , e ) 160
Rationale: "actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 6 miles / gallon . additional 6 miles / gallon is required to match the actual mileage . imo option d ."
Answer: d
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 70400 ?
Options: a ) 89100 , b ) 81028 , c ) 27772 , d ) 29889 , e ) 22312
Rationale: 70400 * 9 / 8 * 9 / 8 = 89100 . answer : a
Answer: a
Problem: an empty fuel tank is filled with brand z gasoline . when the tank is 1 / 4 empty , it is filled with brand y gasoline . when the tank is half empty again , it is filled with brand z gasoline . when the tank is half empty again , it is filled with brand y gasoline . at this time , what percent of the gasoline in the tank is brand z ?
Options: a ) 31.25 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 45 %
Rationale: work with fraction of brand z in the tank . 1 st step : brand z is 1 2 nd step : brand z is 1 / 4 3 rd step : brand z is ( 1 / 2 ) * ( 1 / 4 ) + 1 / 2 = 5 / 8 4 th step : brand z is ( 1 / 2 ) * ( 5 / 8 ) = 5 / 16 answer ( a )
Answer: a
Problem: if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 29 , find the value of ab .
Options: a ) 5 , b ) 8 , c ) 4 , d ) 10 , e ) 3
Rationale: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 29 - 9 = 20 ab = 10 . answer is d ."
Answer: d
Problem: in an election , candidate a got 55 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 261800 , b ) 355800 , c ) 356500 , d ) 356800 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 55 % therefore , the number of valid votes polled in favour of candidate a = 55 % of 476000 = 55 / 100 × 476000 = 26180000 / 100 = 261800 a )"
Answer: a
Problem: a 600 meter long train crosses a signal post in 30 seconds . how long will it take to cross a 3 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 3 min , e ) 5 min
Rationale: "s = 600 / 30 = 20 mps s = 3600 / 20 = 180 sec = 4 min answer : d"
Answer: d
Problem: a certain number when divided by 39 leaves a remainder 20 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 0 , e ) 1
Rationale: "39 + 20 = 59 / 13 = 7 ( remainder ) answer : a"
Answer: a
Problem: a sum fetched a total simple interest of $ 4196.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8929
Rationale: "e 8929 principal = $ 100 x 4196.25 / 9 x 5 = $ 419625 / 45 = $ 8929 ."
Answer: e
Problem: if the sum of 5 consecutive even positive integers is a , then the sum of the next 5 even consecutive integers in terms of a is :
Options: a ) a + 5 , b ) a + 10 , c ) a + 25 , d ) a + 50 , e ) 2 a + 5
Rationale: in case of consecutive integers or integers in arithmetic progression mean = median i . e . median = a / 5 = mean = third integer first integer = a / 5 - 4 second integer = a / 5 - 2 third integer = a / 5 fourth integer = a / 5 + 2 fifth integer = a / 5 + 4 i . e . sixth integer = a / 5 + 6 seventh integer = a / 5 + 8 eighth integer = a / 5 + 10 ninth integer = a / 5 + 12 tenth integer = a / 5 + 14 now mean of next 5 integers = median = a / 5 + 5 i . e . sum of next 5 integers = ( a / 5 + 10 ) * 5 = a + 50 answer : option d
Answer: d
Problem: an escalator moves towards the top level at the rate of 12 ft . sec and its length is 196 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 14 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec
Rationale: "time taken to cover the entire length = tot . dist / resultant speed = 196 / ( 12 + 2 ) = 14 sec answer : a"
Answer: a
Problem: pipe a fills a tank in 12 minutes . pipe b can fill the same tank 3 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 4 mins , b ) 6 mins , c ) 5 mins , d ) 3 mins , e ) 7 mins
Rationale: "a ' s rate is 1 / 12 and b ' s rate is 1 / 4 . the combined rate is 1 / 12 + 1 / 4 = 1 / 3 the pipes will fill the tank in 3 minutes . the answer is d ."
Answer: d
Problem: a sum of rs . 2730 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1629 , b ) 1680 , c ) 1677 , d ) 1698 , e ) 1679
Rationale: ( x * 8 * 3 ) / 100 = ( ( 2730 - x ) * 3 * 5 ) / 100 24 x / 100 = 40950 / 100 - 15 x / 100 39 x = 40950 = > x = 1050 second sum = 2730 â € “ 1050 = 1680 answer : b
Answer: b
Problem: if the radius of a circle is decreased 60 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 84 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.4 * old radius so new area = ( 0.4 ) ^ 2 old area = > 0.16 of old area = > 16 % old area ans : d"
Answer: d
Problem: the speed at which a man can row a boat in still water is 22 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 80 metres ?
Options: a ) 12.59 , b ) 11.53 , c ) 15.69 , d ) 14.56 , e ) 18.98
Rationale: speed of the boat downstream = 22 + 3 = 25 kmph = 25 * 5 / 18 = 6.94 m / s hence time taken to cover 80 m = 80 / 6.94 = 11.53 seconds . answer : b
Answer: b
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.70 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.46
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.7 = 3 * x - - > x = $ 0.46 . answer : e ."
Answer: e
Problem: if one - third of one - fourth of a number is 18 , then 3 - tenth of that number is : a . 35
Options: a ) 23 , b ) 87 , c ) 26 , d ) 64.8 , e ) 01
Rationale: explanation : the number is 1 / 3 of 1 / 4 is = 15 then 1 / 3 ã — 1 / 4 = 18 number is 216 then 216 ã — 3 / 10 = 64.8 answer : d
Answer: d
Problem: during a certain season , a team won 75 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 180 , b ) 170 , c ) 156 , d ) 150 , e ) 125
Rationale: we are first given that a team won 75 percent of its first 100 games . this means the team won 0.75 x 100 = 75 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 75 + 0.5 t – 50 = 0.7 t 25 = 0.2 t 250 = 2 t 125 = t answer is e .
Answer: e
Problem: if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability e that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."
Answer: d
Problem: p , q and r together earn rs . 1890 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ?
Options: a ) s . 40 , b ) s . 70 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: "explanation : amount earned by p , q and r in 1 day = 1890 / 9 = 210 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 210 = 40 = > amount earned by r in 1 day = 40 answer : option a"
Answer: a
Problem: the greatest number that divides 690 and 875 leaving remainders 10 and 25 respectively is :
Options: a ) 170 , b ) 130 , c ) 150 , d ) 120 , e ) 180
Rationale: "explanation : 690 - 10 = 680 , 875 – 25 = 850 highest number that can divide 680 and 850 exactly is hcm of the numbers . hcf of 680 and 850 = 170 answer : a"
Answer: a
Problem: a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 25 speak english well , while 65 of them do not speak english . if 55 % of students do not speak french , how many students were surveyed ?
Options: a ) 190 , b ) 175 , c ) 225 , d ) 200 , e ) 250
Rationale: number of students who speak french are 65 + 25 = 90 of total students , the percentage of students who do not speak french was 55 % - - > percentage of who do is 45 % 90 - - - - - - - 45 % x - - - - - - - 100 % x = 90 * 100 / 45 = 200 = number of all students answer is d
Answer: d
Problem: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 510 kilograms of pears that day , how many kilograms did he sell in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 340 , d ) 280 , e ) 320
Rationale: "3 x = 510 x = 170 therefore , the salesman sold 170 kg in the morning and 2 ⋅ 170 = 340 kg in the afternoon . so answer is c ."
Answer: c
Problem: find the sum of all 3 digit natural numbers , which are divisible by 8 .
Options: a ) 61376 , b ) 54411 , c ) 612314 , d ) 64170 , e ) 64171
Rationale: the three digit natural numbers divisible by 8 are 104 , 112 , 120 , … . 992 . let sndenote their sum . that is , sn = 104 112 120 128 , 992 g + + + + + . now , the sequence 104 , 112 , 120 , g , 992 forms an a . p . a = 104 , d = 8 , l = 992 n = l - a / d n = 112 s 112 = n / 2 ( a + l ) = 61376 option a
Answer: a
Problem: each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.65 % , what fraction of the products was checked by worker y ?
Options: a ) 1 / 5 , b ) 1 / 2 , c ) 2 / 3 , d ) 1 / 4 , e ) 2 / 5
Rationale: "x : 0.5 % is 0.15 % - points from 0.65 % . y : 0.8 % is 0.15 % - points from 0.65 % . therefore the ratio of products checked by y : x is 1 : 1 . thus , worker y checked 1 / 2 of the products . the answer is b ."
Answer: b
Problem: the radius of the two circular fields is in the ratio 4 : 10 the area of the second field is what percent greater than the area of the first ?
Options: a ) 72 %
b ) 96 %
c ) 94 %
d ) 84 %
e ) 82 %
Rationale: r = 4 ï € r 2 = 16 r = 10 ï € r 2 = 100 100 ï € â € “ 84 ï € 100 - - - - ? = > 84 % . answer : d
Answer: d
Problem: a river 2 m deep and 45 m wide is flowing at the rate of 5 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 m 3 , b ) 4580 m 3 , c ) 7500 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 5000 * 2 * 45 ) / 60 = 7500 m 3 answer : option c"
Answer: c
Problem: if the range q of the 6 numbers 4 , 314 , 710 and x is 12 , what is the difference between the greatest possible value of x and least possible value of x ?
Options: a ) 0 , b ) 2 , c ) 12 , d ) 13 , e ) 15
Rationale: the range q of a set is the difference between the largest and smallest elements of a set . without x , the difference between the largest and smallest elements of a set is 14 - 3 = 11 < 12 , which means that in order 12 to be the range of the set x must be either the smallest element so that 14 - x = 12 - - - > x = 2 or x must the largest element so that x - 3 = 12 - - > x = 15 . the the difference between the greatest possible value of x and least possible value of x is 15 - 2 = 13 . answer : d .
Answer: d
Problem: a person is traveling at 60 km / hr and reached his destiny in 4 hr . 30 m then find the distance ?
Options: a ) 150 km , b ) 270 km , c ) 246 km , d ) 196 km , e ) 205 km
Rationale: "t = 4 hr 30 m = 9 / 2 hr d = t * s = 60 * 9 / 2 = 270 km answer is b"
Answer: b
Problem: if 80 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 55 %
Rationale: "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 80 - x ) + x + ( 55 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 135 x = 55 ans : e"
Answer: e
Problem: a train 300 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 72 , b ) 67 , c ) 54 , d ) 26 , e ) 27
Rationale: "length = speed * time speed = l / t s = 300 / 20 s = 15 m / sec speed = 15 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 54 kmph answer : c"
Answer: c
Problem: a train is 385 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 42 seconds , b ) 30 seconds , c ) 40 seconds , d ) 50 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 385 + 140 = 525 meter time = distance / speed = 525 ∗ 2 / 25 = 42 seconds option a"
Answer: a
Problem: ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of a * b ?
Options: a ) 10000 , b ) 11000 , c ) 19000 , d ) 20000 , e ) 21000
Rationale: "yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 a * b = 110 * 100 = 11000 ans : b"
Answer: b
Problem: the distance between two cities a and b is 330 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 10 a . m , b ) 10.30 a . m , c ) 11 a . m , d ) 11.30 a . m , e ) none of these
Rationale: explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 330 . therefore , 60 x + 75 ( x - 1 ) = 330 . = > x = 3 . so , they meet at ( 8 + 3 ) i . e , 11 a . m . answer : c
Answer: c
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 m and a distance of one meter is left from all sides of the boundary of the length of the garden is :
Options: a ) 450 sq mtrs , b ) 460 sq mtrs , c ) 480 sq mtrs , d ) 490 sq mtrs , e ) 470 sq mtrs
Rationale: "length of garden = 1 + 2 * 11 + 1 = 24 m breadth of garden = 1 + 9 * 2 + 1 = 20 m area = 24 * 20 = 480 sq mtrs answer : c"
Answer: c
Problem: there are 10 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 156 , b ) 167 , c ) 132 , d ) 352 , e ) 380
Rationale: "the total number of stations = 12 from 12 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 12 p ₂ ways . ² ⁰ p ₂ = 12 * 11 = 132 . answer : c"
Answer: c
Problem: total dinning bill of 9 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 21.84 , b ) 12.84 , c ) 16.98 , d ) 24.84 , e ) 15.84
Rationale: "dinner bill of 9 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 9 = $ 16.98 answer : c"
Answer: c
Problem: find the length of the longest pole that can be placed in a room 12 m long 8 m broad and 9 m high .
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "length of longest pole = length of the diagonal of the room = sqrt ( 12 ^ 2 + 8 ^ 2 + 9 ^ 2 = sqrt ( 289 ) = 17 m . answer is e ."
Answer: e
Problem: find the average of first 4 multiples of 8 ?
Options: a ) 20 , b ) 12.6 , c ) 22.5 , d ) 31.3 , e ) 40.8
Rationale: "average = ( 8 + 16 + 24 + 32 ) / 4 = 20 answer is a"
Answer: a
Problem: if 9 ^ y = 3 ^ 14 , what is y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: "9 ^ y = 3 ^ 2 y = 3 ^ 14 2 y = 14 y = 7 the answer is e ."
Answer: e
Problem: how many zeroes are there at the end of the number n , if n = 90 ! + 180 ! ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "the number of zeroes at the end of 90 ! will be less than the number of zeroes at the end of 180 ! hence it is sufficient to calculate the number of zeroes at the end of 90 ! the number of zeroes = [ 90 / 5 ] + [ 90 / 25 ] + [ 90 / 125 ] = 18 + 3 + 0 = 21 the answer is c ."
Answer: c
Problem: ms . harris invested in fund x and fund b . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund x paid 23 % and fund b paid 17 % . the interest earned in fund b was exactly $ 200 greater than the interest earned in fund x . how much did ms . morris invest in fund x ?
Options: a ) $ 32000 , b ) $ 36000 , c ) $ 40000 , d ) $ 42000 , e ) $ 45,000
Rationale: 0.17 b - 0.23 x = 200 | * 100 17 b - 23 x = 20,000 x + b = 100,000 b = 100,000 - x 17 ( 100,000 - x ) - 23 x = 20,000 1 , 700,000 - 17 x - 23 x = 20,000 1 , 680,000 = 40 x divide by 40 first two digits : 42 . . . so answer is d .
Answer: d
Problem: in a forest 150 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 10 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 3,000 , d ) 1,500 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 10 / 50 * 100 = 20 % . so , 150 tagged deers comprise 10 % of total # of deers - - > total # of deers = 150 * 20 = 3,500 . answer : c"
Answer: c
Problem: a 11 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 5 / 8 , b ) 1 / 5 , c ) 6 / 11 , d ) 3 / 11 , e ) 2 / 5
Rationale: "a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 3 meters from either end . the probability of this is 6 / 11 . the answer is c ."
Answer: c
Problem: if the price of a certain computer increased 30 percent from b dollars to 351 dollars , then 2 b =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = b after 30 % price increase price = b + ( 30 / 100 ) * b = 1.3 b = 351 ( given ) i . e . b = 351 / 1.3 = $ 270 i . e . 2 b = 2 * 270 = 540 answer : option a"
Answer: a
Problem: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 5780 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 5780 = x = 5780 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2000 . answer : c"
Answer: c
Problem: how many seconds will a train 100 meters long take to cross a bridge 170 meters long if the speed of the train is 36 kmph ?
Options: a ) 54 sec , b ) 65 sec , c ) 25 sec , d ) 45 sec , e ) 27 sec
Rationale: "d = 100 + 170 = 270 s = 36 * 5 / 18 = 10 mps t = 270 / 10 = 27 sec answer : e"
Answer: e
Problem: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 12 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 95 , d ) 88 , e ) 93
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 12 total people can seat = 81 + 12 = 93 answer : e"
Answer: e
Problem: some persons can do a piece of work in 16 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "16 / ( 2 * 2 ) = 4 days answer : b"
Answer: b
Problem: stacy was 5 days late returning items to the library . stacy had checked out 40 books , 2 movies , and 3 magazines . books are fined $ 0.25 per day , movies are fined $ 3.00 per day , and magazines are fined $ 0.50 per day . what is the average fine per item per day stacy paid ?
Options: a ) $ 0.25 , b ) $ 0.30 , c ) $ 0.35 , d ) $ 0.40 , e ) none of the above
Rationale: explanation : 40 2 3 $ 0.25 $ 3.00 $ 0.50 $ 10.00 + $ 6.00 + $ 1.50 = $ 17.50 / 45 = $ 0.39 e
Answer: e
Problem: if an average hard drive had a capacity of 0.4 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 512 , c ) 4096 , d ) 1024 , e ) 1536
Rationale: "0.4 * 2 ^ 10 = 0.4 * 1024 = 409.6 the answer is c ."
Answer: c
Problem: in may , the grounds keeper at spring lake golf club built a circular green with an area of 36 π square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 100 pi
b ) 144 pi
c ) 70
d ) 80
e ) 90
Rationale: area of circle 36 pi sq feet = pi r ^ 2 therefore r = 6 now green radi doubled i . e r = 12 area = 144 pi b
Answer: b
Problem: a house wife saved $ 5 in buying an item on sale . if she spent $ 48 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 48 + 5 = $ 53 saving = 5 / 48 * 100 = 100 / 11 = 10 % approximately answer is c"
Answer: c
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 200 , find the original price per kg ?
Options: a ) s . 7 , b ) s . 4 , c ) s . 5 , d ) s . 1 , e ) s . 9
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 200 - - - 80 ? - - - 2 = > rs . 5 answer : c"
Answer: c
Problem: find the remainder when 6 ^ 50 is divided by 215
Options: a ) 34 , b ) 35 , c ) 36 , d ) 37 , e ) 38
Rationale: "( 6 ^ 3 ) ^ 16 * 6 ^ 2 / 215 ( 215 + 1 ) ^ 16 * 6 ^ 2 / 215 1 ^ 16 * 6 ^ 2 / 215 = 36 answer : c"
Answer: c
Problem: a train 140 m long is running at 60 kmph . in how much time wiu it pass a platform 260 m long ?
Options: a ) 21 sec , b ) 22 sec , c ) 23 sec , d ) 24 sec , e ) 26 sec
Rationale: "s = d / t d = 140 + 260 = 400 m s = 60 * 5 / 18 m / sec = 50 / 3 m / sec t = 400 / ( 50 / 3 ) = 1200 / 50 = 24 sec answer : d"
Answer: d
Problem: the total marks obtained by a student in mathematics and physics is 50 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 15 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 50 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 50 + 20 ) / 2 = 35 . answer : c"
Answer: c
Problem: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 70 paise per sq . metre
Options: a ) s 595 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 70 = 59500 p in rs = 59500 / 100 = rs 595 answer : a"
Answer: a
Problem: rahul played weel in this season . his current batting averagge is 46 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 3 , d ) 6 , e ) 5
Rationale: "46 x + 78 = 54 ( x + 1 ) = > 8 x = 24 = > x = 3 answer : c"
Answer: c
Problem: find the simple interest on rs . 69,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 8625 , d ) 9500 , e ) none of them
Rationale: p = rs . 69000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 69,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8625 answer is c .
Answer: c
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 7 years hence ?
Options: a ) 22 , b ) 77 , c ) 74 , d ) 98 , e ) 71
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 7 years , their ages will be 47 and 27 . sum of their ages = 47 + 27 = 74 . answer : c"
Answer: c
Problem: malar and roja combined will complete a task in 35 days , but malar alone can complete same work in 60 days . calculate in how many days roja can complete this work ?
Options: a ) 85 days , b ) 45 days , c ) 90 days , d ) 84 days , e ) 95 days
Rationale: malar - 35 days = > 1 / 35 roja - 60 days = > 1 / 60 malar one day work = 1 / 35 - 1 / 60 = 1 / 84 = = > 84 days answer d
Answer: d
Problem: the measure of the side of a square is quadrupled . if x represents the perimeter of the original square , what is the value of the new perimeter ?
Options: a ) 3 x
b ) 4 x
c ) 9 x
d ) 12 x
e ) 27 x
Rationale: original perimeter = x hence original side = x / 4 new side = 4 x / 4 new perimeter = 4 * 4 x / 4 = 4 x correct option : b
Answer: b
Problem: tough and tricky questions : word problems . micheal , saren and donald decided to club together to buy a present . each of them gave equal amount of money . luckily saren negotiated a 20 % discount for the present so that each of them paid 4 dollars less . how much did they pay for a present ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: answer c . we know that saren negotiated a discount of 20 % , so each of them paid $ 4 less . since there are three people , the 20 % of the original price amounts to $ 12 . 5 times 12 $ is 60 $ , so the original price , before saren negotiated the discount , had been $ 60 . they paid $ 12 less than the base price , so they spent $ 48 .
Answer: c
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 25 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 767 m , b ) 240 m , c ) 187 m , d ) 176 m , e ) 165 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 25 = 375 m . let the length of the platform be x m . then , ( x + 375 ) / 36 = 15 = > x = 165 m . answer : e"
Answer: e
Problem: a club wants to mix 25 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 25 * 8 + 5 * w ) / ( 25 + w ) = > 150 + 6 w = 200 + 5 w = > w = 50 answer c"
Answer: c
Problem: if pintu is coded as 79523 in a certain code language , how would you code lumbo in the same language ?
Options: a ) 13426 , b ) 14236 , c ) 13436 , d ) 33426 , e ) 15263
Rationale: "1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . lumbo is 33426 . . . answer : d"
Answer: d
Problem: a shopkeeper has 280 kg of apples . he sells 30 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 30 x 20 % + 60 x 30 % = 24 this profit will remain same for any total quantity unless the % of products remains the same . hence ' a ' is the answer"
Answer: a
Problem: pradeep has to obtain 20 % of the total marks to pass . he got 390 marks and failed by 25 marks . the maximum marks are
Options: a ) 300 , b ) 2075 , c ) 800 , d ) 1000 , e ) 3900
Rationale: "explanation : let their maximum marks be x . then , 20 % of x = 390 + 25 = > 20 / 100 x = 415 x = ( 41500 / 20 ) x = 2075 . answer : b"
Answer: b
Problem: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6500 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 8870 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6500 * 6 ) – 30,130 ] = rs . ( 39000 – 30,130 ) = rs . 8870 answer c"
Answer: c
Problem: if 30 men take 15 days to to complete a job , in how many days can 25 men finish that work ?
Options: a ) 18 , b ) 17 , c ) 16 , d ) 15 , e ) 14
Rationale: ans . 18 days
Answer: a
Problem: if 7 a = 8 b and ab ≠ 0 , what is the ratio of a / 8 to b / 7 ?
Options: a ) 16 / 14 , b ) 8 / 7 , c ) 1 , d ) 7 / 8 , e ) 64 / 49
Rationale: "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 7 a = 8 b here ' s one pair : a = 8 and b = 7 what is the ratio of a / 8 to b / 7 ? in other words , what is the value of ( a / 8 ) / ( b / 7 ) ? plug in values to get : ( a / 8 ) / ( b / 7 ) = ( 8 / 8 ) / ( 7 / 7 ) = 1 / 1 = 1 c"
Answer: c
Problem: an empty fuel tank is filled with brand z gasoline . when the tank is 3 / 4 empty , it is filled with brand y gasoline . when the tank is half empty again , it is filled with brand z gasoline . when the tank is half empty again , it is filled with brand y gasoline . at this time , what percent of the gasoline in the tank is brand z ?
Options: a ) 40 % , b ) 41 % , c ) 43.75 % , d ) 42 % , e ) 44 %
Rationale: "work with fraction of brand z in the tank . 1 st step : brand z is 1 2 nd step : brand z is 1 / 2 3 rd step : brand z is ( 3 / 4 ) * ( 1 / 2 ) + 1 / 2 = 7 / 8 4 th step : brand z is ( 1 / 2 ) * ( 7 / 8 ) = 7 / 16 = 43.75 % answer ( c )"
Answer: c
Problem: what will be the fraction of 20 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 8 , e ) none of above
Rationale: "explanation : it will 20 * 1 / 100 = 1 / 5 answer : option b"
Answer: b
Problem: a cistern is filled by a tap in 6 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 81 , b ) 85 , c ) 88 , d ) 91 , e ) 95
Rationale: "filling rate - leak rate = net rate 1 / 6.5 - leak rate = 1 / 7 leak rate = 2 / 13 - 1 / 7 = 1 / 91 the answer is d ."
Answer: d
Problem: 3 candidates contested in an election and received 4136 , 7636 , 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?
Options: a ) 45 % , b ) 49 % , c ) 50 % , d ) 51 % , e ) 62 %
Rationale: total number of votes polled = 4136 + 7636 + 11628 = 23400 required percentage = 11628 * 100 / 23400 = 50 % answer is c
Answer: c
Problem: in a hostel , the number of students decreased by 12 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 5.3 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 12 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.88 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.88 * 1.2 ) = > f ( new ) = 0.9469 f therefore the new cost of food must be 94.69 % of the old cost , or the cost of food must decrease by 5.3 % ( option e )"
Answer: e
Problem: if the radius of a cylinder is made 3 times and so is the height , what is the new volume of the cylinder divided by the old one ?
Options: a ) 27 . , b ) 2 . , c ) 6 . , d ) 4 . , e ) 10 .
Rationale: "let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 3 r ) ^ 2 ( 3 h ) v ' = 27 v a ) 27"
Answer: a
Problem: the sum of number of boys and girls in a school is 1150 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 92 , e ) 70
Rationale: "we have x + x % of 1150 = 1150 x + x / 100 * 1150 = 1150 25 / 2 * x = 1150 x = 1150 * 2 / 25 = 92 answer is d"
Answer: d
Problem: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 35 days to complete the same work . then q alone can do it in
Options: a ) 20 , b ) 22 , c ) 25 , d ) 28 , e ) 30
Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 35 work done by p , q and r in 1 day = 1 / 10 + 1 / 35 = 9 / 70 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 9 / 70 = > work done by p in 1 day = 9 / 140 = > work done by q and r in 1 day = 9 / 140 hence work done by q in 1 day = 9 / 140 â € “ 1 / 35 = 1 / 28 so q alone can do the work in 28 days answer is d ."
Answer: d
Problem: kim has 3 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 6 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25
Rationale: "total pairs = 6 c 2 = 15 ; same color pairs = 3 c 1 * 1 c 1 = 3 ; prob = 1 / 5 ans b"
Answer: b
Problem: simplify : 3005 - 3000 + 10
Options: a ) 2505 , b ) 2509 , c ) 2705 , d ) 2508 , e ) none of them
Rationale: 3005 - 3000 + 10 = 3005 - ( 3000 / 10 ) = 3005 - 300 = 2705 . answer is c
Answer: c
Problem: a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 8 / 15 . how many tennis balls did the retailer order originally .
Options: a ) 110 , b ) 114.28 , c ) 140 , d ) 160 , e ) 214
Rationale: white : yellow = x : ( x + 50 ) = 8 : 15 - - > 15 x = 8 x + 400 - - > x = 57.14 . the total # of balls originally x + x = 57.14 + 57.14 = 114.28 . answer : b .
Answer: b
Problem: when a merchant imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 94.50 , what was the total value of the item ?
Options: a ) $ 2,350 , b ) $ 2,850 , c ) $ 3,250 , d ) $ 3,400 , e ) $ 3,750
Rationale: let x be the value in excess of $ 1,000 . 0.07 x = 94.5 x = $ 1,350 the total value was $ 1,350 + $ 1,000 = $ 2,350 . the answer is a .
Answer: a
Problem: how many numbers are divisible by both 2 and 3 up to 300 ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: divide 300 by 6 , as the numbers which are divisible by both 2 and 3 are also divisible by 6 . the quotient obtained after dividing 300 by 6 is 50 , hence answer is 50 . option a
Answer: a
Problem: the result when a number subtracted from 150 is the same as the number added to 68 . what is the number ?
Options: a ) 110 , b ) 100 , c ) 109 , d ) 218 , e ) 210
Rationale: answer let the number be x . then , x - 68 = 150 - x â ‡ ’ 2 x = 150 + 68 = 218 â ‡ ’ 2 x = 218 â ˆ ´ x = 109 correct option : c
Answer: c
Problem: the radius of a cylinder is 9 m , height 12 m . the volume of the cylinder is :
Options: a ) 2200 , b ) 5500 , c ) 3054.9 , d ) 1100 , e ) 4400
Rationale: "cylinder volume = ï € r ( power 2 ) h = 22 / 7 ã — 9 ã — 9 ã — 12 = 3054.9 m ( power 3 ) answer is c ."
Answer: c
Problem: how many numbers up to 300 and 700 are divisible by 2 , 3 and 7 both together ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: ( 700 – 300 ) / 42 = 9 22 / 42 = > 9 numbers answer : a
Answer: a
Problem: if x * y = xy – 2 ( x + y ) for all integers x and y , then 3 * ( – 3 ) =
Options: a ) – 16 , b ) – 9 , c ) – 4 , d ) 4 , e ) 16
Rationale: "3 * ( - 3 ) = 3 * ( - 3 ) - 2 ( 3 + ( - 3 ) ) = - 9 - 0 = - 9 option ( b )"
Answer: b
Problem: total 90 cows 30 cow gives each 2 liter milk 30 cow gives each 3 / 4 liter milk 30 cow gives each 1 / 4 liter milk this is split into 3 son per each 30 cows & 30 liter milk how ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 30
Rationale: "30 cow 2 liter each = 60 liter 30 cow 3 / 4 liter each = 3 / 4 = 0.75 * 30 = 22.5 30 cow 1 / 4 liter each = 1 / 4 = 0.25 * 30 = 7.5 add 60 + 22.5 + 7.5 = 90 milk split into 3 son each 30 liter then 90 / 3 = 30 answer : e"
Answer: e
Problem: the ratio between the length and the breadth of a rectangular park is 1 : 3 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 124545 m , b ) 134561 m , c ) 156787 m , d ) 15450 m , e ) 120000 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 1 x metres and breadth = 3 x metres . then , 2 ( 1 x + 3 x ) = 1600 or x = 200 . length = 200 m and breadth = 600 m . area = ( 600 x 200 ) m 2 = 120000 m e"
Answer: e
Problem: the ratio of two quantities is incorrect when written as 10 to 14 . how should this ratio be written ?
Options: a ) 5 : 14 , b ) 10 : 7 , c ) 20 : 24 , d ) 5 : 7 , e ) it can not be determined from the information given
Rationale: a ratio should be reduced to the lowest common denominator . 10 : 14 means 10 x : 14 x which can be written as 5 ( 2 ) : 7 ( 2 ) . . . answer : d
Answer: d
Problem: cereal a is 11 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 1 : 3 , d ) 1 : 4 , e ) 3 : 4
Rationale: "2 % is 3 % - points below 5 % and 11 % is 6 % - points above 5 % . the ratio of a : b should be 3 : 6 = 1 : 2 . the answer is a ."
Answer: a
Problem: in a family 16 people eat only vegetarian , 9 people eat only non veg . , 12 people eat both veg and non veg . . how many people eat veg in the family ?
Options: a ) 28 , b ) 26 , c ) 22 , d ) 31 , e ) 21
Rationale: total people eat veg = only veg + both veg and non veg total = 16 + 12 = 28 answer = a
Answer: a
Problem: if the price of sugar rises from rs . 10 per kg to rs . 11 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 9 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 11 = x = 91 kg . ∴ reduction in consumption = 9 % . answer a"
Answer: a
Problem: the sum of the even numbers between 1 and n is 85 * 86 , where n is an odd number , then n = ?
Options: a ) 163 , b ) 171 , c ) 179 , d ) 185 , e ) 191
Rationale: "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 85 * 86 then a = 85 and n = 171 . the answer is b ."
Answer: b
Problem: total dinning bill of 6 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 21.84 , b ) 22.84 , c ) 23.84 , d ) 24.84 , e ) 25.48
Rationale: dinner bill of 6 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 6 = $ 25.48 answer : e
Answer: e
Problem: in a t . v . factory , an average of 63 tvs are produced per day for the fist 25 days of the months . a few workers fellill for the next 5 daysreducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?
Options: a ) 35 , b ) 33 , c ) 48 , d ) 50 , e ) 52
Rationale: production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 63 = 165 â ˆ ´ average for last 5 days = 165 / 5 = 33 b
Answer: b
Problem: a part - time employee ’ s hourly wage was increased by 25 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 9 % , b ) 15 % , c ) 20 % , d ) 50 % , e ) 100 %
Rationale: "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 25 % wage increase , the employee makes $ 1.25 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.25 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.25 to get : new # of hours = 100 / 1.25 ≈ 80 hours so , the number of hours decreases from 100 hours to ( approximately ) 80 hours . this represents a 20 % decrease ( approximately ) . answer : c"
Answer: c
Problem: a man rows his boat 120 km downstream and 92 km upstream , taking 4 hours each time . find the speed of the stream ?
Options: a ) 6 kmph , b ) 4 kmph , c ) 2 kmph , d ) 8 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 120 / ( 4 ) = 30 kmph speed upstream = d / t = 92 / ( 4 ) = 23 kmph the speed of the stream = ( 30 - 23 ) / 2 = 4 kmph answer : b"
Answer: b
Problem: a student completes a 3 part exam as follows . the student completes sections a in 4 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 10 : 3 , b ) 9 : 2 , c ) 7 : 1 , d ) 8 : 3 , e ) 11 : 2
Rationale: "the time spent on section b and section c is 28 minutes each . the ratio of c to a is 28 : 4 = 7 : 1 the answer is c ."
Answer: c
Problem: a is twice as good a workman as b and they took 10 days together to do the work b alone can do it in .
Options: a ) 25 days , b ) 88 days , c ) 30 days , d ) 11 days , e ) 13 days
Rationale: wc = 2 : 1 2 x + x = 1 / 10 x = 1 / 30 = > 30 days answer : c
Answer: c
Problem: which number can we add to 425897 to get a number exactly divisible by 456 ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "425897 / 456 = 933 with a remainder of 449 . we need to add 456 - 449 = 7 the answer is c ."
Answer: c
Problem: the speed at which a man can row a boat in still water is 9 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ?
Options: a ) 16 seconds , b ) 34 seconds , c ) 14 seconds , d ) 18 seconds , e ) 15 seconds
Rationale: "speed of the boat downstream = 9 + 3 = 12 kmph = 12 * 5 / 18 = 10 / 3 m / s hence time taken to cover 60 m = 60 * 3 / 10 = 18 seconds . answer : d"
Answer: d
Problem: the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 588 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 28 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .
Rationale: "answer is a : 28 let w be the width , so length is 3 w . therefore : w * 3 w = 588 , solving for , w = 14 , so 3 w - w = 2 w = 2 * 14 = 28"
Answer: a
Problem: a train covers a distance of 12 km in 10 minutes . if it takes 8 seconds to pass a telegraph post , then the length of the train is
Options: a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 8 ) m = 160 m answer : option d"
Answer: d
Problem: how many numbers from 15 to 65 are exactly divisible by 5 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12
Rationale: "option ' d ' 15 / 5 = 3 and 65 / 5 = 13 = = > 13 - 3 = 10 numbers"
Answer: d
Problem: if the area of a circle decreases by 66 % , then the radius of a circle decreases by
Options: a ) 20 % , b ) 18 % , c ) 36 % , d ) 64 % , e ) none of these
Rationale: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 66 ) % = ( 100 − 10 √ 64 ) % = 100 - 58 = 42 % answer e"
Answer: e
Problem: two cards are drawn together from a pack of 52 cards the probability that one is the spade and one is a heart is ?
Options: a ) 85 / 852 , b ) 45 / 69 , c ) 18 / 456 , d ) 13 / 102 , e ) 23 / 125
Rationale: "let s be the sample space then n ( s ) = 52 c 2 = ( 52 * 51 ) / ( 2 * 1 ) = 1326 let e be the event of getting 1 spade kings and 1 heart let n ( e ) = number of ways of chossing 1 spade out of 13 and 1 heart out of 13 = ( 13 c 1 * 13 c 1 ) = 13 * 13 = 169 p ( e ) = n ( e ) / n ( s ) = 169 / 1326 = 13 / 102 answer ( d )"
Answer: d