Cheukting/mathqa huggingface dataset:
Question (general): paul ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percent does he lose ?
Options: a ) 0 , b ) 25 , c ) 50 , d ) 30 , e ) 40
Rationale: let the original salary = $ 100 new final salary = 150 % of ( 50 % of rs . 100 ) = $ ( ( 150 / 100 ) * ( 50 / 100 ) * 100 ) = $ 75 . decrease = 25 % answer option b ) 25 .
Answer: b
Question (general): a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction u of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction u of n to the total would be 4 a / 24 a or 1 / 6 answer b"
Answer: b
Question (physics): if an object travels 80 feet in 4 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 7.25 , b ) 9.47 , c ) 11.58 , d ) 13.64 , e ) 15.92
Rationale: "80 feet / 4 seconds = 20 feet / second ( 20 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 13.64 miles / hour ( approximately ) the answer is d ."
Answer: d
Question (physics): two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer t between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) t = 18 , e ) 20
Rationale: "since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ."
Answer: d
Question (general): what is the greatest prime factor of 42 ^ 2 + 75 ^ 2 + 6300
Options: a ) 3 , b ) 7 , c ) 11 , d ) 13 , e ) 79
Rationale: "42 ^ 2 = ( 50 - 8 ) ( 50 - 8 ) = 1764 75 ^ 2 = ( 100 - 25 ) ( 100 - 25 ) = 5625 1764 + 5625 + 6300 = 13689 this number is divisible by 3 and 9 divide by 9 and get 1521 , the sum of this number is again a multiple of 9 , thus we can divide it one more time by 9 . we get 169 , and 169 is 13 ^ 2 . thus the answer is 13 . answer : d"
Answer: d
Question (physics): 12 men can complete a piece of work in 30 days . in how many days can 10 men complete that piece of work ?
Options: a ) 23 , b ) 27 , c ) 36 , d ) 27 , e ) 11
Rationale: "12 * 30 = 10 * x = > x = 36 days answer : c"
Answer: c
Question (general): if a - b = 4 and a ^ 2 + b ^ 2 = 80 , find the value of ab
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 32
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 80 - 16 = 64 = > ab = 32 answer : e"
Answer: e
Question (general): in the xy - plane the point ( - 2 - 3 ) is the centre of a circle , the point ( - 2 , 3 ) lies inside the circle and the point ( 6 , - 3 ) lies outside the circle . if the radius r of the circle r is an integer then r =
Options: a ) 6 , b ) 5 , c ) 4 , d ) 7 , e ) 2
Rationale: can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 6 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 6 , - 3 ) - - - > lesser than 8 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,3 ) - - - - > greater than 6 units . thus the radius is > 6 but < 8 and as it is an integer , the only possible value of radius = 7 units . d is the correct answer .
Answer: d
Question (physics): the timing of a college is from 11 p . m to 4.20 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 56 minutes , b ) 52 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 5 hours 20 minutes = 280 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 280 â € “ 20 ) / 5 = 52 minutes answer b"
Answer: b
Question (physics): efrida and frazer who live 10 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is three miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : b ."
Answer: b
Question (general): a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is ?
Options: a ) 130 , b ) 152 , c ) 225 , d ) 260 , e ) 180
Rationale: "let the total journey be x km then , ( 3 x / 5 ) + ( 7 x / 20 ) + 6.5 = x 12 x + 7 x + 20 * 6.5 = 20 x x = 130 km answer is a"
Answer: a
Question (other): find the fraction which has the same ratio to 2 / 3 that 3 / 5 has to 6 / 7
Options: a ) 1 / 5 , b ) 2 / 22 , c ) 3 / 4 , d ) 7 / 15 , e ) 5 / 6
Rationale: "p : 2 / 3 = 3 / 5 : 6 / 7 as the product of the means is equal to the product of the extremes . p * 6 / 7 = 2 / 3 * 3 / 5 p * 6 / 7 = 6 / 15 p = 7 / 15 = > p = 7 / 15 answer : d"
Answer: d
Question (general): how many of the positive divisors g of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "4 , 8,12 , 20,24 , 40,60 . ( 7 ) is the answer other way : factors of 120 = 2 ^ 3 * 3 * 5 separate 2 ^ 2 ( which means 4 ) now , calculate the number of other factors . g = 2 * 3 * 5 = total positive factors are 2 * 2 * 2 = 8 this 8 factors include 120 so subtract 1 from 8 ans is 7 = d"
Answer: d
Question (general): ( 9568422 x 558 ) = ?
Options: a ) 5846381256 , b ) 5339179476 , c ) 5346381356 , d ) 5846381406 , e ) 5346381456
Rationale: 9568422 x 558 = 5339179476 ans b
Answer: b
Question (gain): in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 70 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that an advanced trigonometry student is selected ?
Options: a ) 8 % , b ) 16 % , c ) 20 % , d ) 24 % , e ) 40 %
Rationale: "let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.7 x the number of students in beginner trigonometry is 4 / 5 * ( 2.5 x ) - 0.7 x = 1.3 x the number of students in advanced trigonometry is 0.2 x the percentage in advanced trigonometry is 0.2 x / 2.5 x = 8 % the answer is a ."
Answer: a
Question (geometry): if the diameter of circle r is 60 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 50 %
b ) 46 %
c ) 36 %
d ) 26 %
e ) 38 %
Rationale: let diameter of circle r , dr = 60 and diameter of circle s , ds = 100 radius of circle r , rr = 30 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 30 / 50 ) ^ 2 = ( 6 / 10 ) ^ 2 = 36 % answer : c
Answer: c
Question (gain): a small company reduced its faculty by approximately 13 percent to 263 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 224 , e ) e ) 302
Rationale: if x is the original number of employees , then after 13 % reduction in employees number is . 87 x but we are given . 87 x = 263 x = 302 so the original number of employees is 302 correct answer - e
Answer: e
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg . what is the weight of the new person ?
Options: a ) 90 , b ) 65 , c ) 85 , d ) 95 , e ) 80
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 70 = > 20 = x - 70 = > x = 20 + 70 = 90 answer is a ."
Answer: a
Question (physics): a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter m of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) m = 7 * 3 = 21 . c"
Answer: c
Question (physics): a train running at the speed of 120 km / hr crosses a pole in 12 seconds . what is the length of the train ?
Options: a ) 200 m , b ) 250 m , c ) 300 m , d ) 350 m , e ) 400 m
Rationale: "speed = ( 120 * 5 / 18 ) m / sec = ( 100 / 3 ) m / sec length of the train = ( speed x time ) = ( 100 / 3 * 12 ) m = 400 m . answer : e"
Answer: e
Question (general): the function f ( y ) represents the number of ways that prime numbers can be uniquely summed to form a certain number y such that y = a + b + c + d … where those summed variables are each prime and a ≤ b ≤ c ≤ d . . . for instance f ( 8 ) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5 . what is f ( 12 ) ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: it is so better to start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d
Answer: d
Question (general): what is the remainder when 220 * 165 * 110 * 55 is divided by 15 ?
Options: a ) 12 , b ) 15 , c ) 10 , d ) 11 , e ) 18
Rationale: "oa is ' c ' . oe : take the remainder from each of 220 / 15 , 165 / 15 and so on . . 220 / 15 gives remainder = 10 165 / 15 gives remainder = 0 110 / 15 gives remainder = 5 55 / 15 gives remainder = 10 the net remainder is the product of above individual remainders . i . e = 10 * 0 * 5 * 10 break them into pairs 10 * 0 / 15 gives remainder 10 and 5 * 10 / 15 gives remainder 5 so 10 * 5 / 15 gives remainder 5 . answer : c"
Answer: c
Question (physics): a person can swim in still water at 20 km / h . if the speed of water 12 km / h , how many hours will the man take to swim back against the current for 40 km ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 20 s = 12 us = 20 - 12 = 8 d = 40 t = 40 / 8 = 5 answer : c"
Answer: c
Question (general): a person was asked to state his age in years . his reply was , ` ` take my age 3 years hence , multiply it by 3 and subtract 3 times my age 3 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 92 , c ) 27 , d ) 26 , e ) 19
Rationale: "explanation : let the present age of person be x years . then , 3 ( x + 3 ) - 3 ( x - 3 ) = x < = > ( 3 x + 9 ) - ( 3 x - 9 ) = x < = > x = 18 . . answer : a ) 18"
Answer: a
Question (general): the average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 48 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 63 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 48 + 10 x 1.5 48 + 15 = 63 kg ans : ' b '"
Answer: b
Question (physics): a man rows his boat 105 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 5 kmph , b ) 7 kmph , c ) 12 kmph , d ) 8 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 105 / ( 2 1 / 2 ) = 42 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 42 - 18 ) / 2 = 12 kmph answer : c"
Answer: c
Question (physics): a can do a job in 20 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 14 days , b ) 16 days , c ) 24 days , d ) 11 days , e ) 19 days
Rationale: "c 1 / 20 + 1 / 30 = 1 / 12 12 * 2 = 24 days"
Answer: c
Question (general): if the average of 744 , 745 , 747 , 748 , 749 , 752 , 752 , 753 , 755 and x is 750 , what is the value of x ?
Options: a ) 750 , b ) 752 , c ) 754 , d ) 755 , e ) 756
Rationale: "sum of the deviations of the numbers in the set from the mean is always zero 744 , 745 , 747 , 748 , 749 , 752 , 752 , 753 , 755 mean is 750 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 750 + 5 = 755 d"
Answer: d
Question (geometry): the ratio , by volume , of soap to alcohol to water in a certain solution is 2 : 50 : 100 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 50 , b ) 200 , c ) 400 , d ) 625 , e ) 800
Rationale: "soap : alcohol initial ratio soap : alcohol : water - - > 2 : 50 : 100 initial soap : alcohol = 2 / 50 = 2 : 50 after doubled soap : alcohol = 2 * 2 / 50 = 4 : 50 initial soap : water = 2 / 100 = 2 : 100 after halved soap : water : 1 / 2 * 2 / 100 = 1 / 100 = 1 : 100 = 4 : 400 after soap : alcohol : water - - > 4 : 50 : 400 given alcohol 100 cumeter . ratio is 8 : 100 : 800 ( 4 : 50 : 400 ) for 100 cu meter of alcohol - - - 800 cu m water is required answer : e"
Answer: e
Question (general): if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "possible values of n = 12 , 24 , 36 and 48 . but it is 12 that can divide all the possible values of n . if we consider 48 , it will not divide 12 , 24 and 36 . hence , 12 is the value that must divide n . answer : b"
Answer: b
Question (general): little john had $ 20.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?
Options: a ) $ 17.05 , b ) $ 17.55 , c ) $ 17.15 , d ) $ 17.35 , e ) $ 17.25
Rationale: "john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 20.10 - 3.05 = $ 17.05 answer : a"
Answer: a
Question (general): 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 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1625
Rationale: "since pumping in additional 300 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 300 = 0.8 * { total } - - > { total } = 1,625 . answer : e ."
Answer: e
Question (geometry): the area of sector of a circle whose radius is 12 metro and whose angle at the center is 30 еў is ?
Options: a ) 35 m 2 , b ) 36 m 2 , c ) 37 m 2 , d ) 38 m 2 , e ) 40 m 2
Rationale: "30 / 360 * 22 / 7 * 12 * 12 = 37 m 2 answer : c"
Answer: c
Question (other): there are two positive numbers in the ratio 3 : 11 . if the larger number exceeds the smaller by 32 , then what is the smaller number ?
Options: a ) 8 , b ) 11 , c ) 12 , d ) 15 , e ) 17
Rationale: "let the two positive numbers be 3 x and 11 x respectively . 11 x - 3 x = 32 8 x = 32 = > x = 4 thus , the smaller number = 3 x = 12 . answer : c"
Answer: c
Question (geometry): if the volume and surface area of a sphere are numerically the same , then its radius is : ?
Options: a ) 2
b ) 4
c ) 1
d ) 5
e ) 3
Rationale: 4 / 3 π r ( power 3 ) = 4 π r ( power 2 ) r = 3 answer is e .
Answer: e
Question (general): there are 200 female managers in a certain company . find the total number t of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 300 , b ) t = 400 , c ) t = 500 , d ) 600 , e ) none of these
Rationale: "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."
Answer: c
Question (general): 60 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 61 , e ) 81
Rationale: "explanation : 60 + 5 * 12 / ( 180 / 3 ) = 60 + 5 * 12 / ( 60 ) = 60 + ( 5 * 12 ) / 60 = 60 + 1 = 61 . answer : d"
Answer: d
Question (gain): to a sugar solution of 3 liters containing 40 % sugar , one liter of water is added . the percentage of sugar in the new solution is ?
Options: a ) 20 % , b ) 30 % , c ) 25 % , d ) 15 % , e ) 50 %
Rationale: quantity of sugar = 40 * 3 / 100 = 1.2 kg new percentage = 1.2 / 4 * 100 = 30 % answer is b
Answer: b
Question (general): if 2 ^ 98 = 256 l + n , where land n are integers and 0 ≤ n ≤ 4 , what is the value of n ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: if 2 ^ 98 = 256 l + n and 0 < = n < = 4 , what is the value of n ? to solve this , note that 2 ^ 8 = 256 , so 2 ^ 98 = 2 ^ [ ( 8 * 12 ) + 2 ] = 4 * [ 256 * 256 * . . . . . . 12 times ] as this is a multiple of 256 , n can only be 0 . answer : a
Answer: a
Question (gain): a shopkeeper labeled the price of his articles so as to earn a profit of 20 % on the cost price . he then sold the articles by offering a discount of 5 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 24 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 120 . sp = rs . 120 - 5 % of 120 = rs . 120 - 6 = rs . 124 . gain = rs . 124 â € “ rs . 100 = rs . 24 therefore , gain / profit percent = 24 % . answer : option a"
Answer: a
Question (gain): by selling 11 pencils for a rupee a man loses 30 % . how many for a rupee should he sell in order to gain 30 % ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 11 , e ) 9
Rationale: "70 % - - - 12 130 % - - - ? 70 / 130 * 11 = 6 answer : d"
Answer: d
Question (physics): a can do a job in 18 days and b can do it in 30 days . a and b working together will finish thrice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 22 ½ days , c ) 33 3 / 4 days , d ) 12 ½ days , e ) none of these
Rationale: "explanation : 1 / 18 + 1 / 30 = 8 / 90 = 4 / 45 45 / 4 = 45 / 4 * 3 = 33 3 / 4 days answer : c"
Answer: c
Question (geometry): the length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size . if the area of the new rectangle is equal to 1800 square meters , what is the area of the original rectangle ?
Options: a ) 300 square meters
b ) 400 square meters
c ) 500 square meters
d ) 600 square meters
e ) 700 square meters
Rationale: if l and w be the original length and width of the rectangle and its area is given by l ? w after increase the length becomes 2 l and the width becomes 3 w . the area is then given by ( 2 l ) ? ( 3 w ) and is known . hence ( 2 l ) ? ( 3 w ) = 1800 solve the above equation to find l ? w 6 l ? w = 1800 l ? w = 1800 / 6 = 300 square meters , area of original rectangle correct answer a
Answer: a
Question (general): there are 200 female managers in a certain company . find the total number y of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 300 , b ) y = 400 , c ) y = 500 , d ) y = 600 , e ) none of these
Rationale: "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."
Answer: c
Question (gain): a and b r 2 men who enter into business and they invest rs 1000 , rs 2000 respectively . how will they divide the income of rs 5000
Options: a ) 33361667 , b ) 33391667 , c ) 33331666 , d ) 33331668 , e ) 33331669
Rationale: they invested in the ratio 1 : 2 a ' s share = 1 / 3 * 5000 = 1666 b ' s share = 2 / 3 * 5000 = 3333 answer : c
Answer: c
Question (general): if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 ø 2 ) ø 3 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: 4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 4 ø 3 = 2 ^ 4 / 2 ^ 3 = 2 the answer is a .
Answer: a
Question (other): a survey was taken among 100 brainiacs . of those surveyed , twice as many brainiacs likerebus teasers as math teasers . if 18 brainiacs like both rebus teasers and math teasers and 4 like neither kind of teaser , how many brainiacs like math teasers but not rebus teasers ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: let x brainiacs like only rebus teasers and y brainiacs like only math teasers . now , x + y = 100 - 18 - 4 = 78 . also given that , x + 18 = 2 ( y + 18 ) x = 2 y + 18 . 78 - y = 2 y + 18 3 y = 60 y = 20 so 20 brainiacs like math teasers but not rebus teasers answer : d
Answer: d
Question (gain): in a certain pond , 80 fish were caught , tagged , and returned to the pond . a few days later , 80 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 3,200 , d ) 4,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 2 / 80 ) * 100 = 2.5 % so , x * 2.5 % = 80 x = 3200 ans c ."
Answer: c