Cheukting/mathqa huggingface dataset:
Question (general): one man adds 3 liters of water to 12 liters of milk and another 4 liters of water to 10 liters of milk . what is the ratio of the strengths of milk in 2 mixtures ?
Options: a ) 11 : 21 , b ) 15 : 33 , c ) 28 : 25 , d ) 3 : 2 , e ) 31 : 33
Rationale: "strength of milk in the mixture = quantity of milk / total quantity of mixture strength of milk in the 1 st mixture = 12 / 15 strength of the milk 2 nd mixture = 10 / 14 the ratio of their strengths = 12 / 15 : 10 / 14 = 28 : 25 answer is c"
Answer: c
Question (general): 27 is a perfect cube . when x is added to the prime factor of 27 , the result is a prime number . what is x ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 8 , e ) 11
Rationale: 27 is 3 * 3 * 3 then a 3 + 1 = 4 b 3 + 3 = 6 c 3 + 5 = 8 d 3 + 8 = 11 e 3 + 11 = 14 here d is the only addition that gives a prime number .
Answer: d
Question (general): a part - time employee ’ s hourly wage was increased by 10 % . 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 ) 25 % , d ) 50 % , e ) 100 %
Rationale: "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 10 % wage increase , the employee makes $ 1.10 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.10 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.10 to get : new # of hours = 100 / 1.10 ≈ 90 hours so , the number of hours decreases from 100 hours to ( approximately ) 90 hours . this represents a 10 % decrease ( approximately ) . answer choice a is the closest answer ."
Answer: a
Question (gain): the price of stock decreased by 5 % last year and rose by 10 % this year . what is the net percentage change in the price of the stock ?
Options: a ) 0.2 % , b ) 0.8 % , c ) 1.2 % , d ) 1.6 % , e ) 4.5 %
Rationale: "( 100 % - 5 % ) * ( 100 % + 10 % ) = 0.95 * 1.10 = 1.045 = 104.5 % . the net percentage change in the price of the stock is ( + ) 4.5 % the answer is e"
Answer: e
Question (physics): the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 7 seconds than it was moving after 5 seconds ?
Options: a ) 4 , b ) 28 , c ) 15 , d ) 48 , e ) 63
Rationale: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 5 ) = 5 ^ 2 + 2 * 5 = 35 z ( 7 ) = 7 ^ 2 + 2 * 7 = 63 therefore z ( 7 ) - z ( 3 ) = 63 - 35 = 28 km / hr option b"
Answer: b
Question (gain): a soccer team played 280 games and won 65 percent of them . how many games did it win ?
Options: a ) 182 , b ) 100 , c ) 104 , d ) 150 , e ) 124
Rationale: "65 % of 280 = x 0.65 * 280 = x 182 = x answer : a"
Answer: a
Question (general): the difference between two numbers is 2395 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is
Options: a ) 120 , b ) 239 , c ) 476 , d ) 523 , e ) 526
Rationale: let the smaller number be x . then , larger number = ( 2395 + x ) therefore 2395 + x = ( 6 x + 15 ) ‹ = › 5 x = 2380 ‹ = › x = 476 . answer : c
Answer: c
Question (geometry): right triangle xyzs the base of the prism in the figure above . if xy = xz = â ˆ š 9 and the height of the prism is 6 , what is the volume of the prism ?
Options: a ) 3
b ) 27
c ) 13
d ) 12
e ) 15
Rationale: volume of prism = area of base * height = 1 / 2 * ( square root of 9 ) * ( square root of 9 ) * 6 = 27 answer : b
Answer: b
Question (general): on dividing 22 by a number , the quotient is 7 and the remainder is 1 . find the divisor .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 7
Rationale: "d = ( d - r ) / q = ( 22 - 1 ) / 7 = 21 / 7 = 3 c"
Answer: c
Question (general): the smallest number which when diminished by 5 , is divisible by 12 , 16 , 18 , 21 and 28 is
Options: a ) 1008 , b ) 1013 , c ) 1022 , d ) 1032 , e ) 1043
Rationale: "required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 5 = 1008 + 5 = 1013 answer : b"
Answer: b
Question (general): the ratio between x and y is 7 / 5 ; x is multiplied by y and y is multiplied by x , what is the ratio between the new values of x and y ?
Options: a ) 7 / 5 , b ) 5 / 7 , c ) 1 , d ) 49 / 25 , e ) it can not be determined
Rationale: ratio = 7 k / 5 k = 7 / 5 , 14 / 10 , etc . x is multiplied by y and y is multiplied by x - - > ( 7 k * 9 k ) / ( 9 k * 7 k ) = 1 answer : c
Answer: c
Question (general): when x is multiplied by 3 , the result is 14 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) 10 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: the equation that can be formed is : 3 x - 14 = 26 - x or , 4 x = 40 or , x = 10 . a answer .
Answer: a
Question (gain): raman , lakshmi and muthu enter into partnership . raman invests some money at the beginning , lakshmi invests double the amount after 6 months , and muthu invests thrice the amount after 8 months . if the annual gain be rs . 36000 . lakshmi ' s share is ?
Options: a ) 12000 , b ) 14000 , c ) 8000 , d ) 5000 , e ) 3000
Rationale: x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 36000 = 12000 answer : a
Answer: a
Question (general): in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 10 per square m ?
Options: a ) s . 9500 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 62000
Rationale: length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 10 * 950 = rs . 9500 a
Answer: a
Question (general): how many multiples of 4 are less than 6540 , and also multiples of 7 ?
Options: a ) 234 , b ) 208 , c ) 340 , d ) 237 , e ) 267
Rationale: "lcm of 4 & 7 = 28 tried dividing 6540 by 28 got quotient 233.5 ' so a is answer"
Answer: a
Question (physics): 31 of the scientists that attended a certain workshop were wolf prize laureates , and 18 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 24 , d ) d ) 29 , e ) d ) 36
Rationale: "lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 13 . . so total who won n = 11 + 18 = 29 . . d"
Answer: d
Question (physics): if 4 men can colour 48 m long cloth in 2 days , then 2 men can colour 36 m long cloth in
Options: a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 2 = 3 day . c"
Answer: c
Question (general): how many integers between 324,700 and 458,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,339
Rationale: "there is one number in hundred with 1 in th tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 324,700 and 458,600 is 458,600 - 324,700 = 133,900 - one number per each hundred gives 133,900 / 100 = 1,339 numbers . answer : e"
Answer: e
Question (general): a library has an average of 540 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 300 , b ) 276 , c ) 290 , d ) 285 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 540 x 5 + 240 x 25 ) / 30 ) = 290 answer : option c"
Answer: c
Question (general): on the number line , the number p is twice as many units from - 2 as - 2 is from 5 . if p is less than – 2 , what is the value of p ?
Options: a ) – 16 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: "distance between - 2 and 5 = 7 since number p is twice as many units from - 2 as - 2 is from 5 , therefore p can be - 16 since , p is less than - 2 , the value of p = - 16 answer a"
Answer: a
Question (gain): when sold at a 70 % discount , a sweater nets the merchant a 40 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 78.58 %
Rationale: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 70 % of 100 = 30 . . profit = 40 % . . therefore the wholesale purchase cost = x . . . . 1.4 x = 30 or x = 21.42 . . . marked price was 100 so . . . so answer is 78.58 % . . e"
Answer: e
Question (other): on a certain farm the ratio of horses to cows is 4 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 13 : 7 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 30 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: "originally , there were 4 k horses and k cows . 7 ( 4 k - 15 ) = 13 ( k + 15 ) 28 k - 13 k = 195 + 105 15 k = 300 k = 20 the difference between horses and cows is ( 4 k - 15 ) - ( k + 15 ) = 3 k - 30 = 30 the answer is a ."
Answer: a
Question (general): the total age of a and b is 12 years more than the total age of b and c . c is how many year younger than a
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : given that a + b = 12 + b + c = > a – c = 12 + b – b = 12 = > c is younger than a by 12 years answer : option b"
Answer: b
Question (geometry): if the diameter of circle r is 40 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 16 % , b ) 18 % , c ) 20 % , d ) 22 % , e ) 24 %
Rationale: "let diameter of circle r , dr = 40 and diameter of circle s , ds = 100 radius of circle r , rr = 20 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 20 / 50 ) ^ 2 = ( 4 / 10 ) ^ 2 = 16 % answer : a"
Answer: a
Question (general): if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Question (physics): mary can do a piece of work in 26 days . rosy is 30 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
Options: a ) 22 , b ) 20 , c ) 24 , d ) 26 , e ) 30
Rationale: "ratio of times taken by mary and rosy = 130 : 100 = 13 : 10 suppose rosy takes x days to do the work . 13 : 10 : : 26 : x = > x = 20 days . hence , rosy takes 20 days to complete the work . answer : b"
Answer: b
Question (general): if 2 ^ 4 , 3 ^ 3 , and 13 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 198 , b ) 288 , c ) 363 , d ) 396 , e ) 468
Rationale: i will go with e ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 13 ^ 1 = 468
Answer: e
Question (general): during a certain two - week period , 58 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 10 a , b ) 9 a , c ) 8 2 / 3 a , d ) 11 a , e ) 12 a
Rationale: "total movies = 100 . comedies = 58 . action + drama = 42 . since there were 5 times as many dramas as action movies , then action + 5 * action = 42 - - > action = a = 7 . comedies = = 8 2 / 3 a answer : c ."
Answer: c
Question (general): a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 56 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 500 , d ) 610 , e ) 700
Rationale: "let the maximum marks be x then , 33 % of x = 175 + 56 33 x / 100 = 231 x = 700 answer is e"
Answer: e
Question (other): if s and t are both odd prime numbers ands < t , then how many different positive integer factors does 2 sthave ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: s and t are both odd prime numbers - it means either s or t is not 2 and since prime numbers have only two factors - 1 and the number itself s and t each will have ( 1 + 1 ) = 2 factors hence 2 st will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer
Answer: d
Question (general): the maximum number of student amoung them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 910 , c ) 1001 , d ) 1911 , e ) none of these
Rationale: "solution required number of student = h . c . f of 1001 and 910 = 91 . answer a"
Answer: a
Question (general): a class of 20 students took a science test . 10 students had an average ( arithmetic mean ) score of 80 . the other students had an average score of 60 . what is the average score of the whole class ?
Options: a ) 70 , b ) 60 , c ) 55 , d ) 65 , e ) 85
Rationale: hear , 10 students had average score of 80 , so , 80 x 10 = 800 and 10 students had average score of 60 , so , 60 x 10 = 600 total no of student are 20 ( 800 + 600 ) / 20 = 70 correct ans is a
Answer: a
Question (gain): if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 900 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 922.50 . what is the value of x ?
Options: a ) 9000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: simple way to solve this question is to use options . from si , we know that x * y = 45,000 . now , put the value of x = 9000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 9000 + 5 % of 9000 = 9450 . 2 nd year , amount = 9450 + 5 % of 9450 = 9922.50 . we can see after 2 years interest = 9922.50 - 9000 = 922.50 . hence , it satisfies the question . hence a is the correct answer
Answer: a
Question (other): teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 153 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 175.50 , d ) rs . 258.50 , e ) none of these
Rationale: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 153 ) / \ x − 153 22.50 = > x − ( 153 / 22.50 ) = 1 . = > x − 153 = 22.50 . = > x = 175.50 rs . answer : c"
Answer: c
Question (general): the number of boxes in a warehouse can be divided evenly into 7 equal shipments by boat or 28 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 28 , b ) 33 , c ) 54 , d ) 81 , e ) 162
Rationale: "answer is the lcm of 7 and 28 = 28 answer a"
Answer: a
Question (physics): in what time will a railway train 50 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 5 sec , b ) 4 sec , c ) 3 sec , d ) 6 sec , e ) 1 sec
Rationale: "t = 50 / 36 * 18 / 5 = 5 sec answer : a"
Answer: a
Question (other): the marks obtained by vijay and amith are in the ratio 8 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 12 : 5 , b ) 12 : 1 , c ) 6 : 5 , d ) 12 : 2 , e ) 6 : 3
Rationale: 8 : 5 3 : 2 - - - - - - - 24 : 15 : 10 24 : 10 12 : 5 answer : a
Answer: a
Question (gain): 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 22 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 11.36 , c ) 7.4 , d ) 5 , e ) 6
Rationale: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 22 run rate needed = 250 / 22 = 11.36 answer : option b"
Answer: b
Question (general): x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 9 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9
Rationale: "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 9 ^ 2 = 1 / 9 answer : c"
Answer: c
Question (physics): a train running at the speed of 90 km / hr crosses a pole in 5 seconds . find the length of the train .
Options: a ) 150 meter , b ) 145 meter , c ) 140 meter , d ) 125 meter , e ) none of these
Rationale: "explanation : speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time = 25 * 5 = 125 meter option d"
Answer: d
Question (general): find the mean proportional between 64 & 81 ?
Options: a ) a ) 59 , b ) b ) 61 , c ) c ) 63 , d ) d ) 72 , e ) e ) 67
Rationale: "formula = √ a × b a = 64 and b = 81 √ 64 × 81 = 8 × 9 = 72 d"
Answer: d
Question (general): if ( a + b ) = 12 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 6 . , e ) - 2 .
Rationale: "given a + b = 12 = > a = 12 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 12 - b + 3 - c = > 15 - ( b + c ) = > 15 - 9 = 6 . option d . . ."
Answer: d
Question (geometry): if the area of a circle is 64 pi square feet , find its circumference .
Options: a ) 65 pi feet , b ) 43 pi feet , c ) 42 pi feet , d ) 18 pi feet , e ) 16 pi feet
Rationale: "the area is given by pi * r * r . hence pi * r * r = 64 pi r * r = 64 ; hence r = 8 feet the circumference is given by 2 * pi * r = 2 * pi * 8 = 16 pi feet correct answer e"
Answer: e
Question (general): what is the lowest positive integer that is divisible by each of the integers 1 through 8 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 5020
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , and 2 ^ 3 . the lcm is 1 * 2 ^ 3 * 3 * 5 * 7 = 840 the answer is b ."
Answer: b
Question (geometry): what is the perimeter of an isosceles right angled triangle . the area of the isosceles right angled triangle is 50 .
Options: a ) 25
b ) 36
c ) 25
d ) 30
e ) 34.14
Rationale: an isosceles right angled triangle has both the base and height same . the area of an isosceles triangle = 1 / 2 * base * height since height = base 1 / 2 * height * height = 1 / 2 * height ^ 2 = 50 height ^ 2 = 100 height = 10 = base since we know the base and height . we will calculate the hypotenuse using pythagoras base ^ 2 + height ^ 2 = hypotenuse ^ 2 10 ^ 2 + 10 ^ 2 = hypotenuse ^ 2 hypotenuse ^ 2 = 200 hypotenuse = 14.14 perimeter of the triangle = 10 + 10 + 14.14 = 34.14 ans : e
Answer: e
Question (physics): here 10 programmers , type 10 lines within 10 minutes then 60 lines can type within 60 minutes . how many programmers are needed ?
Options: a ) 16 , b ) 10 , c ) 6 , d ) 60 , e ) 50
Rationale: 10 10 programmer 10 line 10 mins . 10 programmer 20 line 20 mins . . . . . 10 programmer 60 line 60 mins . answer : d
Answer: d
Question (gain): in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are strategy majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 13
Rationale: "pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are strategy majors is s = 13 . the answer is e ."
Answer: e
Question (general): in a store , the total price for 25 shirts is $ 400 and the total price for 75 sweaters is $ 1500 . by how much does the average ( arithmetic mean ) price of a sweater exceed that of a shirt in this store ?
Options: a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 5
Rationale: the average price of a shirt is : $ 400 / 25 = $ 16 . the average price of a sweater is : $ 1500 / 75 = $ 20 . the difference in price is : $ 20 - $ 16 = $ 4 . the answer is d .
Answer: d
Question (physics): jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 6 hours . how long would it take taimour to paint the fence alone ?
Options: a ) 6 hours , b ) 8 hours , c ) 18 hours , d ) 24 hours , e ) 32 hours
Rationale: "i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 6 = > 1 / 18 working alone taimour can do the job in 1 = 1 / 18 * hours = > 18 answer c"
Answer: c
Question (general): if the least common multiple of two prime numbers x and y is 10 , where x < y , then the value of 3 x + y is
Options: a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 21
Rationale: "lcm ( x , y ) = 10 and both x an y are prime . the only values of x and y can be 2 and 5 ( x = 2 and y = 5 ) 3 x + y = 3 * 2 + 5 = 11 correct option : c"
Answer: c
Question (gain): if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 800 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 820 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 40,000 . now , put the value of x = 8000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 8000 + 5 % of 8000 = 8400 . 2 nd year , amount = 8400 + 5 % of 8400 = 8820 . we can see after 2 years interest = 8820 - 8000 = 820 . hence , it satisfies the question . hence a is the correct answer"
Answer: a
Question (gain): i had 30 donuts when i left home this morning but only 9 when i came back home . what percentage of the donuts are missing ?
Options: a ) 70 , b ) 65 , c ) 55 , d ) 75 , e ) 60
Rationale: 30 - 9 = 21 21 / 30 or 7 / 10 7 / 10 = 70 / 100 = 70 % answer is a
Answer: a
Question (geometry): a semicircle has a radius of 10 . what is the approximate perimeter of the semicircle ?
Options: a ) 27 , b ) 33 , c ) 39 , d ) 45 , e ) 51
Rationale: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 10 + 2 * 10 which is about 51 . the answer is e ."
Answer: e
Question (general): find the average of the first 19 natural numbers ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: average of the first ' n ' natural numbers = ( n + 1 ) / 2 we get ( 19 + 1 ) / 2 = 10 answer : c
Answer: c