Cheukting/mathqa huggingface dataset:
Question (other): 210 reputed college students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 .
Answer: b
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 18 kmph , find the speed of the stream ?
Options: a ) 8 kmph , b ) 9 kmph , c ) 7 kmph , d ) 6 kmph , e ) 5 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 18 / 3 = 6 kmph . answer : d"
Answer: d
Question (general): a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 62 . if the marks secured by reema was written as 50 instead of 85 then find the correct average marks up to two decimal places .
Options: a ) 63 , b ) 74.31 , c ) 72.43 , d ) 73.43 , e ) can not be determined
Rationale: "total marks = 35 x 62 = 2170 corrected total marks = 2170 - 50 + 85 = 2205 correct average = 2205 / 35 = 63 answer : a"
Answer: a
Question (geometry): on the xy - coordinate plane , point a lies on the y - axis and point b lies on the x - axis . points a , b , and c form a right triangle with a 90 - degree angle at point c and the triangle has an area of 20 . if ac is parallel to the x - axis , and bc is parallel to the y - axis , which of the following could be the coordinates of point c ?
Options: a ) ( 8 , - 3 )
b ) ( 4 , 5 )
c ) ( - 5 , 7 )
d ) ( - 2 , - 20 )
e ) ( - 15 , - 3 )
Rationale: the area of the triangle formed will be : 1 / 2 * base * height = 1 / 2 * | ( x - coordinate of point c ) | * | ( y - coordinate of point c ) | = 20 thus | product of coordinates of point c | = 40 the answer is d .
Answer: d
Question (physics): 63 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) a ) 87 , b ) b ) 77 , c ) c ) 66 , d ) d ) 55 , e ) e ) 97
Rationale: "( 63 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 140 140 – 63 = 77 answer : b"
Answer: b
Question (physics): steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 90 mph . what is his average speed of travel for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 70 mph , e ) 66.67 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles . distance covered in the next 3 hours = speed * time = 90 * 3 = 270 miles . therefore , total distance covered = 80 + 270 = 350 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 350 / 5 = 70 miles per hour . choice d"
Answer: d
Question (probability): if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be odd ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 3 . answer : b ."
Answer: b
Question (general): in march mrs bil ' s earnings were 80 percent of the bil family ' s total income . in april mrs bil earned 10 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs bil ' s earnings were approximately what percent of the bil family ' s total income ?
Options: a ) 83 , b ) 56 , c ) 34 , d ) 12 , e ) 26
Rationale: lets say the family income is 100 in may , lee earned 80 family income is 20 in june , lee earned 20 % more than may , so it is ( 80 + 20 * 80 / 100 = 96 ) family income is same 20 in june lee ' s income percent is 96 * 100 / 116 ~ 83 ans is a
Answer: a
Question (general): how many prime numbers are between 29 / 4 and 87 / 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 29 / 4 = 7 . xxx 87 / 5 = 17 . xxx so we need to find prime numbers between 7 ( exclusive ) - 16 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b
Answer: b
Question (general): in digging a pond 25 m * 10 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 1750 , b ) 1000 , c ) 2866 , d ) 2787 , e ) 1121
Rationale: "25 * 10 * 5 = 1750 answer : a"
Answer: a
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 48 kmph , find the speed of the stream ?
Options: a ) 16 kmph , b ) 19 kmph , c ) 14 kmph , d ) 11 kmph , e ) 13 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 48 / 3 = 16 kmph . answer : a"
Answer: a
Question (general): what is the total number of integers between 100 and 500 ( exclusive ) that are divisible by 5 ?
Options: a ) 51 , b ) 63 , c ) 79 , d ) 66 , e ) 42
Rationale: 105 , 110 , 115 , . . . , 490,495 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 495 - 105 ) / ( 5 ) + 1 = 78 + 1 = 79 answer is c
Answer: c
Question (gain): a shopkeeper sold 10 articles at the cost price of 12 articles . then find the profit % or lost %
Options: a ) - 10 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: here 10 articles selling price = 12 articles cost price so the difference = 12 - 10 = 2 % of profit = 2 * 100 / 10 = 20 % correct option is d
Answer: d
Question (physics): venus travels around the sun at a speed of approximately 21.9 miles per second . the approximate speed is how many miles per hour ?
Options: a ) 64,420 , b ) 78,840 , c ) 83,160 , d ) 88,970 , e ) 94,320
Rationale: 21.9 * 3600 = 78,840 the answer is b .
Answer: b
Question (general): 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: 150 ml solution contains 45 ml sulphuric acid 400 ml solution contains 48 ml sulphuric acid adding 550 ml solution contains 93 ml sulphuric acid 93 / 550 ≈ 90 / 540 = 1 / 6 answer is d
Answer: d
Question (other): ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 18 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 9 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 18 = > x = 3 so deepak age is = 3 ( 3 ) = 9 answer : d"
Answer: d
Question (physics): a and b can do a piece of work in 8 days . b and c can do it in 12 days and a and c in 16 days . working together they will complete the work in how many days ?
Options: a ) 3.33 days , b ) 8.33 days , c ) 3.99 days , d ) 7.38 days , e ) 2.88 days
Rationale: a + b = 1 / 8 b + c = 1 / 12 c + a = 1 / 16 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ( a + b + c ) = 1 / 8 + 1 / 12 + 1 / 16 = 13 / 48 a + b + c = 13 / 96 96 / 13 = 7.38 days answer : d
Answer: d
Question (gain): a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 19 % home electronics ; 10 % food additives ; 24 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 90 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "14 % microphotonics ; 19 % home electronics ; 10 % food additives ; 24 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 19 + 10 + 24 + 8 ) = 25 % basic astrophysics . 25 % of 360 ° is 90 ° . answer : b ."
Answer: b
Question (general): a will was written such that an estate would be divided among 4 beneficiaries with the remainder donated to charity . one stipulation in the will is that no one beneficiary can receive an amount within 20 % of another ' s amount . if one of the beneficiaries received $ 40000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 4 beneficiaries ?
Options: a ) $ 12436 , b ) $ 13344 , c ) $ 71234 , d ) $ 15736 , e ) $ 19403
Rationale: 1 st - 40,000 . 2 nd - 0.8 * 40,000 = 32,000 3 rd - 0.8 * 32,000 = 25,600 4 th - 0.8 * 25,600 = ~ 20,480 range = 40,000 - 20,480 = 19520 answer : e .
Answer: e
Question (probability): a box contains 2 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 7 / 5 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Rationale: "my complicated version of your simple approach let the 5 black balls be bbbbb and 2 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 7 ! ) / ( 5 ! x 2 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 6 slots and 4 black ( bbbb ) and 2 red ( rrr ) they can be arranged in ( 7 ! ) / ( 4 ! x 2 ! ) hence required probability = [ ( 7 ! ) / ( 5 ! x 2 ! ) ] / [ ( 6 ! ) / ( 4 ! x 2 ! ) ] = 7 / 5 b"
Answer: b
Question (other): sachin is younger than rahul by 4 years . if their ages are in the respective ratio of 7 : 9 , how old is sachin ?
Options: a ) 24.9 , b ) 24.6 , c ) 24.2 , d ) 24.8 , e ) 24.5
Rationale: "let rahul ' s age be x years . then , sachin ' s age = ( x - 7 ) years . ( x - 7 ) / x = 7 / 9 2 x = 63 = > x = 31.5 hence , sachin ' s age = ( x - 7 ) = 24.5 years . answer : e"
Answer: e
Question (general): if a ( a + 5 ) = 6 and b ( b + 5 ) = 6 , where a ≠ b , then a + b =
Options: a ) − 5 , b ) − 9 , c ) 2 , d ) 46 , e ) 48
Rationale: "i . e . if a = 1 then b = - 6 or if a = - 6 then b = 1 but in each case a + b = - 6 + 1 = - 5 answer : option a"
Answer: a
Question (other): the l . c . m . of two numbers is 36 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 53 , e ) 54
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 36 or x = 6 . the numbers are 12 and 18 . hence , required sum = ( 12 + 18 ) = 30 . answer : option b"
Answer: b
Question (physics): a man can do a piece of work in 6 days , but with the help of his son , he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9
Rationale: "son ' s 1 day ' s work = ( 1 / 3 ) - ( 1 / 6 ) = 1 / 6 the son alone can do the work in 6 days answer is c"
Answer: c
Question (geometry): a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 70 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160 , b ) 240 , c ) 385 , d ) 440 , e ) 560
Rationale: "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 70 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 70 = 315 . total area = 70 + 315 = 385 answer : c ."
Answer: c
Question (general): what is the remainder when 7 ^ 74 - 5 ^ 74 is divided by 8 ?
Options: a ) 0 , b ) 2 , c ) 0 , d ) 3 , e ) none of these
Rationale: "easiest way for me : 7 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 48 + 1 ) ^ 37 - ( 24 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : c"
Answer: c
Question (general): the sum of the present ages of a , b , c is 57 years . 3 years ago their ages were in the ratio 1 : 2 : 3 . what is the present age of a ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: three years ago : a : b : c = 1 : 2 : 3 let a = 1 x , b = 2 x , and c = 3 x . today : ( x + 3 ) + ( 2 x + 3 ) + ( 3 x + 3 ) = 57 x = 8 so the present age of a is x + 3 = 11 the answer is d .
Answer: d
Question (general): a parking garage rents parking spaces for $ 12 per week or $ 30 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 264
Rationale: "12 $ per week ! an year has 52 weeks . annual charges per year = 52 * 12 = 624 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 30 = 360 $ 624 - 360 = 264 ans e"
Answer: e
Question (gain): the profit earned by selling an article for rs . 753 is equal to the loss incurred when the same article is sold for rs . 455 . what should be the sale price for making 50 % profit ?
Options: a ) 706 , b ) 786 , c ) 906 , d ) 896 , e ) 696
Rationale: "let c . p = rs . x then as given , ( 753 - x ) = ( x - 455 ) 2 x = 1208 x = 604 there fore s . p = 150 % of 604 = > rs . = rs . 906 answer : c"
Answer: c
Question (geometry): the sum of a number and its square is 1406 . what is the number ?
Options: a ) 1409
b ) 1402
c ) 1221
d ) 1406
e ) 8828
Rationale: explanation : by option verification 37 + 37 × 37 = 1406 answer : d
Answer: d
Question (general): 1 , 1 , 2 , 1 , 2 , 3 , 1 , 2 , 3 , 4 , 1 , 2 , __ ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "1,1 , 2,1 , 2,3 , 1,2 , 3,4 , 1,2 , __ ? looking at the series 1 12 123 1234 12 ( 3 ) 45 so the answer is 3 . answer : c"
Answer: c
Question (gain): the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 756 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1806 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 756 × 100 ) / ( 6 × 12 ) = rs . 1050 bg = bd – td = > 756 = bd - 1050 = > bd = 1050 + 756 = 1806 answer : option d"
Answer: d
Question (gain): one fourth of one third of two fifth of a number is 35 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 420 , c ) c ) 180 , d ) d ) 200 , e ) e ) 220
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 35 then x = 35 * 30 = 1050 40 % of 1050 = 420 answer : option b"
Answer: b
Question (physics): a flagstaff 17.5 m high casts a shadow of length 40.25 m . what will be the height of a building , which casts a shadow of length 28.75 m under similar conditions ?  
Options: a ) 12.5 m , b ) 10.5 m , c ) 14 , d ) 12 , e ) 10
Rationale: explanation : let the required height of the building be x meter more shadow length , more height ( direct proportion ) hence we can write as ( shadow length ) 40.25 : 28.75 : : 17.5 : x ⇒ 40.25 × x = 28.75 × 17.5 ⇒ x = 28.75 × 17.5 / 40.25 = 2875 × 175 / 40250 = 2875 × 7 / 1610 = 2875 / 230 = 575 / 46 = 12.5 answer : option a
Answer: a
Question (general): in a party every person shakes hands with every other person . if there were a total of 153 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 153 n ( n - 1 ) / 2 = 153 â ˆ ´ n = 18 answer : option d"
Answer: d
Question (general): in the xy - coordinate system , if ( m , n ) and ( m + 1 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 1 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 4 - - - > 5 = 2 k + 4 - - - > k = 1 / 2 . the answer is , therefore , ( a ) ."
Answer: a
Question (gain): if a lends rs . 25000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 1125 , b ) 1225 , c ) 1325 , d ) 1145 , e ) 2125
Rationale: "( 25000 * 1.5 * 3 ) / 100 = > 1125 answer : a"
Answer: a
Question (gain): 50 is what percent of 125 ?
Options: a ) 35 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 55 %
Rationale: 50 / 125 × 100 = 50 % answer : b
Answer: b
Question (other): in a certain corporation , there are 300 male employees and 150 female employees . it is known that 10 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 5 , b ) 5 / 15 , c ) 6 / 15 , d ) 3 / 10 , e ) 4 / 15
Rationale: p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.1 * 300 / 450 = 30 / 450 = 1 / 15 the sum of the probabilities is 6 / 15 = 2 / 5 the answer is c .
Answer: c
Question (general): the least number by which 72 must be multiplied in order to produce a multiple of 112 , is
Options: a ) 6 , b ) 12 , c ) 14 , d ) 18 , e ) 20
Rationale: "solution required numbers is divisible by 72 as well as by 112 , if it is divisible by their lcm , which is 1008 . now , 1008 when divided by 72 , gives quotient = 14 . required number = 14 . answer c"
Answer: c
Question (general): find the number , difference between number and its 3 / 5 is 58 .
Options: a ) 140 , b ) 143 , c ) 144 , d ) 145 , e ) 146
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 58 , = > ( 2 / 5 ) x = 58 = > 2 x = 58 * 5 , = > x = 145 answer : option d"
Answer: d
Question (general): the unit digit in the product ( 891 * 781 * 912 * 463 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 1 * 1 * 2 * 3 ) = 6 answer : c"
Answer: c
Question (general): find the value of 3 + 2 . ( 8 - 3 )
Options: a ) 25 , b ) 13 , c ) 17 , d ) 24 , e ) 19
Rationale: "3 + 2 . ( 8 - 3 ) = 3 + 2 ( 5 ) , = 3 + 2 * 5 , = 3 + 10 , = 13 , correct answer : ( d )"
Answer: d
Question (general): two numbers a and b are such that the sum of 5 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 3 , b ) 1 : 1 , c ) 3 : 4 , d ) 4 : 3 , e ) 5 : 5
Rationale: "5 / 100 a + 4 / 100 b = 2 / 3 ( 6 / 100 a + 8 / 100 b ) = > 1 / 20 a + 1 / 25 b = 1 / 25 a + 4 / 75 b = > ( 1 / 20 - 1 / 25 ) b = 1 / 25 a + 4 / 75 b ( 1 / 20 - 1 / 25 ) a = ( 4 / 75 - 1 / 25 ) b 1 / 100 a = 1 / 75 b a / b = 100 / 75 = 4 / 3 req ratio = 4 : 3 answer d"
Answer: d
Question (general): when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 5 of the remaining balance , what will be the final balance in her bank account ?
Options: a ) 300 , b ) 360 , c ) 400 , d ) 500 , e ) 575
Rationale: "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 5 of 300 = 60 total amount in her account = 360 answer b"
Answer: b
Question (general): in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 32 . in the company , what is the maximum number of non - managers in a department that has 9 managers ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: "9 / 7 * 32 = 41.1 the answer is c ."
Answer: c
Question (gain): a man ' s speed with the current is 22 km / hr and the speed of the current is 5 km / hr . the man ' s speed against the current is
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "man ' s rate in still water = ( 22 - 5 ) km / hr = 17 km / hr . man ' s rate against the current = ( 17 - 5 ) km / hr = 12 km / hr . answer : d"
Answer: d
Question (physics): machine z takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine z to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of z is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and a reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of z . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Question (general): a certain pair of used shoes can be repaired for $ 13.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 32.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?
Options: a ) 17.69 , b ) 14.85 , c ) 21.3 , d ) 16.5 , e ) 18.51
Rationale: "1 ) cost of repairing = 13.5 ( for one year ) , therefore for 2 years it would be $ 27 . 2 ) cost of new pair which will last for 2 years is $ 32 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe . i . e ( 32 - 27 ) / ( 27 ) * 100 = 18.51 % . ans is e"
Answer: e
Question (general): the average weight of a group of boys is 20 kg . after a boy of weight 31 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 31 kg joins the group , total weight of boys = 20 x + 31 so 20 x + 31 = 21 ( x + 1 ) = > x = 10 . answer : e"
Answer: e
Question (general): if x = 55 + 2 q and y = 4 q + 41 , then for what value of q , x is equal to y ?
Options: a ) - 14 , b ) 14 , c ) - 7 , d ) 7 , e ) 0
Rationale: explanation : x = y < = > 55 + 2 q = 4 q + 41 < = > 2 q = 14 < = > q = 7 . answer : d
Answer: d
Question (general): a man can swim in still water at 4 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 1.9 , c ) 1.1 , d ) 1.5 , e ) 0.75
Rationale: "m = 4 s = x ds = 4 + x us = 4 + x 4 + x = ( 4 - x ) 2 4 + x = 8 - 2 x 3 x = 4 x = 0.75 answer : e"
Answer: e