Cheukting/mathqa huggingface dataset:
Question (general): n and m are each 3 - digit integers . each of the numbers 1 , 2 , 3 , 7 , 8 and 9 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 19 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: "you have 6 digits : 1 , 2 , 3 , 7 , 8 , 9 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 1 and 9 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 2 * * and 3 * * ) . make the 2 * * number as large as possible and make the 3 * * number as small as possible . 298 and 317 ( difference is 19 ) or try and make a pair with ( 7 * * and 8 * * ) . make the 7 * * number as large as possible and make the 8 * * number as small as possible . we get 793 and 812 ( difference is 19 ) a"
Answer: a
Question (general): the captain of a cricket team of 11 members is 29 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 26 years
Rationale: "explanation : let the average age of the whole team by x years . 11 x â € “ ( 29 + 32 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 52 2 x = 52 x = 26 . so , average age of the team is 26 years . answer e"
Answer: e
Question (geometry): if the sides of a triangle are 31 cm , 29 cm and 15 cm , what is its area ?
Options: a ) 220.75 cm 2 , b ) 258 cm 2 , c ) 225.50 cm 2 , d ) 222.25 cm 2 , e ) 217.5 cm 2
Rationale: "the triangle with sides 31 cm , 29 cm and 15 cm is right angled , where the hypotenuse is 31 cm . area of the triangle = 1 / 2 * 29 * 15 = 217.5 cm 2 answer : e"
Answer: e
Question (other): in what ratio should a variety of rice costing rs . 6.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 4 , d ) 5 / 3 , e ) 7 / 6
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 6.5 ) = 5 / 4 answer : c"
Answer: c
Question (other): a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 7 / 16 , b ) 7 / 12 , c ) 7 / 19 , d ) 7 / 12 , e ) 7 / 15
Rationale: "drawing two balls of same color from seven green balls can be done in ⁷ c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = ⁷ c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 7 / 15 answer : e"
Answer: e
Question (general): the average monthly salary of 20 employees in an organisation is rs . 1400 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) 3600 , b ) 3890 , c ) 88798 , d ) 2789 , e ) 3500
Rationale: "explanation : manager ' s monthly salary rs . ( 1500 * 21 - 1400 * 20 ) = rs . 3500 . answer : e"
Answer: e
Question (physics): 4 men and 6 women can complete a work in 8 days , while 3 men and 7 women can complete it in 10 days . in how many days will 10 women complete it ?
Options: a ) 21 days , b ) 40 days , c ) 27 days , d ) 18 days , e ) 17 days
Rationale: "let 1 man ' s 1 day work = x and 1 woman ' s 1 day work = y . then , 4 x + 6 y = 1 / 8 and 3 x + 7 y = 1 / 10 solving these two equations , we get : x = 11 / 400 and y = 1 / 400 1 woman ' s 1 day work = ( 1 / 400 * 10 ) = 1 / 40 . hence , 10 women will complete the work in 40 days . answer : b"
Answer: b
Question (gain): a furniture dealer purchased a desk for $ 180 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) $ 40 , b ) $ 60 , c ) $ 80 , d ) $ 120 , e ) $ 100
Rationale: "purchase price = 180 selling price = x 180 + 0.4 * x = x 0.6 * x = 180 x = 300 profit = 300 - 180 = 120 answer : d"
Answer: d
Question (physics): a train 400 m long can cross an electric pole in 10 sec and then find the speed of the train ?
Options: a ) 165 kmph , b ) 144 kmph , c ) 172 kmph , d ) 175 kmph , e ) 178 kmph
Rationale: "length = speed * time speed = l / t s = 400 / 10 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : b"
Answer: b
Question (gain): a man can row his boat with the stream at 30 km / h and against the stream in 14 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 4 kmph , c ) 5 kmph , d ) 7 kmph , e ) 8 kmph
Rationale: "ds = 30 us = 14 s = ? s = ( 30 - 14 ) / 2 = 8 kmph answer : e"
Answer: e
Question (physics): 3 men and 7 women can complete a work in 10 days . but 4 men and 6 women need 8 days to complete the same work . in how many days will 10 women complete the same work ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: explanation : work done by 4 men and 6 women in 1 day = 1 / 8 work done by 3 men and 7 women in 1 day = 1 / 10 let 1 man does m work in 1 day and 1 woman does w work in 1 day . the above equations can be written as 4 m + 6 w = 1 / 8 - - - ( 1 ) 3 m + 7 w = 1 / 10 - - - ( 2 ) solving equation ( 1 ) and ( 2 ) , we get m = 11 / 400 and w = 1 / 400 amount of work 10 women can do in a day = 10 × ( 1 / 400 ) = 1 / 40 ie , 10 women can complete the work in 40 days answer : option b
Answer: b
Question (other): what is the characteristic of the logarithm of 0.0000134 ?
Options: a ) 5 , b ) - 5 , c ) 6 , d ) - 6 , e ) 7
Rationale: log ( 0.0000134 ) . since there are four zeros between the decimal point and the first significant digit , the characteristic is – 5 . answer : b
Answer: b
Question (general): in the game of dubblefud , red chips , blue chips and green chips are each worth 2 , 4 and 5 points respectively . in a certain selection of chips , the product of the point values of the chips is 16000 . if the number of blue chips in this selection doubles the number of green chips , how many red chips are in the selection ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: this is equivalent to : - 2 x * 4 y * 5 z = 16000 y / 2 = z ( given ) 2 x * 4 y * 5 y / 2 = 16000 2 x * y ^ 2 = 16000 / 10 2 x * y ^ 2 = 1600 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 2 as 2 * 2 * y ^ 2 = 1600 y ^ 2 = 400 y = 20 number of red chips = 2 hence b
Answer: b
Question (gain): compound interest of rs . 2000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .
Options: a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 315 , e ) none of the above
Rationale: "10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 2000 [ 1 + ( 5 / 100 ) ] ^ 3 - 2000 = 2000 [ ( 21 / 20 ) ^ 3 - 1 ] = 2000 ( 9261 - 8000 ) / 8000 = 2 * 1261 / 8 = 315 answer : d"
Answer: d
Question (geometry): the radius of a cone is 49 m , slant height is 35 m . find the curved surface area ?
Options: a ) 5160 , b ) 5390 , c ) 6430 , d ) 6720 , e ) 7280
Rationale: "cone curved surface area = ï € rl 22 / 7 ã — 49 ã — 35 = 154 ã — 35 = 5390 m ( power 2 ) answer is b ."
Answer: b
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 10 minutes , then the area of the park ( in sq . m ) is :
Options: a ) 153601 , b ) 153600 , c ) 153602 , d ) 153603 , e ) 240000
Rationale: "perimeter = distance covered in 10 min . = ( 12000 / 60 ) x 10 m = 2000 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 2000 or x = 200 . length = 600 m and breadth = 400 m . area = ( 600 x 400 ) m 2 = 240000 m 2 . answer : e"
Answer: e
Question (physics): a train covers a distance of 11 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) m , b ) m , c ) m , d ) m , e ) m
Rationale: "speed = ( 11 / 10 * 60 ) km / hr = ( 66 * 5 / 18 ) m / sec = 55 / 3 m / sec . length of the train = 55 / 3 * 6 = 110 m . answer : c"
Answer: c
Question (general): on average , the boys in the class have 20 pencils and the girls have 38 pencils . if the overall class average is 30 pencils , what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: ( 38 g + 20 b ) / ( g + b ) = 30 38 g + 20 b = 30 ( g + b ) 8 g = 10 b b / g = 4 / 5 the answer is d .
Answer: d
Question (gain): in a certain village , 200 litres of water are required per household per month . at this rate , if there are 5 households in the village , how long ( in months ) will 2000 litres of water last ?
Options: a ) 9 , b ) 5 , c ) 6 , d ) 2 , e ) 4
Rationale: "i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 200 litres of water are required per household per month . at this rate , if there aren 5 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 200 * 5 = 1000 ( m * n ) water available is 2000 ( p ) it will last 2 months ( p / m * n ) ans : d"
Answer: d
Question (physics): sum of two numbers prime to each other is 20 and their l . c . m . is 99 . what are the numbers ?
Options: a ) 8 and 12 , b ) 14 and 6 , c ) 19 and 1 , d ) 11 and 9 , e ) 12 and 9
Rationale: "as two numbers are prime , only two options satisfy ie option c and d . but option c will not make the product of numbers i . e 99 answer : d"
Answer: d
Question (physics): a train 180 m in length crosses a telegraph post in 20 seconds . the speed of the train is ?
Options: a ) 37 kmph , b ) 35 kmph , c ) 32 kmph , d ) 38 kmph , e ) 36 kmph
Rationale: "s = 180 / 20 * 18 / 5 = 32 kmph answer : c"
Answer: c
Question (gain): rs . 925 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 925 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1067 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 925 ) = rs . 31 rate = ( 100 x 31 / 925 x 3 ) = 124 / 111 % new rate = ( 124 / 111 + 4 ) % = 568 / 111 % new s . i . = rs . ( 925 x 568 / 111 x 3 / 100 ) rs . 142 ∴ new amount = rs . ( 925 + 142 ) = rs . 1067 . answer c"
Answer: c
Question (general): exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 35 , c ) 36 , d ) 60 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 7 and 12 ( in order 3 / 7 and 5 / 12 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 12 , which is 84 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 84 people in the room . therefore there are 3 / 7 * 84 = 36 people in the room under the age of 21 . answer : c ."
Answer: c
Question (physics): sides of a rectangular park are in the ratio 3 : 2 and its area is 2460 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) s . 122 , b ) s . 129 , c ) s . 129.76 , d ) s . 120 , e ) s . 121
Rationale: "3 x * 2 x = 2460 = > x = 20.24 2 ( 79.76 + 50 ) = 259.52 m 259.52 * 1 / 2 = rs . 129.76 answer : c"
Answer: c
Question (general): what is the sum of all the odd numbers between 24 and 50 , inclusive ?
Options: a ) 592 , b ) 481 , c ) 330 , d ) 475 , e ) 483
Rationale: "to solve this problem , all you have to do is take every even number between 24 and 50 and add them together . so we have 25 + 27 + 29 + 31 + 33 + 35 + 37 + 39 + 41 + 43 + 45 + 47 + 49 , which is 481 . final answer : b"
Answer: b
Question (general): if the average of r , b , c , 14 and 15 is 12 . what is the average value of r , b , c and 29
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: r + b + c + 14 + 15 = 12 * 5 = 60 = > r + b + c = 60 - 29 = 31 r + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d
Answer: d
Question (gain): if 15 % of a is the same as 30 % of b , then a : b is :
Options: a ) 1 : 4 , b ) 4 : 3 , c ) 6 : 7 , d ) 3 : 5 , e ) 2 : 1
Rationale: expl : 15 % of a i = 30 % of b = 15 a / 100 = 30 b / 100 = 2 / 1 = 2 : 1 answer : e
Answer: e
Question (physics): let a be the event that a randomly selected two digit number is divisible by 2 and let b be the event that a randomly selected two digit number is divisible by 5 . what is p ( a and b ) ?
Options: a ) 1 / 18 , b ) 1 / 10 , c ) 1 / 5 , d ) 1 / 3 , e ) 1 / 2
Rationale: "p ( a and b ) = 1 / 2 * 1 / 5 = 1 / 10 the answer is b ."
Answer: b
Question (geometry): what is the angle between the 2 hands of the clock at 8 : 24 pm ?
Options: a ) 100 ° , b ) 107 ° , c ) 106 ° , d ) 108 ° , e ) none of these
Rationale: "required angle = 240 – 24 × ( 11 / 2 ) = 240 – 132 = 108 ° answer d"
Answer: d
Question (physics): two friends c and d leave point c and point d simultaneously and travel towards point d and point c on the same route at their respective constant speeds . they meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively . how long will d take to cover the entire journey between point d and point c ?
Options: a ) 90 , b ) 80 , c ) 75 , d ) 60 , e ) 65
Rationale: let x per minute be the speed of c and y per minute be the speed of d . after meeting at a point , c travels for 32 mins and d travels for 50 mins . so distance covered by each of them post point of crossing c = 32 x and d = 50 y the distance covered by c and d before they cross each would be distance covered by d and c post crossing respectively . therefore distance covered by d before he meets c = 32 x time taken by d cover 32 x distance = 32 x / y mins therefore total time taken by d = 32 x / y + 50 mins . . . . . . . . . . . . . . . . . i we need to find value of x in terms of y to arrive at final answer . total distance = 32 x + 50 y combined speed of c and d = x + y therefore time taken before c and d meet en - route = ( 32 x + 50 y ) / ( x + y ) time taken by d reach destination after meeting c = 50 mins total travel time for d = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 mins . . . . . . . . . . . . . . . . . . . ii equate i and ii 32 x / y + 50 = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 ( 32 x + 50 y ) / y = ( 82 x + 100 y ) / ( x + y ) 32 x ^ 2 + 50 xy + 32 xy + 50 y ^ 2 = 82 xy + 100 y ^ 2 32 x ^ 2 + 82 xy - 82 xy + 50 y ^ 2 - 100 y ^ 2 = 0 32 x ^ 2 - 50 y ^ 2 = 0 32 x ^ 2 = 50 y ^ 2 16 x ^ 2 = 25 y ^ 2 taking square root . . ( since x and y denote speed , square root ca n ' t be negative ) 4 x = 5 y y = 4 x / 5 . . . . . . . . . . . . iii substitute in i = 32 x / ( 4 x / 5 ) + 50 = 32 x * 5 / 4 x + 50 = 40 + 50 = 90 mins a
Answer: a
Question (gain): a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 225 for it , the cost price of the cricket bat for a is :
Options: a ) 150 , b ) 120 , c ) 130 , d ) 160 , e ) 210
Rationale: "a 150 125 % of 120 % of a = 225 125 / 100 * 120 / 100 * a = 225 a = 225 * 2 / 3 = 150 ."
Answer: a
Question (gain): the workforce of company x is 50 % female . the company hired 20 additional male workers , and as a result , the percent of female workers dropped to 50 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 225 , b ) 220 , c ) 230 , d ) 235 , e ) 240
Rationale: "let x be the total worker then 0.5 x = female worker and 0.5 x is male worker then 20 male worker added 05 x / ( 0.5 x + 20 ) = 50 / 100 or 50 x = 50 * ( 0.5 x + 100 ) = 25 x + 5000 or 25 x = 5000 , x = 5000 / 25 = 200 total worker = 200 + 20 = 220 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 = 5 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 25
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 / 5 ^ 2 = 9 / 25 answer : e"
Answer: e
Question (other): in a class of 50 students , 20 play baseball , 15 play cricket and 11 play football . 7 play both baseball and cricket , 4 play cricket and football and 5 play baseball and football . if 18 students do not play any of these given sports , how many students play exactly two of these sports ?
Options: a ) 10 , b ) 46 , c ) 67 , d ) 68 , e ) 446
Rationale: notice that 7 play both baseball and cricket does not mean that out of those 7 , some does not play football too . the same for cricket / football and baseball / football . [ color = # ffff 00 ] { total } = { baseball } + { cricket } + { football } - { hc + ch + hf } + { all three } + { neither } for more checkadvanced overlapping sets problems [ / color ] 50 = 20 + 15 + 11 - ( 7 + 4 + 5 ) + { all three } + 18 - - > { all three } = 2 ; those who play only baseball and cricket are 7 - 2 = 5 ; those who play only cricket and football are 4 - 2 = 2 ; those who play only baseball and football are 5 - 2 = 3 ; hence , 5 + 2 + 3 = 10 students play exactly two of these sports . answer : a .
Answer: a
Question (physics): the speed of a train is 90 kmph . what is the distance covered by it in 10 minutes ?
Options: a ) 15 , b ) 87 , c ) 99 , d ) 77 , e ) 55
Rationale: "90 * 10 / 60 = 15 kmph answer : a"
Answer: a
Question (physics): in one hour , a boat goes 11 km / hr along the stream and 5 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 2 kmph , b ) 3 kmph , c ) 8 kmph , d ) 9 kmph , e ) 7 kmph
Rationale: "speed in still water = ( 11 + 5 ) / 2 = 8 kmph ans - c"
Answer: c
Question (general): a positive number x is multiplied by 5 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 5 / 3 , e ) 1 / 2
Rationale: "sq rt ( 5 x / 3 ) = x = > 5 x / 3 = x ^ 2 = > x = 5 / 3 ans - d"
Answer: d
Question (general): the price of commodity x increases by 40 paise every year , while the price of commodity y increases by 15 paise every year . if in 2001 , the price of commodity x was rs . 4.20 and that of y was rs . 6.30 , in which year commodity x will cost 40 paise more than the commodity y ?
Options: a ) 2010 , b ) 2001 , c ) 2012 , d ) 2011 , e ) 2009
Rationale: "suppose commodity x will cost 40 paise more than y after z years . then , ( 4.20 + 0.40 z ) - ( 6.30 + 0.15 z ) = 0.40 0.25 z = 0.40 + 2.10 z = 2.50 / 0.25 = 250 / 25 = 10 . therefore , x will cost 40 paise more than y 10 years after 2001 i . e . , 2011 . answer is d ."
Answer: d
Question (general): 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 8 years hence ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 76 , e ) 90
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 5 years , their ages will be 48 and 28 . sum of their ages = 48 + 28 = 76 . answer : d"
Answer: d
Question (gain): a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 2 / 7 % his yearly income diminishes by rs . 61.50 . his capital is
Options: a ) 22.378 , b ) 87.86 , c ) 246.0 , d ) 78.88 , e ) 127.71
Rationale: "explanation : capital = rs . x , then 5 / 7 x = 61.5 x = 87.86 answer : b ) rs . 87.86"
Answer: b
Question (general): the product of two numbers is 468 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 23 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 468 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 468 ) = 1225 x + y = 35 . option e"
Answer: e
Question (geometry): the ratio , by volume , of soap to alcohol to water in a certain solution is 4 : 20 : 60 . 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 ) 1200 , b ) 1250 , c ) 1300 , d ) 1400 , e ) 1450
Rationale: "soap : alcohol initial ratio soap : alcohol : water - - > 4 : 20 : 60 initial soap : alcohol = 4 / 20 = 4 : 20 after doubled soap : alcohol = 2 * 4 / 20 = 8 : 20 initial soap : water = 4 / 60 = 4 : 60 after halved soap : water : 1 / 2 * 4 / 60 = 2 / 60 = 2 : 60 after soap : alcohol : water - - > 8 : 20 : 240 - - > 2 : 5 : 60 given alcohol 100 cubic centimeter . ratio is 40 : 100 : 1200 ( 2 : 5 : 60 ) for 100 cubic centimeter of alcohol - - - 1200 cubic cm water is required ."
Answer: a
Question (general): if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 13 . what is the value of f ( 6 ) ?
Options: a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 4
Rationale: "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 13 then f ( 5 ) = 13 - 5 = 8 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 8 - 6 = 2 . answer : d . questions on funtions to practice :"
Answer: d
Question (geometry): what will be the area of a semi - circle of 14 metres diameter ?
Options: a ) 154 sq metres
b ) 77 sq metres
c ) 308 sq metres
d ) 22 sq metres
e ) none of these
Rationale: area of semicircle = ½ π r 2 = ½ × 22 ⁄ 7 × 7 × 7 = 77 m 2 answer b
Answer: b
Question (gain): the owner of a furniture shop charges his customer 10 % more than the cost price . if a customer paid rs . 2200 for a computer table , then what was the cost price of the computer table ?
Options: a ) 2299 , b ) 2000 , c ) 2670 , d ) 6725 , e ) 2601
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 2200 ( 100 / 110 ) = rs . 2000 answer : b"
Answer: b
Question (gain): one fourth of a solution that was 10 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options: a ) 24 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "say the second solution ( which was 1 / 4 th of total ) was x % salt , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.16 - - > x = 0.34 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.16 - - > x = 0.34 . answer : b ."
Answer: b
Question (general): if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 85 , what is the value of c â ˆ ’ a ?
Options: a ) 25 , b ) 80 , c ) 90 , d ) 140 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 170 - - 2 subtracting 1 from 2 we have c - a = 80 ; answer : b"
Answer: b