regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 4 pumps work to empty the tank in 1 day ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: the required number of working hours per day x , more pumps , less working hours per day ( indirect ) less days , more working hours per day ( indirect ) pumps 4 : 3 , days 1 : 2 } : : 8 : x therefore 4 * 1 * x = 3 * 2 * 8 , x = ( 3 * 2 * 8 ) / 4 x = 12 correct answer ( d )
Answer: d
Problem: peter invests a sum of money and gets back an amount of $ 810 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
Options: a ) 670 , b ) 683 , c ) 698 , d ) 744 , e ) 700
Rationale: since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 810 = 44 interest earned for 3 years = 44 * 3 = 132 amount invested = 815 - 132 = 683 answer : b
Answer: b
Problem: a envelop weight 9.2 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.6 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.36 kg
Rationale: "800 * 9.2 7360.0 gm 7.36 kg answer : e"
Answer: e
Problem: what least number should be added to 1022 , so that the sum is completely divisible by 25 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 5
Rationale: "1022 ã · 25 = 40 with remainder = 22 22 + 3 = 25 . hence 3 should be added to 1022 so that the sum will be divisible by 25 answer : option b"
Answer: b
Problem: a hostel had provisions for 250 men for 44 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 55 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 44 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 44 250 × 44 = 200 x 5 × 44 = 4 x x = 5 × 11 = 55 answer a"
Answer: a
Problem: the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8339 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6825 , b ) rs . 6721 , c ) rs . 6725 . , d ) rs . 4298 , e ) rs . 6729
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8339 ( 100 / 124 ) = rs . 6725 . answer : c"
Answer: c
Problem: 63 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 22 , b ) 77 , c ) 29 , d ) 64 , e ) 21
Rationale: "63 + 5 * 12 / ( 180 / 3 ) = 63 + 5 * 12 / ( 60 ) = 63 + ( 5 * 12 ) / 60 = 63 + 1 = 64 . answer : d"
Answer: d
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.45 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 318 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: 12 * 1.75 + 0.45 * 12 * 55 = 318 hence - a
Answer: a
Problem: if ( - 6 ) ^ ( 2 x ) = 6 ^ ( 7 + x ) and x is an integer , what is the value of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 8 , e ) 7
Rationale: "since x is an integer , ( - 6 ) ^ 2 x is always positive . so , 6 ^ 2 x = 6 ^ ( 7 + x ) 2 x = 7 + x x = 7 answer : e"
Answer: e
Problem: a hen leaps 3 leaps for every 2 leaps of a duck , but 4 leaps of the duck are equal to 3 leaps of the hen . what is the ratio of the speed of the hen to that of the duck ?
Options: a ) 2 : 1 , b ) 3 : 4 , c ) 4 : 3 , d ) 1 : 4 , e ) 5 : 6
Rationale: "given ; 4 duck = 3 hen ; or , duck / hen = 3 / 4 ; let hen ' s 1 leap = 4 meter and ducks 1 leap = 3 meter . then , ratio of speed of hen and duck = 4 * 3 / 3 * 2 = 2 : 1 ' ' answer : 2 : 1 ;"
Answer: a
Problem: praveen starts business with rs . 3640 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 7500 , b ) s . 8000 , c ) s . 8500 , d ) s . 9000 , e ) s . 9360
Rationale: "let hari ’ s capital be rs . x . then , 3640 * 12 / 7 x = 2 / 3 = > 14 x = 131040 = > x = 9360 . answer : e"
Answer: e
Problem: salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 20 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 60 % , b ) 50 % , c ) 40 % , d ) 30 % , e ) 20 %
Rationale: "let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.20 0.2 x = 0.10 x = 0.5 = 50 % the answer is b ."
Answer: b
Problem: how many positive integers q between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?
Options: a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26
Rationale: 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .
Answer: e
Problem: rs . 850 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 . 850 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1058 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 850 ) = rs . 106 rate = ( 100 x 106 / 850 x 3 ) = 212 / 51 % new rate = ( 212 / 51 + 4 ) % = 416 / 51 % new s . i . = rs . ( 850 x 416 / 51 x 3 / 100 ) rs . 208 . ∴ new amount = rs . ( 850 + 208 ) = rs . 1058 . answer c"
Answer: c
Problem: a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 2.5 grams per cubic centimeter and mineral y weighs 4 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )
Options: a ) 3 , 400,000 , b ) 2 , 800,000 , c ) 55,000 , d ) 28,000 , e ) 280
Rationale: "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 2.5 gms in 400,000 cm ^ 3 , x = 2.5 * 400,000 = 1 , 000,000 grams in 1 cm ^ 3 , y is 4 gms in 600,000 cm ^ 3 , y = 4 * 600,000 = 2 , 400,000 gms total gms in 1 m ^ 3 = 1 , 000,000 + 2 , 400,000 = 3 , 400,000 answer : a"
Answer: a
Problem: it takes ten minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video , rounded to the nearest hundredth ?
Options: a ) 13.42 , b ) 13.86 , c ) 14.25 , d ) 14.63 , e ) 14.88
Rationale: "the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 10 ) = 1 / 600 of the video per second . the combined rate is 1 / 15 + 1 / 600 = 41 / 600 of the video per second . the time required to load the video is 600 / 41 = 14.63 seconds . the answer is d ."
Answer: d
Problem: a certain scholarship committee awarded scholarships in the amounts of $ 1250 , $ 2500 and $ 4000 . the committee awarded twice as many $ 2500 scholarships as $ 4000 and it awarded 3 times as many $ 1250 scholarships as $ 2500 scholarships . if the total of $ 75000 was awarded in $ 1250 scholarships , how many $ 4000 scholarships were awarded ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 15
Rationale: since the starting point is given as the $ 4000 scholarship , assume $ 4000 scholarships to be x by the given information , $ 2500 scholarships = 2 x and $ 1250 scholarships = 6 x gievn : total $ 1250 scholarships = $ 75000 6 x * 1250 = 75000 solve for x = 10 option d
Answer: d
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 6 eggs . if the cost of each pound of rice is $ 0.33 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 33 , d ) 44 , e ) 55
Rationale: "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 33 cents ; a half - liter of kerosene costs as much as 6 eggs - - > 6 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 12 eggs = 12 / 12 * 33 = 33 cents . answer : c ."
Answer: c
Problem: a pupil ' s marks were wrongly entered as 73 instead of 40 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 18 , b ) 82 , c ) 66 , d ) 27 , e ) 77
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 40 ) = > x / 2 = 33 = > x = 66 . answer : c"
Answer: c
Problem: a baseball card decreased in value 25 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32.5 % , d ) 36 % , e ) 72 %
Rationale: "let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 25 / 100 ) * 100 = 75 after second year , value of baseball card = ( 1 - 10 / 100 ) * 75 = 67.5 total percent decrease of the card ' s value over the two years = ( 100 - 67.5 ) / 100 * 100 % = 31.5 % answer c"
Answer: c
Problem: if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: "total nos of ways in which we can choose n = 96 n ( n + 1 ) ( n + 2 ) will be divisible by 8 ? case 1 : n = odd then n + 2 = odd & n + 1 will be even i . e this needs get divided by 8 , hence is a multiple of 8 so we have 8 . . 96 = 12 multiples to fill the n + 1 pos hence 12 ways case 2 : n is even then n + 2 will be even & the product will be divisible by 24 & thus 8 so nos of values that can be used for n = 2 . . . . 96 ( all even nos ) i . e 48 nos total = 48 + 12 = 60 ways so reqd p = 60 / 96 = 5 / 8 ; answer : d"
Answer: d
Problem: a car going at 40 miles per hour set out on an 60 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?
Options: a ) 45 , b ) 60 , c ) 53 , d ) 55 , e ) 50
Rationale: "let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 40 m per hour = 1.5 hours distance travelled by car a = 40 * 1.5 = 60 miles since car b catches up car a at 10 : 30 , time = 60 mins = 1 hour speed of car b = 60 / ( 1 ) = 60 miles per hour answer b"
Answer: b
Problem: 1 = 5,2 = 25,3 = 253,4 = 150,5 = 225 then 150 = ?
Options: a ) 1 , b ) 255 , c ) 4 , d ) 445 , e ) 235
Rationale: "1 = 5,2 = 25,3 = 253,4 = 150,5 = 225 then 150 = ? 150 = 4 check the fourth eqn . answer : c"
Answer: c
Problem: a dealer offers a cash discount of 16 % and still makes a profit of 25 % when he further allows 60 articles to be sold at the cost price of 50 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
Options: a ) 50 % , b ) 60 % , c ) 70 % , d ) 75 % , e ) 78 + ( 4 / 7 ) %
Rationale: "given cash discount - 16 % profit - 25 % items sold - 60 price sold at = list price of 50 assume list price = $ 10 total invoice = $ 500 - 16 % cash discount = $ 420 let cost price of 60 items be x so total cost = 60 * x given the shopkeeper had a profit of 25 % 60 * x * 125 / 100 = 420 or x = $ 7 * 4 / 5 = $ 28 / 5 which means his products were listed at $ 10 which is a 78 + ( 4 / 7 ) % markup over $ 28 / 5 answer e"
Answer: e
Problem: if n divided by 8 has a remainder of 1 , what is the remainder when 3 times n is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 7 , d ) 5 , e ) 6
Rationale: as per question = > n = 8 p + 1 for some integer p hence 3 n = > 24 q + 3 = > remainder = > 3 for some integer q hence b
Answer: b
Problem: the volume of a cube is 2197 cc . find its surface .
Options: a ) 864 , b ) 1014 , c ) 1299 , d ) 1268 , e ) 1191
Rationale: a 3 = 2197 = > a = 13 6 a 2 = 6 * 13 * 13 = 1014 answer : b
Answer: b
Problem: 15 business executives and 3 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 150 , b ) 131 , c ) 115 , d ) 90 , e ) 45
Rationale: "there are 15 business exec and in each handshake 2 business execs are involved . hence 15 c 2 = 105 also , each of 15 exec will shake hand with every 3 other chairmen for total of 45 handshake . total = 45 + 105 = 150 ans : a"
Answer: a
Problem: if pintu is coded as 79523 in a certain code language , how would you code mumbo in the same language ?
Options: a ) 43426 , b ) 14236 , c ) 13436 , d ) 14263 , e ) 15263
Rationale: "1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . mumbo is 43426 . . . answer : a"
Answer: a
Problem: a is twice as fast as b . if b alone can do a piece of work in 18 days , in what time can a and b together complete the work ?
Options: a ) 10 , b ) 16 , c ) 18 , d ) 6 , e ) 12
Rationale: "a can do the work in 18 / 2 i . e . , 9 days . a and b ' s one day ' s work = 1 / 9 + 1 / 18 = ( 2 + 1 ) / 18 = 1 / 6 so a and b together can do the work in 6 days . answer : d"
Answer: d
Problem: the area of a triangle is with base 5.5 m and height 6 m ?
Options: a ) 11 m 2 , b ) 16.5 m 2 , c ) 18.5 m 2 , d ) 19.5 m 2 , e ) 12 m 2
Rationale: "1 / 2 * 5.5 * 6 = 16.5 m 2 answer : b"
Answer: b
Problem: working together , printer a and printer b would finish the task in 15 minutes . printer a alone would finish the task in 45 minutes . how many pages does the task contain if printer b prints 3 pages a minute more than printer a ?
Options: a ) 125 , b ) 135 , c ) 145 , d ) 155 , e ) 165
Rationale: "15 * a + 15 * b = x pages in 15 mins printer a will print = 15 / 45 * x pages = 1 / 3 * x pages thus in 15 mins printer printer b will print x - 1 / 3 * x = 2 / 3 * x pages also it is given that printer b prints 3 more pages per min that printer a . in 15 mins printer b will print 45 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 45 = > x = 135 pages answer : b"
Answer: b
Problem: the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 8400 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 5725 , b ) rs . 5275 , c ) rs . 6275 , d ) rs . 6720 , e ) none of these
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8400 ( 100 / 125 ) = rs . 6720 . answer : d"
Answer: d
Problem: if you write down all the numbers from 1 to 100 , then how many times do you write 3 ?
Options: a ) 11 , b ) 18 , c ) 20 , d ) 21 , e ) 22
Rationale: "explanation : explanation : clearly , from 1 to 100 , there are ten numbers with 3 as the unit ' s digit - 3 , 13 , 23 , 33 , 43 , 53 , 63 , 73 , 83 , 93 ; and ten numbers with 3 as the ten ' s digit - 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 . so , required number = 10 + 10 = 20 . answer : c"
Answer: c
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 10 and 11 . the larger of the two numbers is :
Options: a ) 276 , b ) 253 , c ) 322 , d ) 345 , e ) 395
Rationale: "clearly , the numbers are ( 23 x 10 ) and ( 23 x 11 ) . larger number = ( 23 x 11 ) = 253 . answer : option b"
Answer: b
Problem: at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 5 years ?
Options: a ) 4 % , b ) 3 6 / 7 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 250 = ( 1750 x 5 xr ) / 100 250 = ( 175 xr ) / 2 500 = ( 175 xr ) r = 500 / 175 r = 2 6 / 7 % answer : option c"
Answer: c
Problem: tim and é lan are 60 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 30 miles . , b ) 35 miles . , c ) 40 miles . , d ) 60 miles . , e ) 65 miles .
Rationale: tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice c meet the 2 : 1 ( tim : elan = 40 : 20 ) ratio of maintaining total distance traveled 60 miles so correct answer c
Answer: c
Problem: if y is 90 % greater than x , than x is what % less than y ?
Options: a ) 35.7 % , b ) 39.8 % , c ) 43.2 % , d ) 47.4 % , e ) 51.2 %
Rationale: "y = 1.9 x x = y / 1.9 = 10 y / 19 x is 9 / 19 less which is 47.4 % less than y . the answer is d ."
Answer: d
Problem: what is the length of a bridge ( in meters ) , which a train 166 meters long and travelling at 45 km / h can cross in 40 seconds ?
Options: a ) 310 , b ) 318 , c ) 326 , d ) 334 , e ) 342
Rationale: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 40 seconds , the train can travel 25 / 2 * 40 = 500 meters 500 = length of train + length of bridge length of bridge = 500 - 166 = 334 meters the answer is d ."
Answer: d
Problem: the average weight of 10 persons increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 107 kg , b ) 80 kg , c ) 120 kg , d ) 90 kg , e ) 100
Rationale: "solution total weight increased = ( 10 x 4.2 ) kg = 42 kg . weight of new person = ( 65 + 42 ) kg = 107 kg . answer a"
Answer: a
Problem: if 5 < x < 9 and y = x + 3 , what is the greatest possible integer value of x + y ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: "x + y = x + x + 3 = 2 x + 3 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 8.5 then x + y = 8.5 + 11.5 = 20 . the answer is b ."
Answer: b
Problem: a certain class of students is being divided into teams . the class can either be divided into 8 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 6 , b ) 36 , c ) 48 , d ) 24 , e ) 72
Rationale: "let total no of students in the class be n so , we are told that n is divisible by both 8 24 so , lets find the least common multiple of 8 24 , ie 24 so our answer is ( d ) 24"
Answer: d
Problem: a rectangular tiled patio is composed of 90 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 90 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 11 , e ) 28
Rationale: "r * c = 90 and ( 11 + 4 ) ( c - 2 ) = 90 - - > r = 11 and c = 8 . answer : d ."
Answer: d
Problem: what is the units digit of ( 3 ^ 5 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 5 = 3 ^ 4 * 1 + 1  3 ^ 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 5 ) ( 4 ^ 13 )  ( 3 ^ 1 ) ( ~ 4 ) = ( ~ 3 ) ( ~ 4 ) = ~ 2 . therefore , the answer is a ."
Answer: a
Problem: the sum of three consecutive even numbers is 63 . find the middle number of the three ?
Options: a ) 14 , b ) 23 , c ) 25 , d ) 29 , e ) 21
Rationale: "middle no = 63 / 3 = 21 ans e"
Answer: e
Problem: a cube is divided into 512 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 216 , b ) 264 , c ) 296 , d ) 312 , e ) 324
Rationale: "each face of the cube has 8 x 8 = 64 cubelets . on each face , only the interior cubelets are painted one colour . on each side , 6 x 6 = 36 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 36 = 216 the answer is a ."
Answer: a
Problem: of the 150 employees at company x , 70 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 80 , e ) 100
Rationale: "150 employees 70 are full - time 100 have worked at company x for at least a year 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 150 - 70 = 80 employees not full time 80 - 20 = 60 employees not full time who worked over a year 100 employees have worked at company x for at least a year - 60 employees not full time who worked over a year = 40 full - time employees of company x have worked at the company for at least a year ans b"
Answer: b
Problem: paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to paul and 40 % of his income to quentin , paul ' s new income would be what fraction of quentin ' s new income ?
Options: a ) 11 / 12 , b ) 13 / 17 , c ) 13 / 19 , d ) 15 / 11 , e ) 11 / 19
Rationale: "make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get p = 12 and q 8.8 so 12 / 8.8 = 3 / 2.2 ans : d"
Answer: d
Problem: if 6 - 12 / x = 7 - 7 / x , then x =
Options: a ) - 5 , b ) 19 , c ) - 7 / 5 , d ) 1 , e ) 5 / 6
Rationale: "we ' re given the equation 6 - 12 / x = 7 - 7 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we need to multiply both sides of the equation by x , giving us . . . 6 x - 12 x / x = 7 x - 7 x / x we can then eliminate that denominator , which gives us . . . . 6 x - 12 = 7 x - 7 - 5 = x a"
Answer: a
Problem: the sector of a circle has radius of 14 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 61 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) = 33 + 28 = 61 cm answer : b"
Answer: b
Problem: | x + 3 | – | 4 - x | = | 8 + x | how many s solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Problem: in a games hour 4 different types of players came to the ground ? cricket 11 , hokey 15 , football 21 , softball 15 . how many players are present in the ground ?
Options: a ) 70 , b ) 52 , c ) 62 , d ) 49 , e ) 50
Rationale: "total number of players = 11 + 15 + 21 + 15 = 62 answer is c"
Answer: c
Problem: how long does a train 120 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 120 + 170 = 290 m s = 60 * 5 / 18 = 50 / 3 t = 290 * 3 / 50 = 17.4 sec answer : d"
Answer: d
Problem: what is the ratio of 6 / 7 to the product 3 * ( 7 / 3 ) ?
Options: a ) 3 : 7 , b ) 1 : 3 , c ) 3 : 21 , d ) 6 : 49 , e ) 3 : 49
Rationale: "6 / 7 / 21 / 3 = 6 / 49 . . . imo option d ."
Answer: d
Problem: a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 275.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
Options: a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60
Rationale: "let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 275 = > 125 * s = 200 = > s = 1.6 answer e"
Answer: e
Problem: a batsman makes a score of 50 runs in the 6 th inning and thus increases his average by 2 . find his average after 6 th inning .
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let the average after 6 th inning = x then , average after 5 th inning = x - 2 5 ( x - 2 ) + 50 = 6 x x = 10 - 50 = 40 answer is a"
Answer: a
Problem: 49 ã — 49 ã — 49 = 7 ^ ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 6 , e ) none of these
Rationale: "49 ã — 49 ã — 49 = 7 ? or , 7 ( 2 ) ã — 7 ( 2 ) ã — 7 ( 2 ) = 7 ? or 7 ( 6 ) = 7 ? or , ? = 6 answer d"
Answer: d
Problem: a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 1 , - 4 ) . what is the smallest possible area of that circle ?
Options: a ) 13 π , b ) 26 π , c ) 262 √ π , d ) 5 π , e ) 64 π
Rationale: "the distance between the two points is sqrt ( 20 ) . radius = sqrt ( 20 ) / 2 area = pi * ( sqrt ( 20 ) / 2 ) ^ 2 d . 5 π"
Answer: d
Problem: the sum of the present ages of two persons a and b is 90 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 100
Rationale: "a + b = 90 , a = 2 b 2 b + b = 90 = > b = 30 then a = 60 . 5 years , their ages will be 65 and 35 . sum of their ages = 65 + 35 = 100 . answer : e"
Answer: e
Problem: the distance between two cities a and b is 330 km . a train starts from a at 8 a . m . and travels towards b at 60 km / hr . another train starts from b at 9 a . m . and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 12 , b ) 10 , c ) 11 , d ) 09 , e ) 03
Rationale: "suppose they meet x hrs after 8 a . m . then , ( distance moved by first in x hrs ) + [ distance moved by second in ( x - 1 ) hrs ] = 330 60 x + 75 ( x - 1 ) = 330 = > x = 3 so , they meet at ( 8 + 3 ) i . e . , 11 a . m . answer : c"
Answer: c
Problem: a high school has 360 students 1 / 2 attend the arithmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 3 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .
Options: a ) 45 , b ) 40 , c ) 35 , d ) 50 , e ) 55
Rationale: "basically , this question is asking you to figure out how many students are being double - counted . a - club has 180 members ( 1 / 2 of 360 ) b - club has 225 members ( 5 / 8 of 360 ) c - club has 270 members ( 3 / 4 of 360 ) we can create an equation to solve this : 180 + 225 + 270 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 135 ) . 180 + 225 + 270 = 360 + x + 270 x = 405 - 360 = 45 a"
Answer: a
Problem: the cash difference between the selling prices of an article at a profit of 8 % and 6 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 50 , d ) 54 : 53 , e ) 52 : 51
Rationale: "let c . p . of the article be rs . x . then , required ratio = 108 % of x / 106 % of x = 108 / 106 = 54 / 53 = 54 : 53 answer : d"
Answer: d
Problem: reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 588 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 3.6 , b ) 7 , c ) 18 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 588 12 r 2 = 588 r 2 = 49 r = 7 . answer : b"
Answer: b
Problem: what is x if x + 5 y = 24 and y = 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 14
Rationale: "substitute y by 2 in x + 5 y = 24 x + 5 ( 2 ) = 24 x + 10 = 24 if we substitute x by 14 in x + 10 = 24 , we have 14 + 10 = 24 . hence x = 14 correct answer e"
Answer: e
Problem: the wages earned by robin is 20 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 18.75 % , b ) 33 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: "let wage of erica = 10 wage of robin = 1.2 * 10 = 12 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 12 ) / 12 * 100 % = 4 / 12 * 100 % = 33 % answer b"
Answer: b
Problem: there are two numbers . if 10 % of the first number is added to the second number , then the second number increases to its 6 - fifth . what is the ratio of the first number to the second number ?
Options: a ) 3 : 2 , b ) 4 : 3 , c ) 8 : 7 , d ) 5 : 8 , e ) 2 : 1
Rationale: let the two numbers be x and y . ( 1 / 10 ) * x + y = ( 6 / 5 ) * y ( 1 / 10 ) * x = ( 1 / 5 ) * y x / y = 2 / 1 = 2 / 1 the answer is e .
Answer: e
Problem: each child has 2 pencils and 13 skittles . if there are 6 children , how many pencils are there in total ?
Options: a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08
Rationale: 2 * 6 = 12 . answer is b .
Answer: b
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 60 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.2 , b ) 2.2 , c ) 3.2 , d ) 4.2 , e ) 5
Rationale: "40 * ( 40 / 100 ) = 16 - - - 60 ? - - - 12 = > rs . 3.2 answer : c"
Answer: c