Cheukting/mathqa huggingface dataset:
Question (general): 3 men and 3 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )
Options: a ) 12 , b ) 15 , c ) 18 , d ) 36 , e ) 24
Rationale: the list should be wmwmw . hence , from women 3 ! and men 3 ! , we get ( 3 ! ) ( 3 ! ) = 36 . therefore , the correct answer is d .
Answer: d
Question (geometry): carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 12 inches by 15 inches and jordan ' s rectangle is 6 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 24
b ) 26
c ) 28
d ) 30
e ) 32
Rationale: area of first rectangle is 12 * 15 = 180 hence area of second would be 6 x = 180 x x = 30 answer is d
Answer: d
Question (gain): the calendar of the year 2080 can be used again in the year ?
Options: a ) 2105 , b ) 1955 , c ) 1945 , d ) 1935 , e ) 2108
Rationale: "explanation : given year 2080 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2080 + 28 = 2108 answer : e"
Answer: e
Question (general): sum of 42 odd numbers is ?
Options: a ) 1764 , b ) 1774 , c ) 1784 , d ) 1794 , e ) 1754
Rationale: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 42 odd numbers = 42 ^ 2 = 1764 answer : a"
Answer: a
Question (gain): a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 5,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 11.11 %
Rationale: the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 5,500 = 4,500 gallons and sodium chloride is 500 gallons ( 5 % of initial solution of 10,000 gallons ) then sodium chloride is 500 / 4,500 * 100 = ~ 11.11 % of the remaining solution of 4,500 gallons . answer : e .
Answer: e
Question (general): 4 , 25,49 , 121,169 , 289,361 ,
Options: a ) 149 , b ) 169 , c ) 189 , d ) 529 , e ) 219
Rationale: "23 ^ 2 = 529 because follow sequence of square of the prime numbers answer : d"
Answer: d
Question (geometry): a larger cube has 8 cubic inch as a volume and in the cube there are 8 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 8 smaller cubes and the surface area of the larger cube , in square inch ?
Options: a ) 24
b ) 64
c ) 81
d ) 108
e ) 120
Rationale: volume of larger cube = 8 = 2 ^ 3 side of larger cube = 2 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 2 ^ 2 = 24 surface area of 27 smaller cubes = 8 * 6 * 1 = 48 difference = 48 - 24 = 24 answer : a
Answer: a
Question (physics): the distance from steve ' s house to work is 20 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 20 km = > speed = 10 kmph b"
Answer: b
Question (physics): a and b can do a piece of work in 4 days . with the help of c they finish the work in 3 days . c alone can do that piece of work in ?
Options: a ) 4 days , b ) 21 days , c ) 13 days , d ) 12 days , e ) 3 days
Rationale: "c = 1 / 3 – 1 / 4 = 1 / 12 = > 12 days answer : d"
Answer: d
Question (physics): in a garden , there are 10 rows and 16 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 32 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 16 plants . there are 15 gapes between the two corner trees ( 15 x 2 ) metres and 1 metre on each side is left . therefore length = ( 30 + 2 ) m = 32 m . answer : a"
Answer: a
Question (general): on a certain date , pat invested $ 9,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 36,000 , in how many years total will the total value of the investment plus interest increase to $ 72,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "36,000 = 9,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 72,000 = 9,000 ( 1 + x ) ^ n 8 = ( 1 + x ) ^ n 2 ^ 3 = ( 1 + x ) ^ n ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Question (general): 30 pens and 75 pencils were purchased for 510 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) can not be determined , e ) none of the above
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 510 – 150 ) = 360 ∴ average price of a pen = 360 ⁄ 60 = 12 answer c"
Answer: c
Question (geometry): a rectangular carpet has an area of 60 sq . m . if its diagonal and longer side together equal 5 times the shorter side , the length of the carpet is :
Options: a ) 5 m
b ) 12 m
c ) 13 m
d ) 14.5 m
e ) 15.5 m
Rationale: let , length = x meters and breadth = y meters then xy = 60 and ( x 2 + y 2 ) + x = 5 therefore , x = 60 and ( x 2 + y 2 ) = ( 5 y - x ) 2 or xy = 60 and 24 y 2 - 10 xy = 0 . therefore , 24 y 2 - 10 * 60 = 0 or y 2 = 25 or = 5 . therefore , x = ( 60 / 5 ) m = 12 m . so , length of the carpet = 12 m answer : b
Answer: b
Question (physics): a train is 357 meter long is running at a speed of 42 km / hour . in what time will it pass a bridge of 137 meter length ?
Options: a ) 44 , b ) 42.343 , c ) 50 , d ) 39.252 , e ) 27.851
Rationale: "speed = 42 km / hr = 42 * ( 5 / 18 ) m / sec = 35 / 3 m / sec total distance = 357 + 137 = 494 meter time = distance / speed = 494 * ( 3 / 35 ) = 42.343 seconds . answer : b"
Answer: b
Question (general): a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 34 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 18 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 34 pints will require 9 / 17 * 34 = 18 points . . second way . . get both red and white paints in same denominator . . . 3 / 4 + 2 / 3 = ( 9 / 12 ) + ( 8 / 12 ) pints . . from here we get the ratio of red : white = 9 : 8 . . so in 34 pints red will be 9 / ( 9 + 8 ) * 34 = 18 . . answer : c"
Answer: c
Question (geometry): in a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 48 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?
Options: a ) a 8
b ) b 22
c ) c 27
d ) d 40
e ) e 51
Rationale: l = 48 / 12 = 4 ft w = 72 / 12 = 6 ft area of paper = 24 area of cube = 4 * side ^ 2 side of cube = 2 v of cube = 8
Answer: a
Question (general): the value of ( 0.137 + 0.098 ) ² - ( 0.137 - 0.098 ) ² / 0.137 × 0.098 is
Options: a ) 0.039 , b ) 0.235 , c ) 0.25 , d ) 4 , e ) 5
Rationale: solution given expression = ( a + b ) ² - ( a - b ) ² / ab = 4 ab / ab = 4 . answer d
Answer: d
Question (general): a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6900 ?
Options: a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6991 , e ) s . 7391
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6900 * 6 ) - 34009 ] = rs . ( 41400 - 34009 ) = rs . 7391 . answer : e"
Answer: e
Question (gain): mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 457 ?
Options: a ) 26.4 % , b ) 21 % , c ) 20 % , d ) 19 % , e ) none of these
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 457 , discount = 621 - 457 = 164 discount % = 164 / 621 * 100 = 26.4 % answer : a"
Answer: a
Question (geometry): a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 8 cubic feet . if a small block has half the width , half the depth , and half the length of a normal block , what is the volume of cheese in a small block in cubic feet ?
Options: a ) 1 , b ) 5 , c ) 4 , d ) 6 , e ) 2
Rationale: "volume of cube = lbh = 8 new cube l , b , h are decreases of . 5 l , . 5 b , . 5 h new volume of cube = . 5 l * . 5 b * . 5 h = . 125 * lbh = . 125 * 8 = 1 answer : a"
Answer: a
Question (gain): boy sells a book for rs . 450 he gets a loss of 10 % , to gain 10 % , at price he should sell ?
Options: a ) rs . 400 , b ) rs . 450 , c ) rs . 550 , d ) rs . 600 , e ) rs . 650
Rationale: "find selling price to gain 10 % . now , we are asked to find selling price to gain 10 % profit . hint : selling price = ( 100 + gain % ) × c . p . 100 selling price = ( 100 + 10 ) × 500 100 selling price = ( 110 ) × 500 100 therefore , selling price = rs . 550 c"
Answer: c
Question (physics): how many seconds does sandy take to cover a distance of 700 meters , if sandy runs at a speed of 18 km / hr ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
Rationale: "18 km / hr = 18000 m / 3600 s = 5 m / s time = 700 / 5 = 140 seconds the answer is c ."
Answer: c
Question (general): 5358 x 51 = ?
Options: a ) 272258 , b ) 272358 , c ) 273258 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 1 ) = 5358 x 50 + 5358 x 1 = 267900 + 5358 = 273258 . c )"
Answer: c
Question (general): a company purchased raw material worth 1 / 4 of it capital , 1 / 10 of the remaining is spent on machinery . how much fraction of the capital was left with the company after its expenditures on raw material and machinery ?
Options: a ) 1 / 5 , b ) 2 / 8 , c ) 5 / 9 , d ) 27 / 40 , e ) 15 / 30
Rationale: the amount spent by the company on raw material is 1 / 4 , so remaining is 3 / 4 . 1 / 10 of the remaining is spent on machinery , 1 / 10 * 3 / 4 = 3 / 40 total amount spent on raw material and machinery is 1 / 4 + 3 / 40 to make the denominator common we use 40 , so 1 / 4 is 10 / 40 10 / 40 + 3 / 40 = 13 / 40 is spent on raw material and machinery remaining 27 / 40 is left with the company answer is d
Answer: d
Question (general): if x = y = 2 z and xyz = 256 then what is the value of x ?
Options: a ) 12 , b ) 8 , c ) 16 , d ) 6 , e ) 2
Rationale: given that x = y = z . so , x = y , x = 2 z , y = 2 z . given xyz = 256 = > ( 2 z ) * ( 2 z ) * z = 256 = > 4 z ^ 3 = 256 = > z = 4 then x = 2 z = 2 ( 4 ) = 8 answer : b
Answer: b
Question (geometry): danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 5184 , what is the area of the side face of the box ?
Options: a ) 123 , b ) 167 , c ) 178 , d ) 199 , e ) 288
Rationale: "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 5184 l * 1.5 l * 2 l = 5184 l = 12 side face area = l * d = l * 2 l = 12 * 2 * 12 = 288 e is the answer"
Answer: e
Question (physics): a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed r of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = r ans = c"
Answer: c
Question (general): if a ã — b = 2 a - 3 b + ab , then 4 ã — 5 + 5 ã — 4 is equal to :
Options: a ) 31 , b ) 32 , c ) 43 , d ) 45 , e ) 26
Rationale: "explanation : 4 ã — 5 + 5 ã — 4 = ( 2 ã — 4 - 3 ã — 5 + 4 ã — 5 ) + ( 2 ã — 5 - 3 ã — 4 + 5 ã — 4 ) = ( 8 - 15 + 20 + 10 - 12 + 20 ) = 31 . answer : a"
Answer: a
Question (physics): my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 100 years . can you tell my grandson age in years ?
Options: a ) 50 years , b ) 20 years , c ) 5 years , d ) 10 years , e ) 90 years
Rationale: let m be my age in years . if s is my son ' s age in years , then my son is 52 s weeks old . if g is my grandson ' s age in years , then my grandson is 365 g days old . thus , 365 g = 52 s . since my grandson is 12 g months old , 12 g = m . since my grandson , my son and i together are 120 years , g + s + m = 100 . the above system of 3 equations in 3 unknowns ( g , s and m ) can be solved as follows : g + 365 g / 52 + 12 g = 100 or 52 g + 365 g + 624 g = 5,200 or g = 5,200 / 1,041 = 5 years answer : c
Answer: c
Question (general): what is the difference between the place values of two sevens in the numeral 54179759 ?
Options: a ) 699990 , b ) 99990 , c ) 99980 , d ) 69300 , e ) none of these
Rationale: explanation : required difference = 70000 - 700 = 69300 answer is d
Answer: d
Question (general): the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 34 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 22.67 litres , c ) 11 litres , d ) 07 litres , e ) 38.67 litres
Rationale: "262.85 ( 34 ) + 3 , 104.35 x = 1 , 399.45 ( 34 + x ) solve the equation . 262.85 ( 34 ) + 3 , 104.35 x = 1 , 399.45 ( 34 + x ) 8936.9 + 3 , 104.35 x = 47 , 581.3 + 1 , 399.45 x 8936.9 + 1 , 704.9 x = 47 , 581.3 1 , 704.9 x = 38 , 644.40 x ≈ 22.67 answer is b ."
Answer: b
Question (general): the equation of line s is y = 4 / 3 * x - 100 . what is the smallest possible distance in the xy - plane from the point with coordinates ( 0 , 0 ) to any point on line s ?
Options: a ) 48 , b ) 50 , c ) 60 , d ) 75 , e ) 100
Rationale: this can be solve in two steps and without any complex calculation . given : equation of line s as y = ( 4 / 3 ) x - 100 . so the line intercept the axes at ( 0 , - 100 ) and ( 75,0 ) . this can be considered a right angle triangle with right angle at ( 0,0 ) . so base = 100 , height = 75 and hypotenuse = 125 ( by pythagoras triplet ) so a perpendicular from the ( 0,0 ) to hypotenuse will be the answer . area of triangle = 0.5 * 100 * 75 = 0.5 * 125 * x = > x = 60 ; so answer is 60 = c
Answer: c
Question (general): jim â € ™ s taxi service charges an initial fee of $ 2.0 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 5.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: "let the fixed charge of jim â € ™ s taxi service = 2 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2 + ( 3.6 / . 4 ) * . 35 = 2 + 9 * . 35 = 5.15 $ answer a"
Answer: a
Question (gain): to a sugar solution of 10 liters containing 50 % sugar , 10 liter of water is added . the percentage of sugar in the new solution is ?
Options: a ) 25 % , b ) 30 % , c ) 15 % , d ) 20 % , e ) 18 %
Rationale: "quantity of sugar = 50 * 10 / 100 = 5 kg new percentage = 5 / 20 * 100 = 25 % answer is a"
Answer: a
Question (physics): joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 2 / 3 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 144 , c ) 175 , d ) 216 , e ) 264
Rationale: total paint initially = 360 gallons paint used in the first week = ( 2 / 3 ) * 360 = 240 gallons . remaning paint = 120 gallons paint used in the second week = ( 1 / 5 ) * 120 = 24 gallons total paint used = 264 gallons . option e
Answer: e
Question (general): a two - digit number is such that the product of the digits is 8 . when 18 is added to the number , then the digits are reversed . the number is ?
Options: a ) 1 , b ) 2 , c ) 6 , d ) 8 , e ) 9
Rationale: let the ten ' s and unit digit be x and 8 respectively . x then , 10 x + 8 + 18 = 10 x 8 + x x x 10 x 2 + 8 + 18 x = 80 + x 2 9 x 2 + 18 x - 72 = 0 x 2 + 2 x - 8 = 0 ( x + 4 ) ( x - 2 ) = 0 x = 2 option b
Answer: b
Question (general): how many numbers from 10 to 47 are exactly divisible by 3 ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45 , . 12 numbers . 10 / 3 = 3 and 47 / 3 = 15 = = > 15 - 3 = 12 . therefore 12 digits a )"
Answer: a
Question (gain): a 7 % stock yields 10 % . the market value of the stock is :
Options: a ) rs 60 , b ) rs 70 , c ) rs 90 , d ) rs 75 , e ) rs 50
Rationale: "explanation : for an income of rs . 10 , investment = rs . 100 . for an income of rs 7 , investment = rs . 100 / 10 x 7 = rs 70 market value of rs . 100 stock = rs . 70 answer is b"
Answer: b
Question (gain): there were two candidates in an election . winner candidate received 62 % of votes and won the election by 360 votes . find the number of votes casted to the winning candidate ?
Options: a ) 288 , b ) 744 , c ) 788 , d ) 298 , e ) 930
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 360 62 % - - - - - - - - ? = > 930 answer : e"
Answer: e
Question (physics): a light flashes every 6 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 600 , c ) 650 , d ) 700 , e ) 750
Rationale: "1 flash = 6 sec for 1 min = 10 flashes so for 1 hour = 10 * 60 = 600 flashes . answer : b"
Answer: b
Question (other): uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 6 : 4 . if 60 % of the toyota bought and 40 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 66 % , b ) 64 % , c ) 68 % , d ) 52 % , e ) 72 %
Rationale: "let total no of vehicles bought be 100 , toyota 60 and honda 40 , so total number of suv ' s bought for toyota and honda respectively 60 * 60 / 100 = 36 and 40 * 40 / 100 = 16 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : d"
Answer: d
Question (general): a clothing store purchased a pair of pants for $ 81 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a clothing store owner decided to decrease the selling price by 20 percent . what was the clothing store ' s gross profit on this sale ?
Options: a ) $ 14 , b ) $ 5.4 , c ) $ 4.4 , d ) $ 1.2 , e ) $ 5.0
Rationale: "sale price ( sp ) = 81 + markup ( mp ) - - > mp = sp - 81 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 81 3 sp / 4 = 81 sp = 108 now a discount of 20 % is given so new sp is . 8 * 108 = 86.4 profit = 86.4 - 81 = 5.4 $ answer is b"
Answer: b
Question (general): find the average of all prime numbers between 80 and 100
Options: a ) 88 , b ) 60 , c ) 80 , d ) 89.6 , e ) 92
Rationale: "prime numbers between 80 and 100 are 83 , 89 , 97 required average = ( 83 + 89 + 97 ) / 3 = 269 / 3 = 89.6 answer is d"
Answer: d
Question (general): a certain number when divided by 65 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 65 + 25 = 90 / 15 = 6 ( remainder ) c"
Answer: c
Question (physics): a train 240 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 4 , b ) 6 , c ) 12 , d ) 9 , e ) 13
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 240 * 3 / 55 ] sec = 13 sec answer : e"
Answer: e
Question (general): the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 70 % 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 ) 23 % , c ) 30 % , d ) 31 % , e ) 100 %
Rationale: "let wage of erica = 10 wage of robin = 1.3 * 10 = 13 wage of charles = 1.7 * 10 = 17 percentage by which wage earned by charles is more than that earned by robin = ( 17 - 13 ) / 13 * 100 % = 4 / 13 * 100 % = 31 % answer d"
Answer: d
Question (general): two brothers ram and ravi appeared for an exam . the probability of selection of ram is 3 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 3 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 3 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 3 / 7 x 1 / 5 = 3 / 35 answer : a"
Answer: a
Question (general): two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 60 km more than the other . what is the distance between the two stations ?
Options: a ) 540 km , b ) 767 km , c ) 276 km , d ) 178 km , e ) 176 km
Rationale: "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 60 km more than the other , 25 x – 20 x = 60 5 x = 60 x = 12 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 12 = 540 km . answer : a"
Answer: a
Question (general): a set consists of 18 numbers , all are even or multiple of 5 . if 6 numbers are even and 12 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: { total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 18 = 6 + 12 - { both } + 0 ; { both } = 0 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : a .
Answer: a