Cheukting/mathqa huggingface dataset:
Question (geometry): if the area of a circle is 100 pi square feet , find its circumference .
Options: a ) 65 pi feet , b ) 20 pi feet , c ) 42 pi feet , d ) 18 pi feet , e ) 64 pi feet
Rationale: "the area is given by pi * r * r . hence pi * r * r = 100 pi r * r = 100 ; hence r = 10 feet the circumference is given by 2 * pi * r = 2 * pi * 10 = 20 pi feet correct answer b"
Answer: b
Question (physics): a train of length 250 m runs at a speed of 70 km / hr . what will be the time taken to cross any stationary object standing at the railway station ?
Options: a ) 20 sec , b ) 17.23 sec , c ) 12.86 sec , d ) 9.5 sec , e ) 8.5 sec
Rationale: explanation : length of train = 250 m , speed of train = 70 km / hr length of train is always considered as distance , and hence here distance = 250 m 1 ) first convert speed of km / hr into m / s speed of train = 70 x 5 = 19.44 m / s 18 2 ) we know that , speed = distance / time time taken to cross stationary object = 250 / 19.44 time taken to cross stationary object = 12.86 sec answer is c
Answer: c
Question (physics): two pipes a and b can fill a tank in 4 and 5 hours respectively . if they are turned up alternately for one hour each , the time taken to fill the tank is ?
Options: a ) 4 hrs 29 min , b ) 4 hrs 24 min , c ) 8 hrs 24 min , d ) 4 hrs 44 min , e ) 5 hrs 24 min
Rationale: 1 / 4 + 1 / 5 = 9 / 20 20 / 9 = 2 2 / 9 9 / 20 * 2 = 9 / 10 - - - - 4 hours wr = 1 - 9 / 10 = 1 / 10 1 h - - - - 1 / 4 ? - - - - - 1 / 10 2 / 5 * 60 = 24 = 4 hrs 24 min answer : b
Answer: b
Question (general): if a ( a - 6 ) = 27 and b ( b - 6 ) = 27 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 6 , d ) 46 , e ) 48
Rationale: "i . e . if a = - 3 then b = 9 or if a = 9 then b = - 3 but in each case a + b = - 3 + 9 = 6 answer : option c"
Answer: c
Question (general): when n is divided by 5 the remainder is 3 . what is the remainder when ( n - 1 ) ^ 2 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: n = 5 x + 3 , for some integer x ( n - 1 ) ^ 2 = ( 5 x + 2 ) ^ 2 = 5 y + 4 , for some integer y when we divide this by 5 , the remainder is 4 . the answer is e .
Answer: e
Question (general): how many 1 / 12 s are there in 37 1 / 2 ?
Options: a ) 350 , b ) 450 , c ) 500 , d ) 650 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 12 ) = ( 75 / 2 x 12 / 1 ) = 450 . answer : b"
Answer: b
Question (general): . the price of commodity p increases by 40 paise every year , while the price of commodity q increases by 15 paise every year . if in 2001 , the price of commodity p was rs . 4.20 and that of q was rs . 6.30 , in which year commodity p will cost 40 paise more than the commodity q ?
Options: a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) none of these
Rationale: explanation : let the commodity p costs 40 paise more than the commodity q after n years price of the commodity p in 2001 = rs . 4.20 since the price of the commodity p increases by rs 0.40 every year , price of the commodity p after n years from 2001 = rs . 4.20 + ( n × . 40 ) price of the commodity q in 2001 = rs . 6.30 since the price of the commodity q increases by rs 0.15 every year , price of the commodity q after n years from 2001 = rs . 6.30 + ( n × . 15 ) since the commodity p costs rs . 0.40 more that the commodity q after n years from 2001 , 4.20 + ( n × . 40 ) = 6.30 + ( n × . 15 ) + 0.40 = > ( 40 n - . 15 n ) = 6.30 - 4.20 + 0.40 = 2.5 = > . 25 n = 2.5 ⇒ n = 2.5 / . 25 = 250 / 25 = 101.15 ¯ = > commodity p costs rs . 0.40 more that the commodity q after 10 years from 2001 . i . e . , in 2011 . answer : option d
Answer: d
Question (general): a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 7.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "from the question stem we know that we need a mixture of 100 pounds of peanuts and cashews . if we represent peanuts as x and cashews as y , we get x + y = 100 . since the wholesaler wants to sell the mixture of 100 pounds @ $ 2.50 , we can write this as : $ 2.5 * ( x + y ) = $ 1.5 x + $ 4 y from the equation x + y = 100 , we can rewrite y as y = 100 - x and substitute this into our equation to get : $ 2.5 * ( x + 100 - x ) = $ 1.5 x + $ 4 ( 100 - x ) if you solve for x , you will get x = 60 , and therefore y = 40 . so the wholesaler must use 40 pounds of cashews . you can substitute into the original equation to see that : $ 250 = $ 1.5 ( 60 ) + $ 4 ( 40 ) answer is d ."
Answer: d
Question (general): when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 39 ?
Options: a ) 3 , b ) 8 , c ) 12 , d ) 32 , e ) 35
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 39 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 8 more to make it 39 m + 39 answer - b"
Answer: b
Question (geometry): a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 800 square feet , what is the total length of the fence , in feet ?
Options: a ) 40 , b ) 80 , c ) 100 , d ) 120 , e ) 200
Rationale: "two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 800 ie x ^ 2 = 400 ie x = 20 l = 40 w = 20 total length of fence = 2 * 20 + 40 = 80 my answer is b"
Answer: b
Question (probability): if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on the first 3 flips but not on the last 3 flips ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128
Rationale: "p ( hhhttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 64 the answer is d ."
Answer: d
Question (gain): a merchant marks his goods up by 50 % and then offers a discount of 20 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 20 % , b ) 25 % , c ) 69 % , d ) 31 % , e ) 19 %
Rationale: "let the price be 100 . the price becomes 150 after a 50 % markup . now a discount of 20 % on 150 . profit = 120 - 100 20 % answer a"
Answer: a
Question (general): a number when divided by a divisor leaves a remainder of 27 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 35 , d ) 40 , e ) 59
Rationale: "let the number is n , the divisor = d , i will make the two equations - n = xd + 27 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 40 as d is also integer and 40 is a prime number , the d should be 40 to satisfy the above equation . hence answer is ' d '"
Answer: d
Question (other): the triplicate ratio of 1 : 6 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 216
Rationale: "1 ^ 3 : 6 ^ 3 = 1 : 216 answer : e"
Answer: e
Question (physics): for a race a distance of 224 meters can be covered by p in 14 seconds and q in 32 seconds . by what distance does p defeat q eventually ?
Options: a ) 232 m , b ) 288 m , c ) 324 m , d ) 231 m , e ) 236 m
Rationale: explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 14 = 16 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 18 seconds therefore , distance covered by p in that time = 16 m / s x 18 seconds = 288 metres answer : b
Answer: b
Question (general): in an office , totally there are 2200 employees and 40 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 661 , b ) 600 , c ) 620 , d ) 616 , e ) none of these
Rationale: "number of male employees = 2200 * 40 / 100 = 880 required number of male employees who are less than 50 years old = 880 * ( 100 - 30 ) % = 880 * 75 / 100 = 616 . answer : d"
Answer: d
Question (general): the sum of ages of 5 children born at theintervals of 3 years each is 50 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 5 , c ) 9 , d ) 8 , e ) 10
Rationale: "the age of children x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 , x = 4 . correct answer ( a )"
Answer: a
Question (general): if jake loses 35 pounds , he will weigh thrice as much as his sister . together they now weigh 275 pounds . what is jake ' s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 139 , d ) 147 , e ) 188
Rationale: j = jake ’ s current weight , in pounds s = sister ’ s current weight , in pounds we are told that “ if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j – 35 = 3 s j = 3 s + 35 ( equation 1 ) next , we are told that “ together they now weigh 275 pounds . ” we can also put this into an equation . j + s = 275 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 3 s + 35 = 275 - s 4 s = 240 s = 60 j + 60 = 275 j = 215 answer : e
Answer: e
Question (physics): pipe a fills a tank of capacity 900 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 42 minutes , b ) 14 minutes , c ) 54 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: "in one cycle they fill 40 + 30 - 20 = 50 liters 900 = 50 * n = > n = 18 here n = number of cycles . total time = 18 * 3 = 54 as in one cycle there are 3 minutes . thus 54 minutes answer : c"
Answer: c
Question (general): how many even number in the range between 6 to 100 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 32 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 6 , 8,10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 48 . for 6 , 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 16 . hence , only divisible by 2 but not 3 = 48 - 16 = 32 . hence , answer c"
Answer: c
Question (physics): 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days z do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time z = 3 days to finish the task imo a"
Answer: a
Question (other): of the diplomats who attended a summit conference : 20 spoke latin , 32 did not speak russian and 20 % of the diplomats spoke neither latin nor russian . if 10 % of the diplomats spoke both latin and russian , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: 2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer
Answer: d
Question (general): if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 3 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 3 / 4 , e ) 3 / 5
Rationale: "let boy be represented by b and girl by g . the possible outcomes of two children of same sex and one of opposite sex can be : bbg or gbb or bgb or ggb or bgg or gbg ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) + ( 1 / 2 * 1 / 2 * 1 / 2 ) 1 / 8 + 1 / 8 + 1 / 8 + 1 / 8 + 1 / 8 + 1 / 8 = 6 / 8 = 3 / 4 answer : ( d )"
Answer: d
Question (gain): a man buys 12 lts of liquid which contains 20 % of the liquid and the rest is water . he then mixes it with 10 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 75.45 , b ) 76.45 , c ) 77.45 , d ) 74.45 , e ) 73.45
Rationale: "20 % in 12 lts is 2.4 . so water = 12 - 2.4 = 9.6 lts . 30 % of 10 lts = 3 . so water in 2 nd mixture = 10 - 3 = 7 lts . now total quantity = 12 + 10 = 22 lts . total water in it will be 9.6 + 7 = 16.6 lts . % of water = ( 100 * 16.6 ) / 22 = 75.45 answer : a"
Answer: a
Question (physics): a and b can do a work in 20 days , b and c can do it in 30 days ; a , b and c together can finish it in 40 days . a and c together will do it in ?
Options: a ) 25 days , b ) 30 days , c ) 20 days , d ) 15 days , e ) 10 days
Rationale: a + b + c 1 day work = 1 / 40 a + b 1 day work = 1 / 20 b + c 1 day work = 1 / 30 a + c 1 day work = 2 * 1 / 40 - 1 / 20 + 1 / 30 = 1 / 30 a and c together will do the work in 30 days . answer is b
Answer: b
Question (geometry): the least perfect square , which is divisible by each of 21 , 36 and 66 is :
Options: a ) 213444 , b ) 214344 , c ) 214434 , d ) 231444 , e ) 233444
Rationale: "explanation : l . c . m . of 21 , 36 , 66 = 2772 . now , 2772 = 2 x 2 x 3 x 3 x 7 x 11 to make it a perfect square , it must be multiplied by 7 x 11 . so , required number = 22 x 32 x 72 x 112 = 213444 answer is a"
Answer: a
Question (general): find the greatest number that will divide 54 , 87 and 172 so as to leave the same remainder in each case
Options: a ) 13 , b ) 3 , c ) 15 , d ) 1 , e ) 2
Rationale: explanation : required number = ( 87 - 54 ) , ( 172 - 87 ) , ( 172 - 54 ) = h . c . f of 33,85 and 118 is 1 answer : option d
Answer: d
Question (general): sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 9 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 13 / 18 , e ) 11 / 15
Rationale: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 9 x = 8 / 9 x so if gold card balance is transferred then the rest unspent will be 8 / 9 x - x / 6 = 13 / 18 x so the ans is d"
Answer: d
Question (gain): the number which exceeds 12 % of it by 52.8 is :
Options: a ) 60 , b ) 77 , c ) 269 , d ) 26 , e ) 91
Rationale: "explanation : let the number be x . then , x – 12 % of x = 52.8 x – ( 12 / 100 ) x = 52.8 x ( 1 – 12 / 100 ) = 52.8 ( 88 / 100 ) x = 52.8 x = ( 100 x 52.8 ) / 88 = 60 answer : a"
Answer: a
Question (general): according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 360 6 ounces servings of orange juice ?
Options: a ) a ) 45 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100
Rationale: "its a . total juice rquired = 360 * 6 = 2160 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 2160 / 48 = 45 . answer a"
Answer: a
Question (general): solution for 2.01 + . 3 + . 34
Options: a ) 2.91 , b ) 2.65 , c ) 2.938 , d ) 2.986 , e ) 2.999
Rationale: "2.01 + . 3 + . 34 = 0 0 = 0 - 2.01 - 0.3 - 0.34 0 = - 2.65 answer : b"
Answer: b
Question (physics): two pipes p and q can fill a cistern in 12 and 15 minutes respectively . both are opened together , but at the end of 6 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: "let x be the total time it takes for the cistern to fill . 6 / 12 + x / 15 = 1 x / 15 = 1 / 2 x = 7.5 after the first pipe is turned off , it takes 1.5 more minutes to fill the cistern . the answer is b ."
Answer: b
Question (general): in the xy - coordinate system , what is the slope of the line that goes through the point ( 1 , 1 ) and is equidistant from the two points p = ( 3 , 7 ) and q = ( 9 , 11 ) ?
Options: a ) 0.5 , b ) 0.625 , c ) 0.75 , d ) 0.875 , e ) 1.0
Rationale: "first , get the middle coordinate between ( 3,7 ) and ( 9,11 ) . . . x = 3 + ( 9 - 3 ) / 2 = 6 y = 7 + ( 11 - 7 ) / 2 = 9 second , get the slope of ( 9,6 ) and ( 1,1 ) . m = 6 - 1 / 9 - 1 = 5 / 8 = 0.625 answer : b"
Answer: b
Question (physics): a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 12 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 14 %
Rationale: "total time for travelling 80 miles @ 60 mph = 80 / 60 = 4 / 3 hour = 80 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 80 minutes it will use = 2 gallons . thus , full tank = 2 + 12 = 14 gallons - - - > 2 / 14 = 14 % of the fuel used . e is the correct answer ."
Answer: e
Question (other): the ratio of flour to water to sugar in a recipe is 11 : 5 : 2 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 7.5 cups of water , how much sugar is required ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: the ratio of flour to water is 22 : 5 . the ratio of flour to sugar is 5.5 : 2 = 22 : 8 . the new ratio of flour to water to sugar is 22 : 5 : 8 if we need 7.5 cups of water , then we need 12 cups of sugar . the answer is e .
Answer: e
Question (physics): with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 5 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 187 km , b ) 480 km , c ) 278 km , d ) 297 km , e ) 600 km
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 5 2 x / 15 - x / 8 = 5 = > x = 600 km . answer : e"
Answer: e
Question (gain): a merchant marks goods up by 60 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 20 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let p be the original price of the goods and let x be the rate after the markup . ( 1.6 p ) * x = 1.2 p x = 1.2 / 1.6 = 0.75 which is a discount of 25 % . the answer is b ."
Answer: b
Question (general): a student scored an average of 65 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 165 , c ) 76 , d ) 125 , e ) 26
Rationale: "given m + p + c = 65 * 3 = 195 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 195 = 125 answer : d"
Answer: d
Question (general): find the number of trailing zeros in the product of ( 1 ^ 1 ) * ( 5 ^ 5 ) * ( 10 ^ 10 ) * ( 15 ^ 15 ) * ( 20 ^ 20 ) * ( 25 ^ 25 ) … … … . * ( 50 ^ 50 ) .
Options: a ) 150 , b ) 200 , c ) 250 , d ) 245 , e ) 225
Rationale: looking at the numbers it looks like ( 1 x 5 ) ^ 5 ( 2 x 5 ) ^ 10 . . . ( 10 x 5 ) ^ 50 1 . determine the limiting factor . is it 2 or is it 5 ? we know that all the numbers are multiple of 5 but not of 2 . thus , the limiting factor in this case is 2 . let ' s drop all the 5 . then , we count factors of 2 of even multiples . 2 ^ 10 = 10 4 ^ 20 = 20 + 20 6 ^ 30 = 30 8 ^ 40 = 40 + 40 + 40 10 ^ 50 = 50 250 answer : c
Answer: c
Question (general): how many numbers from 2 to 8 are exactly divisible by 2 ?
Options: a ) a ) 2 , b ) b ) 4 , c ) c ) 5 , d ) d ) 7 , e ) e ) 8
Rationale: "2 / 2 = 1 and 8 / 2 = 4 4 - 1 = 3 3 + 1 = 4 numbers . answer : b"
Answer: b
Question (physics): the length of a bridge in meters , which a train 80 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 215 , b ) 235 , c ) 255 , d ) 275 , e ) 295
Rationale: "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 80 = 375 meters x = 295 meters the answer is e ."
Answer: e
Question (geometry): find the smallest number which should be divided with 3872 to make it a perfect square .
Options: a ) 8 , b ) 6 , c ) 2 , d ) 4 , e ) 1
Rationale: "3872 = 11 * 11 * 2 * 2 * 2 * 2 * 2 required smallest number = 2 2 is the smallest number which should be divided with 3872 to make it a perfect square . answer : c"
Answer: c
Question (general): x and y are both integers . if x / y = 59.80 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 200 , e ) 1024
Rationale: "remainder = 0.80 = - - > 80 / 100 - - > can be written as ( 80 / 4 ) / ( 100 / 4 ) = 20 / 25 so remainders can be 20 , 40 , 60 , 80 we need the sum of only 2 digit remainders - - > 20 + 40 + 60 + 80 = 200 answer : d"
Answer: d
Question (physics): a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 4 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 21 , b ) 26 , c ) 30 , d ) 18 , e ) 16
Rationale: "a - - - - - b - - - - c - - - - - - - - d - - - - e given : de = 4 - ( i ) ab = 5 - ( ii ) ac = 11 - ( iii ) bc = 2 cd - ( iv ) from ( ii ) and ( iii ) , bc = 6 from ( iv ) , cd = 3 length of ae = ac + cd + de = 11 + 3 + 4 = 18 correct option : d"
Answer: d
Question (general): on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction t of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is t = 2 / 14 = 1 / 7 . answer : e
Answer: e
Question (physics): a train leaves delhi at 9 a . m . at a speed of 35 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 229 , b ) 288 , c ) 600 , d ) 888 , e ) 1400
Rationale: "d = 35 * 5 = 175 rs = 40 – 35 = 5 t = 175 / 5 = 35 d = 40 * 35 = 1400 km answer : e"
Answer: e
Question (gain): rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 2000 . then his monthly salary is
Options: a ) rs . 10000 , b ) rs . 6000 , c ) rs . 8000 , d ) rs . 4000 , e ) rs . 2000
Rationale: sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 2000 â ‡ ” 20 / 100 x = 2000 â ‡ ” x = 2000 ã — 5 = 10000 . answer a
Answer: a