Cheukting/mathqa huggingface dataset:
Question (general): a number when divided by 296 leaves 75 as remainder . when the same number is divided by 37 , the remainder will be :
Options: a ) 1 , b ) 5 , c ) 3 , d ) 4 , e ) 11
Rationale: "let x = 296 q + 75 = ( 37 x 8 q + 37 x 2 ) + 1 = 37 ( 8 q + 2 ) + 1 thus , when the number is divided by 37 , the remainder is 1 . answer a"
Answer: a
Question (physics): a certain car increased its average speed by 5 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 2 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: "in the third time interval the average speed of the car was 2 + 5 + 5 = 12 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 12 * 1 / 12 = 1 miles . answer : a ."
Answer: a
Question (physics): two trains of equal length , running with the speeds of 60 and 40 kmph , take 60 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 16 sec , c ) 12 sec , d ) 67 sec , e ) 13 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 60 * 100 / 18 = 1000 / 3 rs = 60 + 40 = 100 * 5 / 18 t = 1000 / 3 * 18 / 500 = 12 sec answer : c"
Answer: c
Question (general): what will be the vulgar fraction of 0.60
Options: a ) 3 / 7 , b ) 3 / 5 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.6 = 60 / 100 = 3 / 5 option b"
Answer: b
Question (general): how many 3 digit positive integers w exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ."
Answer: e
Question (gain): find the missing figures : 0.2 % of ? = 0.02
Options: a ) 50 , b ) 100 , c ) 10 , d ) 1000 , e ) 110
Rationale: "let 0.2 % of x = 0.02 . then , 0.2 * x / 100 = 0.02 x = [ ( 0.02 * 100 ) / 0.2 ] = 100 . answer is b ."
Answer: b
Question (general): find the value of 18396 x 9999 = m ?
Options: a ) 194852714 , b ) 183941604 , c ) 183851704 , d ) 183951714 , e ) 183768244
Rationale: "18396 x 9999 = 18396 x ( 10000 - 1 ) = 18396 x 10000 - 18396 x 1 = 183960000 - 18396 = 183941604 b"
Answer: b
Question (general): the sum of the squares of three numbers is 100 , while the sum of their products taken two at a time is 48 . their sum is :
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 100 xy + yz + zx = 48 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 100 + ( 2 * 48 ) ( x + y + z ) ^ 2 = 196 so x + y + z = 14 answer : e"
Answer: e
Question (general): if , 1 * 3 * 5 = 16 3 * 5 * 7 = 38 then find , 13 * 15 * 17 = ?
Options: a ) 89 , b ) 49 , c ) 68 , d ) 268 , e ) 55
Rationale: d 268 ( 17 * 15 ) + 13 = 268
Answer: d
Question (physics): if 20 men can build a wall 66 metres long in 6 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 53 m , b ) 46 m , c ) 94 m , d ) 49 m , e ) 64 m
Rationale: "let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 6 : 3 : : 56 : x therefore ( 20 x 6 x x ) = ( 35 x 3 x 56 )  x = ( 35 x 3 x 56 ) / 120 = 49 hence , the required length is 49 m . answer is d"
Answer: d
Question (gain): the calendar of the year 2024 can be used again in the year ?
Options: a ) 2288 , b ) 2052 , c ) 2778 , d ) 2719 , e ) 1711
Rationale: "explanation : given year 2024 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 , 2024 + 28 = 2052 answer : b ) 2052"
Answer: b
Question (physics): the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 6 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 20 km , b ) 30 km , c ) 40 km , d ) 50 km , e ) 60 km
Rationale: number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 6 = 30 km imo , correct answer is ` ` b . ' '
Answer: b
Question (geometry): a sixth grade teacher asked her students to draw rectangles with positive integer length and a perimeter of 42 . the difference between the largest and smallest possible ares of the rectangles that the students could have come up with is ?
Options: a ) 50 sq units
b ) 60 sq units
c ) 70 sq units
d ) 80 sq units
e ) 90 sq units
Rationale: sum of length and breadth will be 21 units . 42 / 2 = 21 area will be max when lxb = 11 x 10 = 110 sq units area will be min when lxb = 20 x 1 = 20 sq units . . the difference between the largest and smallest possible ares of the rectangles that the students could have come up with = 110 - 20 = 90 sq units answer : e
Answer: e
Question (general): 3 partners a , b , c starts a business . twice a ' s capital is equal to thrice b ' s capital and b ' s capital is 4 times c ' s capital . out of a total profit of rs . 16500 at the end of the year , b ' s share is
Options: a ) rs . 4000 , b ) rs . 6000 , c ) rs . 7500 , d ) rs . 6600 , e ) none
Rationale: solution let c = x . then , b = 4 x and 2 a = 3 x 4 x = 12 x or a = 6 x . ∴ a : b : c = 6 x : 4 x : x = 6 : 4 : 1 . so b ' s capital = rs ( 16500 x 4 / 11 ) = rs . 6000 . answer b
Answer: b
Question (general): a retailer sells 6 shirts . the first 2 he sells for $ 40 and $ 50 . if the retailer wishes to sell the 6 shirts for an overall average price of over $ 50 , what must be the minimum average price of the remaining 4 shirts ?
Options: a ) $ 37.00 , b ) $ 40.00 , c ) $ 45.50 , d ) $ 48.00 , e ) $ 52.50
Rationale: "first 2 shirts are sold for $ 40 and $ 50 = $ 90 . to get average price of $ 50 , total sale should be 6 * $ 50 = $ 300 so remaining 4 shirts to be sold for $ 300 - $ 90 = $ 210 answer should be 210 / 4 = $ 52.50 that is e"
Answer: e
Question (general): the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8800 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 3300 , b ) s . 4570 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8800 = 35200 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 3200 salary of may is rs . 6500 salary of january = rs . 3300 answer : a"
Answer: a
Question (physics): with both inlets open , a water tank will be filled with water in 20 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 9,000 , b ) 1,500 , c ) 1,750 , d ) 1,200 , e ) 1,300
Rationale: "the work done by inlet a and b together in 1 min = 1 / 20 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 20 ) - ( 1 / 120 ) = 1 / 24 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 24 ) - ( 1 / 120 ) = 50 cubic meter i . e . 1500 cubic meter answer : option b"
Answer: b
Question (other): the ratio between the radii of two spheres is 1 : 3 . find the ratio between their volumes ?
Options: a ) 1 : 28
b ) 1 : 27
c ) 1 : 29
d ) 1 : 39
e ) 1 : 22
Rationale: explanation : r 1 : r 2 = 1 : 3 r 13 : r 23 = 1 : 27 answer : option b
Answer: b
Question (general): every year taylor goes to the same carnival , and he attempts to shoot a basketball into a small hoop , hoping that he will win a 10 - foot tall teddy bear . if the probability that taylor does not make a basket is 1 / 3 , what is the probability that taylor makes exactly one basket in 3 tries ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 7
Rationale: probability of basket = 2 / 3 probability of no basket = 1 / 3 required probability = 3 * 2 / 3 * 1 / 3 * 1 / 3 = 2 / 9 b is the answer .
Answer: b
Question (general): the average of 13 result is 20 . average of the first 8 of them is 20 and that of the last 8 is 40 . find the 8 th result ?
Options: a ) 35 , b ) 37 , c ) 46 , d ) 90 , e ) 100
Rationale: "sum of all the 13 results = 13 * 20 = 260 sum of the first 7 of them = 8 * 20 = 160 sum of the last 7 of them = 8 * 40 = 320 so , the 8 th number = 260 + 160 - 320 = 100 . e"
Answer: e
Question (physics): 16 boys or 24 girls can construct the wall in 6 days . the number of days that 4 boys and 12 girls will take to construct ?
Options: a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 4 boys + 12 girls = 4 ã — 6 / 4 + 12 = 6 + 12 = 18 girls 8 days to complete the work answer : option d
Answer: d
Question (gain): the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 40 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 50 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 40 kg . as the price falls by 20 % , new price for 40 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 40 = rs . 2 per kg . rice can bought now at = 100 / 2 = 50 kg . answer : option d"
Answer: d
Question (general): a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money j did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ j = 20 answer : b
Answer: b
Question (probability): a certain junior class has 1,000 students and a certain senior class has 800 students . among these students , there are 40 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 1 / 20,000 , d ) 1 / 60 , e ) 1 / 15
Rationale: total number of ways of choosing one student from each group is = 800 * 1000 number of cases in which a sibling pair will be got is = 40 thus the probability that the 2 students selected will be a sibling pair is = 40 / ( 800 * 1000 ) = 1 / 20,000 c
Answer: c
Question (general): running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 5 w widgets ?
Options: a ) 4 , b ) 30 , c ) 8 , d ) 10 , e ) 12
Rationale: "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 5 * 6 = 30 days to produce 2 w widgets . answer : b"
Answer: b
Question (general): find value for x from below equation ? x + 1 = 2
Options: a ) - 5 , b ) 1 , c ) 4 , d ) 3 , e ) 2
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = 2 - 1 2 . simplify both sides : x = 1 b"
Answer: b
Question (gain): a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 170 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 278 , c ) 250 , d ) 500 , e ) 821
Rationale: "p - 170 = ( p * 4 * 8 ) / 100 p = 250 answer : c"
Answer: c
Question (general): little john had $ 10.50 . he spent $ 2.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ?
Options: a ) $ 1.85 , b ) $ 3.85 , c ) $ 4.85 , d ) $ 6.85 , e ) $ 5.85
Rationale: "john spent and gave to his two friends a total of 2.25 + 2.20 + 2.20 = $ 6.65 money left 10.50 - 6.65 = $ 3.85 correct answer is b ) $ 3.85"
Answer: b
Question (physics): a and b can do a piece of work in 12 days and 16 days respectively . both work for 3 days and then a goes away . find how long will b take to complete the remaining work ?
Options: a ) 6 days , b ) 12 days , c ) 15 days , d ) 9 days , e ) 8 days
Rationale: "3 / 12 + ( 3 + x ) / 16 = 1 x = 9 days answer : d"
Answer: d
Question (other): what is the square root of 225 ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 45 , e ) 15
Rationale: "15 x 15 = 225 answer e"
Answer: e
Question (general): a motorcycle importer is planning on increasing the price of a certain model by $ 1000 . at this new price 8 fewer motorcycles will be sold per month , but the total revenues will increase by $ 26000 to $ 594000 . what is the number of motorcycles the manufacturer will sell at this new price ?
Options: a ) 61 , b ) 62 , c ) 65 , d ) 63 , e ) 64
Rationale: responding to a pm : to solve this question , i will make an equation in x and then make educated guesses . here ' s how : assuming x motorcycles were sold every month initially . ( 568000 / x + 1000 ) ( x - 8 ) = 594000 ( 568 / x + 1 ) ( x - 8 ) = 594 now 568 = 8 * 71 assuming x = 71 ( we have all integers so it is obvious that 568 / x should be an integer . we get 9 * 66 = 594 ( matches ) so he will sell 71 - 8 = 63 bikes this month answer ( d )
Answer: d
Question (general): 1 / 0.02 is equal to
Options: a ) 50 , b ) 2.5 , c ) 25 , d ) . 25 , e ) none of these
Rationale: explanation : 1 / 0.02 = ( 1 * 100 ) / 2 = 100 / 2 = 50 option a
Answer: a
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 10000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 14
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 10000 x 7 ) + 6000 ( x - 7 ) x = 14 . answer e"
Answer: e
Question (general): what is the remainder when 3 ^ 29 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 29 has the form 4 k + 1 , so the units digit of 3 ^ 29 is 3 . the remainder when dividing by 5 is 3 . the answer is d ."
Answer: d
Question (geometry): obra drove 200 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 % , b ) 12.5 % , c ) 41.66 % , d ) 25 % , e ) 33.3 %
Rationale: "area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 200 π / 480 π = 41.66 % hence , answer is c ."
Answer: c
Question (general): if the price of a certain computer increased 20 percent from d dollars to 351 dollars , then 2 d =
Options: a ) 540 , b ) 585 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = d after 30 % price increase price = d + ( 20 / 100 ) * d = 1.2 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 292,5 i . e . 2 d = 2 * 292.5 = 585 answer : option b"
Answer: b
Question (physics): two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 20 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 7.5 hr , b ) 8 hr , c ) 8.5 hr , d ) 10 hr , e ) none of these
Rationale: "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 20 = 2 / 15 hence , tank will be filled in 15 / 2 = 7.5 hour option ( a )"
Answer: a
Question (general): what must be added to each term of the ratio 2 : 3 , so that it may become equal to 4 : 5 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 9 , e ) 8
Rationale: let the number to be added be x , then ( 2 + x ) : ( 3 + x ) = 4 : 5 ⇒ ( 2 + x ) / ( 5 + x ) = 4 / 5 5 ( 2 + x ) = 4 ( 3 + x ) 10 + 5 x = 12 + 4 x 5 x - 4 x = 12 - 10 x = 2 answer : 2
Answer: a
Question (geometry): obra drove 180 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 37.5 % , b ) 12.5 % , c ) 18.75 % , d ) 25 % , e ) 33.3 %
Rationale: "area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 180 π / 480 π = 37.5 % hence , answer is a ."
Answer: a
Question (general): the average of 8 numbers is 21 . if each of the number is multiplied by 8 , the average of the new set of numbers is :
Options: a ) 168 , b ) 667 , c ) 288 , d ) 1991 , e ) 111
Rationale: "average of new numbers = ( 21 × 8 ) = 168 answer : a"
Answer: a
Question (physics): if 14 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 42 days , d ) 48 days , e ) 56 days
Rationale: "14 * 80 = 20 * x x = 56 days answer : e"
Answer: e
Question (general): in what proportion must flour at $ 0.8 per pound be mixed with flour at $ 0.9 per pound so that the mixture costs $ 0.855 per pound ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 1 : 1 , d ) 2 : 1 , e ) 4 : 5
Rationale: "using weighted average method : let x be the proportion in which the $ 0.8 per pound flour is mixed with $ 0.9 per pound flour . thus 0.8 * x + 0.9 * ( 1 - x ) = 0.855 0.9 – 0.1 x = 0.855 x = 0.45 thus ratio of both flours is 4 : 5 e"
Answer: e
Question (physics): two terms are in 3 : 4 , if 10 is added to each of the terms , they will be 4 : 5 . find second term ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 40 , e ) 35
Rationale: solution : let the two numbers be 3 x and 4 x . then , ( 3 x + 10 ) / ( 4 x + 10 ) = 4 / 5 . = > 15 x + 50 = 16 x + 40 = > x = 10 . . ' . second term = 4 * 10 = 40 . answer is d
Answer: d
Question (physics): a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 18 kilometer long bridge , at the same speed ?
Options: a ) 14 min , b ) 20 min , c ) 18 min , d ) 19 min , e ) 13 min
Rationale: "s = 600 / 40 = 15 mps s = 18000 / 15 = 1200 sec = 20 min . answer : b"
Answer: b
Question (physics): two pipes a and b can fill a tank in 18 hours and 24 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20 hours , b ) 15 hours , c ) 10 hours , d ) 10 2 / 7 hours , e ) 8 hours
Rationale: "part filled by a in 1 hour = 1 / 18 part filled by b in 1 hour = 1 / 24 part filled by ( a + b ) in 1 hour = 1 / 18 + 1 / 24 = 7 / 72 both the pipes together fill the tank in 72 / 7 = 10 2 / 7 hours answer is d"
Answer: d
Question (geometry): the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle
Options: a ) 18 cm , b ) 16 cm , c ) 40 cm , d ) 20 cm , e ) 28 cm
Rationale: "explanation : let breadth = x cm then , length = 2 x cm area = x × 2 x = 2 x ^ 2 sq . cm . new length = ( 2 x − 5 ) cm new breadth = ( x + 5 ) cm new area = ( 2 x − 5 ) ( x + 5 ) sq . cm . given that , new area = initial area + 75 sq . cm . ⇒ ( 2 x − 5 ) ( x + 5 ) = 2 x ^ 2 + 75 ⇒ 2 x ^ 2 + 10 x − 5 x − 25 = 2 x ^ 2 + 75 ⇒ 5 x − 25 = 75 ⇒ 5 x = 75 + 25 = 100 ⇒ x = 1005 = 20 cm length = 2 x = 2 × 20 = 40 cm answer : option c"
Answer: c
Question (gain): the list price of an article is rs . 70 . a customer pays rs . 59.85 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 6 % , e ) 5 %
Rationale: "option e explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 59.85 x = 5 %"
Answer: e
Question (general): for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 9.8 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 9.8 = 6 * 0 + 2 * 7.2 + 8 - 9.8 = 0 + 14.4 - 1.8 12.6 answer a"
Answer: a
Question (physics): two persons start running simultaneously around a circular track of length 250 m from the same point at speeds of 20 kmph and 40 kmph . when will they meet for the first time any where on the track if they are moving in the opposite direction ?
Options: a ) 144 , b ) 15 , c ) 18 , d ) 32 , e ) 38
Rationale: time taken to meet the first time = length of track / relative speed = 250 / ( 20 + 40 ) ( 5 / 18 ) = 250 / 60 * ( 18 / 5 ) = 15 sec . answer : b
Answer: b
Question (general): sixteen percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 63 % , e ) 75 %
Rationale: initially 84 % and 16 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 84 so , the required % is [ ( 3 / 4 ) ∗ 84 / 100 ] ∗ 100 = 63 % answer : d
Answer: d