Cheukting/mathqa huggingface dataset:
Question (general): if x ^ 2 + y ^ 2 = 15 and xy = 3 , then ( x − y ) ^ 2 =
Options: a ) 8 , b ) 9 , c ) 14 , d ) 17 , e ) 20
Rationale: but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 15 - 2 * 3 = 9 . . answer b
Answer: b
Question (geometry): the perimeter of a triangle is 48 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 76 , b ) 88 , c ) 60 , d ) 55 , e ) 35
Rationale: "area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 48 / 2 = 60 cm 2 answer : c"
Answer: c
Question (general): if h = { 1 , 7 , 18 , 20 , 29 , 33 } , how much less is the mean of the numbers in h than the median of the numbers in h ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 1 + 7 + 18 + 20 + 29 + 33 ) / 6 = 18 median = ( 18 + 20 ) / 2 = 19 difference = 1 option a
Answer: a
Question (geometry): what will be the cost of house to paint which area equal to 484 sq ft , if the price per foot of building is rs . 20
Options: a ) 1800 , b ) 1760 , c ) 1400 , d ) 2600 , e ) 3600
Rationale: let the side of the square plot be a ft . a 2 = 484 = > a = 22 length of the fence = perimeter of the plot = 4 a = 88 ft . cost of building the fence = 88 * 20 = rs . 1760 . answer : b
Answer: b
Question (general): x varies inversely as square of y . given that y = 2 for x = 1 . the value of x for y = 6 will be equal to ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 0 , d ) 1 / 9 , e ) 1 / 5
Rationale: "given x = k / y 2 , where k is a constant . now , y = 2 and x = 1 gives k = 4 . x = 4 / y 2 = > x = 4 / 62 , when y = 6 = > x = 4 / 36 = 1 / 9 . answer : d"
Answer: d
Question (probability): two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability r that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability r = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Question (general): there are , in a certain league , 50 teams , and each team face another team for a total of 4 times . how many games are played in the season ?
Options: a ) 6660 , b ) 3600 , c ) 2400 , d ) 4900 , e ) 5400
Rationale: by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 4900 option d .
Answer: d
Question (gain): a cycle is bought for rs . 1000 and sold for rs . 2000 , find the gain percent ?
Options: a ) 11 , b ) 20 , c ) 100 , d ) 77 , e ) 12
Rationale: "1000 - - - - 1000 100 - - - - ? = > 100 % answer : c"
Answer: c
Question (physics): a 360 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 57.6 sec , b ) 20.2 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 360 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 880 m time = distance / speed = 880 x 18 / ( 5 x 55 ) = 57.6 sec ans is : a"
Answer: a
Question (general): 5 x 1.6 - 2 x 1.4 / 1.3 = ?
Options: a ) 3 , b ) 0 , c ) 5 , d ) 4 , e ) 2
Rationale: "given expression = ( 8 - 2.8 ) / 1.3 = 5.2 / 1.3 = 52 / 1.3 = 4 . answer is d ."
Answer: d
Question (physics): the speed of a car is 98 km in the first hour and 70 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 75 kmph , c ) 87 kmph , d ) 56 kmph , e ) 84 kmph
Rationale: "s = ( 98 + 70 ) / 2 = 84 kmph answer : e"
Answer: e
Question (physics): 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 10 days , working 12 hours a day , the number of men required ?
Options: a ) 10 days , b ) 9 days , c ) 6 days , d ) 8 days , e ) 7 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 12 × 10 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 12 × 10 = 8 days d )"
Answer: d
Question (gain): divide rs . 1301 between a and b , so that the amount of a after 7 years is equal to the amount of b after 9 years , the interest being compounded at 4 % per annum .
Options: a ) 625 , b ) 367 , c ) 288 , d ) 209 , e ) 198
Rationale: explanation : let the two parts be rs . x and rs . ( 1301 - x ) . 625 x = 676 ( 1301 - x ) 1301 x = 676 x 1301 x = 676 . so , the parts are rs . 676 and rs . ( 1301 - 676 ) i . e rs . 676 and rs . 625 answer : a ) rs . 625
Answer: a
Question (gain): heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 40 litres of tomato juice ?
Options: a ) 2.8 liters . , b ) 2.5 liters . , c ) 5 liters . , d ) 2.6 liters . , e ) 2.1 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 40 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 5 liters . answer : c"
Answer: c
Question (general): david works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 4 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 3 / 5 , b ) 2 / 5 , c ) 4 / 5 , d ) 1 / 5 , e ) 6 / 5
Rationale: first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 4 x total tips for all months = 6 * x + 4 x = 10 x tips for august / total tips for all months = 4 x / 10 x = 2 / 5 answer : b
Answer: b
Question (physics): a train 330 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 44 sec
Rationale: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 330 × 2 / 15 ) sec = 44 sec answer : e"
Answer: e
Question (physics): walking at 4 / 5 of her normal speed , a worker is 15 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 65
Rationale: "let v be her normal speed and let t be her normal time . d = ( 4 / 5 ) v * ( t + 15 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 4 / 5 ) v * ( t + 15 ) t / 5 = 12 t = 60 the answer is d ."
Answer: d
Question (gain): a cylinder of height h is 8 / 9 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 68 % , d ) 80 % , e ) 100 %
Rationale: basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 8 / 9 new cylinder 3 / 5 so 3 / 5 / 8 / 9 = 3 / 5 * 9 / 8 = 12 / 15 = 4 / 5 = 0.680 or 68 % . answer c
Answer: c
Question (physics): mary passed a certain gas station on a highway while traveling west at a constant speed of 40 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 60 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 2 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 , d ) 4 , e ) 5
Rationale: "d = rt m : r = 40 mph , t = t + 1 / 4 hr d = 40 ( t + 1 / 4 ) p : r = 60 , t = t d = 60 t since they went the same distance : 40 t + 40 / 4 = 60 t 20 t = 40 / 4 t = 1 / 2 or 1 / 2 hr a"
Answer: a
Question (physics): a can do a job in 15 days and b in 30 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 2 / 15 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 30 a + b 1 day work = 1 / 15 + 1 / 30 = 3 / 30 = 1 / 10 a + b 4 days work = 1 / 10 * 4 = 2 / 5 remaining work = 1 - 2 / 5 = 3 / 5 answer is b"
Answer: b
Question (general): the population of a city increases by 9 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 25.97 % , d ) 12 % , e ) none of these
Rationale: "actual increase in population = 8 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 8 / 100 ) ^ 3 = 125.97 ∴ required percentage = 25.97 % answer : c"
Answer: c
Question (physics): a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.5 m and its walls are 5 cm thick . the thickness of the bottom is :
Options: a ) 90 cm , b ) 5 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
Rationale: "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 150 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 150 - x ) = 8000 × 1000 = > ( 150 - x ) = 8000 × 1000 / 320 = 100 = > x = 50 cm = 5 dm . answer : b"
Answer: b
Question (general): if k is the greatest positive integer such that 3 ^ k is a divisor of 18 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "18 / 3 = 6 18 / 9 = 2 6 + 2 = 8 k = 8 answer : e"
Answer: e
Question (general): if 18888 – n is divisible by 11 , and 0 < n < 11 , what is n ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: 18,888 / 11 = 1717 with a remainder of 1 . we need to subtract the remainder to get a multiple of 11 . the answer is a .
Answer: a
Question (gain): after decreasing 56 % in the price of an article costs rs . 4400 . find the actual cost of an article ?
Options: a ) 12000 , b ) 15000 , c ) 1200 , d ) 1000 , e ) 10000
Rationale: "cp * ( 44 / 100 ) = 4400 cp = 100 * 100 = > cp = 10000 answer : e"
Answer: e
Question (general): for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 45 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 29 % , e ) 28 %
Rationale: total sales = 800 comission = ( 20 / 100 ) * 500 + ( 45 / 100 ) * 300 = 100 + 135 = 235 % comission = ( 235 / 800 ) * 100 = 29.4 ~ 29 % answer is d
Answer: d
Question (gain): a shop owner sells 50 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 25 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 50 m cloth ) – ( c . p . of 50 m cloth ) selling price of 40 m cloth = selling price of 50 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 40 m cloth = rs . 4000 and s . p . of 40 m cloth = rs . rs . 5000 profit % = 10 / 40 × 100 = 25 % profit of 25 % was made by the merchant . a
Answer: a
Question (gain): find compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually .
Options: a ) rs . 512 , b ) rs . 552 , c ) rs . 612 , d ) rs . 622 , e ) none
Rationale: "solution amount = rs [ 7500 x ( 1 + 4 / 100 ) ² ] = rs . ( 7500 x 26 / 25 x 26 / 25 ) = rs . 8112 . c . i = rs ( 8112 - 7500 ) = rs . 612 . answer c"
Answer: c
Question (general): a number is 4 less than 6 times the other number . if the sum of both the number is 38 , what are the numbers ?
Options: a ) 632 , b ) 731 , c ) 533 , d ) 434 , e ) none of the above
Rationale: that numbers are x , 6 x - 4 so sum = x + 6 x - 4 = 38 7 x = 42 = = > x = 6 another no is 32 answer is 6 , 32 answer : a
Answer: a
Question (physics): two trains of length 250 m and 120 m are 50 m apart . they start moving towards each other on parallel tracks , at speeds 64 kmph and 42 kmph . after how much time will the trains meet ?
Options: a ) 15 / 10 , b ) 17 / 10 , c ) 16 / 10 , d ) 18 / 10 , e ) 16 / 10
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 64 + 42 ) * 5 / 18 = 7 * 5 = 29.4 mps . the time required = d / s = 50 / 29.4 = 17 / 10 sec . answer : b"
Answer: b
Question (geometry): the area of sector of a circle whose radius is 12 metro and whose angle at the center is 38 ° is ?
Options: a ) 30 m 2 , b ) 40 m 2 , c ) 47.7 m 2 , d ) 50 m 2 , e ) 55 m 2
Rationale: "38 / 360 * 22 / 7 * 12 * 12 = 47.7 m 2 answer : c"
Answer: c
Question (physics): if the l . c . m of two numbers is 750 and their product is 18750 , find the h . c . f of the numbers .
Options: a ) 50 , b ) 30 , c ) 125 , d ) 25 , e ) none of these
Rationale: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18750 / 750 = 25 . answer : d"
Answer: d
Question (general): the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 200,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 200 ( 200,000 / 1,000 = 200 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 200 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 8 = 256 , i . e . the population has to double 8 times . since it takes the population 2 minutes to double once it takes 8 * 2 minutes = 16 minutes to double 8 times . thus , solution d = 16 is correct ."
Answer: d
Question (other): the marks obtained by polly and sandy are in the ratio 3 : 5 and those obtained by sandy and willy are in the ratio of 3 : 2 . the marks obtained by polly and willy are in the ratio of . . . ?
Options: a ) 3 : 4 , b ) 5 : 6 , c ) 7 : 8 , d ) 9 : 10 , e ) 11 : 12
Rationale: "polly : sandy = 3 : 5 = 9 : 15 sandy : willy = 3 : 2 = 15 : 10 polly : sandy : willy = 9 : 15 : 10 polly : willy = 9 : 10 the answer is d ."
Answer: d
Question (general): if the largest 3 digit number is subtracted from the smallest 5 digit number , then the remainder is
Options: a ) 1 , b ) 9000 , c ) 9001 , d ) 90001 , e ) none
Rationale: solution required remainder = ( 10000 - 999 ) = 9001 answer c
Answer: c
Question (gain): x and y started a business investing rs . 50000 and rs 40000 respectively . in what ratio the profit earned after 2 years be divided between x and y respectively ?
Options: a ) 3 : 2 , b ) 9 : 2 , c ) 5 : 4 , d ) 1 : 4 , e ) 18 : 4
Rationale: x : y = 50000 : 40000 = 5 : 4 answer : c
Answer: c
Question (physics): a man can row downstream at 26 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 2 , 9 , b ) 4 , 9 , c ) 8 , 9 , d ) 18 , 8 , e ) 7 , 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 26 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 36 = > x = 18 , y = 8 . answer : d"
Answer: d
Question (other): if log 1087.5 = 3.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 27 , d ) 50 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 3.9421 + 1 ) = 10 ( 4.9421 ) = 49.421 x = antilog ( 49.421 ) therefore , number of digits in x = 50 . answer : d"
Answer: d
Question (gain): if $ 5,000 is invested in an account that earns 12 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.12 / 2 ) ^ 2 = 5412 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 12 / 100 ) = 5400 difference = 5412 - 5400 = 12 $ c"
Answer: c
Question (geometry): the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 180 m , its area is ?
Options: a ) 90 , b ) 882 , c ) 277 , d ) 261 , e ) 281
Rationale: "5 x + 12 x + 13 x = 180 = > x = 6 a = 30 , b = 72 , c = 78 s = ( 30 + 72 + 78 ) / 2 = 90 answer : a"
Answer: a
Question (general): if 2 ^ 4 , 2 ^ 3 , and 11 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 176 , b ) 288 , c ) 363 , d ) 396 , e ) 484
Rationale: i will go with a ( pending elements to match is 2 ^ 2 * 2 ^ 2 * 11 ^ 1 = 176
Answer: a
Question (general): what is the sum of 80 consecutive integers from - 39 inclusive , in a increasing order ?
Options: a ) - 29 , b ) 39 , c ) - 30 , d ) 40 , e ) 60
Rationale: "from - 39 to - 1 - - > 39 nos . zero - - > 1 number from + 1 to + 39 - - > 39 nos . when we add up nos . from - 39 to + 39 sum will be zero . total 79 nos will be added . 80 th number will be 40 . sum of these 80 nos . = 40 . d is the answer ."
Answer: d
Question (gain): the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 70 % profit ?
Options: a ) 277 , b ) 1088 , c ) 277 , d ) 266 , e ) 121
Rationale: "let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 170 % of rs . 640 = 170 / 100 * 640 = rs . 1088 . answer : b"
Answer: b
Question (general): a man has some hens and cows . if the number of heads be 46 and the number of feet equals 136 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "explanation : let number of hens = h and number of cows = c number of heads = 46 = > h + c = 46 - - - ( equation 1 ) number of feet = 136 = > 2 h + 4 c = 136 = > h + 2 c = 68 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 68 - 46 = > c = 22 substituting the value of c in equation 1 , we get h + 22 = 46 = > h = 46 - 22 = 24 i . e . , number of hens = 24 answer : b"
Answer: b
Question (general): find the smallest number which when divided by 13 and 17 leaves respective remainders of 3 and 7 .
Options: a ) 187 , b ) 211 , c ) 207 , d ) 219 , e ) 227
Rationale: "let ' n ' is the smallest number which divided by 13 and 17 leaves respective remainders of 3 and 7 . required number = ( lcm of 13 and 17 ) - ( common difference of divisors and remainders ) = ( 221 ) - ( 10 ) = 211 . answer : b"
Answer: b
Question (general): a ' s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 25 % of the length of the race ?
Options: a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 61 %
Rationale: "first calculate the distance , b has covered with his speed in the time , in which a reached 60 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 20 / 13 of b , therefore , b ' s speed is 13 / 20 of a distance covered by b = speed x time = ( 13 / 20 ) x ( 0.6 ) = 0.39 % ( which means b would have covered 0.39 of the race length during the time in which a has covered 0.6 of the race length . therefore to win , b needs a headstart of ( 1 - 0.39 = ) 0.61 of the race length . so the answer is e"
Answer: e
Question (general): find the constant k so that : - x 2 - ( k + 11 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) 11 , b ) 12 , c ) 17 , d ) 14 , e ) 15
Rationale: "- x 2 - ( k + 11 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 11 ) x - 8 = - x 2 + 6 x - 8 - ( k + 11 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 17 : solve the above for k correct answer c"
Answer: c
Question (physics): what is the maximum number of pieces of birthday cake of size 10 ” by 10 ” that can be cut from a cake 20 ” by 20 ” ?
Options: a ) 4 , b ) 10 , c ) 16 , d ) 20 , e ) 25
Rationale: "the prompt is essentially asking for the maximum number of 10 x 10 squares that can be cut from a larger 20 by 20 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 2 ' pieces ' each , we have ( 2 ) ( 2 ) = 4 total smaller squares ( at maximum ) . a"
Answer: a
Question (geometry): if the sides of a triangle are 65 cm , 60 cm and 25 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 750 cm 2 , c ) 216 cm 2 , d ) 197 cm 2 , e ) 275 cm 2
Rationale: "the triangle with sides 65 cm , 60 cm and 25 cm is right angled , where the hypotenuse is 65 cm . area of the triangle = 1 / 2 * 60 * 25 = 750 cm 2 answer : b"
Answer: b
Question (gain): a man walking at a rate of 15 km / hr crosses a bridge in 30 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1110 m , c ) 950 m , d ) 1500 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 30 minutes = 15 / 18 * 30 * 60 = 1500 m answer is d"
Answer: d
Question (general): the population of a city increases by 7 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.10 % , c ) 27 % , d ) 12 % , e ) none of these
Rationale: "actual increase in population = 6 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 6 / 100 ) ^ 3 = 119.1016 ∴ required percentage = 9.1016 % answer : b"
Answer: b