Cheukting/mathqa huggingface dataset:
Question (geometry): a lady grows cabbage in her garden that is in the shape of a square . each cabbage takes 1 square foot of area in her garden . this year , she has increased her output by 127 cabbages when compared to last year . the shape of the area used for growing the cabbage has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 4096 , b ) 4098 , c ) 5000 , d ) 5096 , e ) can not be determined
Rationale: "explanatory answer the shape of the area used for growing cabbage has remained a square in both the years . let the side of the square area used for growing cabbage this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cabbage last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cabbage grown has increased by 127 , the area would have increased by 127 sq ft because each cabbage takes 1 sq ft space . hence , x 2 - y 2 = 127 ( x + y ) ( x - y ) = 127 . 127 is a prime number and hence it will have only two factors . i . e . , 127 and 1 . therefore , 127 can be expressed as product of 2 numbers in only way = 127 * 1 i . e . , ( x + y ) ( x - y ) = 127 * 1 so , ( x + y ) should be 127 and ( x - y ) should be 1 . solving the two equations we get x = 64 and y = 63 . therefore , number of cabbage produced this year = x 2 = 642 = 4096 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice b , c and d . as 4098,5000 and 5096 are not the square of any number . check choice a : if this year ' s produce is 4096 , last year ' s produce would have been 4096 - 127 = 3969 3969 is the square of 63 . so , 4096 is the answer . choice a"
Answer: a
Question (physics): a snail , climbing a 20 feet high wall , climbs up 8 feet on the first day but slides down 4 feet on the second . it climbs 8 feet on the third day and slides down again 4 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 7 , b ) 16 , c ) 17 , d ) 20 , e ) 21
Rationale: "total transaction in two days = 8 - 4 = 4 feet in 7 days it will climb 20 feet thus reaching the top therefore , total no of days required = 7 a"
Answer: a
Question (general): out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many of q applicants majored in political science and had a gpa higher than 3.0 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35
Rationale: total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) q = 20 - 15 = 5 answer : a
Answer: a
Question (general): the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1270 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?
Options: a ) 2480 , b ) 3490 , c ) 6785 , d ) 8245 , e ) 9255
Rationale: "you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1270 , we get the answer of 8245 . ( ans d )"
Answer: d
Question (general): last week vartan spent 15 percent of his wages on recreation . this week , his wages are 10 percent less than last week ʼ s wages and he spent 30 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week ?
Options: a ) 100 % , b ) 160 % , c ) 180 % , d ) 200 % , e ) 220 %
Rationale: say vartan ' s wages last week were $ 100 , so he spent 0.15 * 100 = $ 15 on recreation ; this week ' s wages is 0.9 * 100 = $ 90 , so he spends 0.3 * 90 = $ 27 on recreation ; 27 / 15 = 1.8 , hence the amount he spends on recreation this week is 180 % of the amount he spent on recreation last week : 15 * 1.8 = 27 . answer : c .
Answer: c
Question (geometry): the circumferences of two circles are 528 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 29963 sq m , b ) 28937 sq m , c ) 43162 sq m , d ) 27688 sq m , e ) 17248 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 528 and 2 ∏ l = 704 s = 528 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 264 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 264 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 264 - 352 ) ( 264 + 352 ) / ∏ = ( 88 ) ( 616 ) / ( 22 / 7 ) = 17248 sq m answer : e"
Answer: e
Question (gain): if 15 % of a is the same as 25 % of b , then a : b is :
Options: a ) 5 : 3 , b ) 4 : 3 , c ) 7 : 16 , d ) 12 : 17 , e ) 11 : 13
Rationale: "expl : 15 % of a i = 25 % of b = 15 a / 100 = 25 b / 100 = 5 / 3 = 5 : 3 answer : a"
Answer: a
Question (general): the ages of old and young total 48 . old is twice as old as young was when old was half as old as young will be when young is 3 times as old was when old was 3 times as old as young . how old is old ?
Options: a ) 23 , b ) 27 , c ) 12 , d ) 43 , e ) 37
Rationale: explanation : from the options itself , we can see that option c old = 30 young = 18 30 + 18 = 48 by reducing this years only by one before 6 years old = 24 ( half of young ) young = 12 ( twice of old ) answer : c
Answer: c
Question (gain): the percentage profit earned by selling an article for rs . 1520 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) 3000 , b ) 1230 , c ) 1750 , d ) 5600 , e ) 3400
Rationale: "c . p . be rs . x . then , ( 1520 - x ) / x * 100 = ( x - 1280 ) / x * 100 1520 - x = x - 1280 2 x = 2800 = > x = 1400 required s . p . = 125 % of rs . 1400 = 125 / 100 * 1400 = rs . 1750 . answer c"
Answer: c
Question (physics): convert 2.5 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "2.5 hectares in ares 1 hectare = 100 ares therefore , 2.5 hectares = 2.5 × 100 ares = 250 ares . answer - e"
Answer: e
Question (general): if a randomly selected non - negative single digit integer is added to { 2 , 3 , 4 , 9 } . what is the probability that the median of the set will increase but the range still remains the same ?
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6
Rationale: "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 4 ) / 2 = 3.5 , thus the number selected must be 4 or greater . for the range to remain the same , the number must be between 2 and 9 inclusive . to satisfy both conditions , the number selected must be 4 , 5 , 6 , 7 , 8 , or 9 . the probability is 6 / 10 = 0.6 the answer is e ."
Answer: e
Question (general): keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 32 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
Options: a ) 60 % , b ) 72 % , c ) 88 % , d ) 95 % , e ) 110 %
Rationale: let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.32 ( 5 b + x ) = b + x 0.6 b = 0.68 x x = 0.88 b the answer is c .
Answer: c
Question (geometry): if the volume of two cubes are in the ratio 125 : 1 , the ratio of their edges is :
Options: a ) 3 : 1 , b ) 5 : 1 , c ) 3 : 5 , d ) 3 : 7 , e ) none of these
Rationale: "explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 125 / 1 = > ( a / b ) 3 = ( 5 / 1 ) 3 a / b = 5 / 1 = > a : b = 5 : 1 option b"
Answer: b
Question (general): in a class of 20 students in an examination in mathematics 2 students scored 100 marks each , 3 get zero each and the average of the rest was 40 . what is the average of the whole class ?
Options: a ) 46 , b ) 49 , c ) 40 , d ) 38 , e ) 35
Rationale: total marks obtained by a class of 20 students = 2 * 100 + 3 * 0 + 15 * 40 = 200 + 600 = 800 : average marks of whole class = 800 / 20 = 40 answer is c .
Answer: c
Question (gain): the cost of an article is decreased by 20 % . if the original cost is $ 40 , find the decrease cost .
Options: a ) 33 , b ) 32 , c ) 68 , d ) 36 , e ) 38
Rationale: "original cost = $ 40 decrease in it = 20 % of $ 40 = 20 / 100 ã — 40 = 800 / 100 = $ 8 therefore , decrease cost = $ 40 - $ 8 = $ 32 answer : b"
Answer: b
Question (physics): two pipes a and b can separately fill a cistern in 24 minutes and 48 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 12 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 48 min , c ) 54 min , d ) 120 min , e ) 130 min
Rationale: "1 / 12 - ( 1 / 24 + 1 / 48 ) = - 1 / 48 third pipe can empty in 48 minutes answer : b"
Answer: b
Question (physics): a can do a piece of work in 20 days , and b can do it in 15 days . how long will they take if both work together ?
Options: a ) 7 days , b ) 8.6 days , c ) 13 days , d ) 5.6 days , e ) 10 days
Rationale: a + b can do the work in 20 * 15 / 20 + 15 = 20 * 15 / 35 = 8.6 days answer is b
Answer: b
Question (geometry): if the sides of a triangle are 28 cm , 26 cm and 12 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 156 cm 2 , c ) 178 cm 2 , d ) 189 cm 2 , e ) 176 cm 2
Rationale: "the triangle with sides 28 cm , 26 cm and 12 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 26 * 12 = 156 cm 2 answer : b"
Answer: b
Question (general): the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.4 kg . the weight of the new student is
Options: a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 10 kg , e ) none of these
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.4 weight of the new student = ( 30 * 27.4 – 29 * 28 ) = 822 - 812 = 10 answer : d"
Answer: d
Question (physics): 22 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
Options: a ) 33 , b ) 32 , c ) 60 , d ) data inadequate , e ) none of these
Rationale: "capacity of the tank = 22 ã — 13.5 = 297 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 297 â  „ 9 = 33 answer a"
Answer: a
Question (general): find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: let the number be x . then , x + 17 = 60 x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 option a
Answer: a
Question (general): the arithmetic mean and standard deviation of a certain normal distribution are 17.5 and 2.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "mean = 17.5 two standard deviations is 2.5 + 2.5 = 5.0 there could be two calues for this . mean + two standard deviations = 22.5 mean - two standard deviations = 12.5 answer choice has 12.5 and so e is the answer ."
Answer: e
Question (general): in a group of 130 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
Options: a ) 0.31 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85
Rationale: "number of people whose age is less than 20 is given by 130 - 90 = 40 probability p that a person selected at random from the group is less than 20 is given by 40 / 130 = 0.31 correct answer a"
Answer: a
Question (general): a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase e in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: "last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase e = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."
Answer: c
Question (general): a city with a population of 126,160 is to be divided into 7 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 16,500 , b ) 16,600 , c ) 16,700 , d ) 16,800 , e ) 16,900
Rationale: "the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 126,160 = p + 6 ( 1.1 ) p 7.6 p = 126,160 p = 16,600 the answer is b ."
Answer: b
Question (general): find the largest 3 digit number which is exactly divisible by 88 ?
Options: a ) 765 , b ) 907 , c ) 944 , d ) 954 , e ) 968
Rationale: "largest 3 digit number is 999 after doing 999 ÷ 88 we get remainder 31 hence largest 3 digit number exactly divisible by 88 = 999 - 31 = 968 e"
Answer: e
Question (general): if a = { 17 , 27 , 31 , 53 , 61 } , what is the sum of mean and median of the numbers in a ?
Options: a ) 69 , b ) 75 , c ) 82 , d ) 91 , e ) 56
Rationale: mean = ( 17 + 27 + 31 + 53 + 62 ) / 5 = 38 median = 31 sum = 38 + 31 = 69 option a
Answer: a
Question (gain): the simple interest on a certain sum of money at the rate of 5 % p . a . for 8 years is rs . 840 . at what rate of intrest the same amount of interest can be received on the same sum after 5 years .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : here firstly we need to calculate the principal amount , then we can calculate the new rate . p = s . i . ∗ 100 / r ∗ t p = 840 ∗ 100 / 5 ∗ 8 p = 2100 required rate = 840 ∗ 100 / 5 ∗ 2100 r = 8 % option d"
Answer: d
Question (probability): two cards are drawn together from a pack of 52 cards . the probability that one is a club and other is a diamond , is :
Options: a ) 29 / 34 , b ) 47 / 100 , c ) 3 / 20 , d ) 13 / 102 , e ) none of these
Rationale: explanation : one card drawn . probability of being it club or diamond = ( 13 x 2 ) / 52 . another card drawn . now , probability of being it of other suit ( the suit among the two , not selected in first draw ) = 13 / 51 . hence , probability of event = ( ( 13 x 2 ) / 52 ) x ( 13 / 51 ) = 13 / 102 . answer : d
Answer: d
Question (geometry): a rectangular tiled patio is composed of 160 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 160 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 160 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 160 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 160 ( 2 r - 4 ) * r = 160 2 r ^ 2 - 4 r - 160 = 0 r can not be negative so r = 10 and c = 16 so , answer will be c"
Answer: c
Question (physics): 8 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 2 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 8 * 10 / 40 = 2 answer is a"
Answer: a
Question (general): a ' s speed is 15 / 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 40 % of the length of the race ?
Options: a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 46 %
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 15 / 13 of b , therefore , b ' s speed is 13 / 15 of a distance covered by b = speed x time = ( 13 / 15 ) x ( 0.6 ) = 0.52 % ( which means b would have covered 0.52 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 - 0.52 = ) 0.48 of the race length . so the answer is b"
Answer: b
Question (geometry): what is the radius of the incircle of the triangle whose sides measure 5 , 12 and 13 units ?
Options: a ) 2 units
b ) 12 units
c ) 6.5 units
d ) 6 units
e ) 7.5 units
Rationale: explanatory answer in a right angled triangle , the radius of the incircle = s - h , where ' s ' is the semi perimeter of the triangle and ' r ' is the radius of the inscribed circle . the semi perimeter of the triangle = a + b + c / 2 = 5 + 12 + 13 / 2 = 15 therefore , r = 15 - 13 = 2 units . choice a
Answer: a
Question (physics): along a yard 414 metres long , 24 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 18 , b ) 19 , c ) 10 , d ) 11 , e ) 12
Rationale: explanation : 24 trees have 23 gaps between them , required distance ( 414 / 23 ) = 18 option a
Answer: a
Question (general): at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 8 . if the price per share of stock k was $ 9 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?
Options: a ) 1.4 % , b ) 5.9 % , c ) 11.1 % , d ) 12.5 % , e ) 23.6 %
Rationale: "opening = 8 closing = 9 rise in price = 1 so , percent increase = 18 ∗ 10018 ∗ 100 = > 12.50 % thus answer will be ( d )"
Answer: d
Question (gain): on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 22 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.8 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "answer is b . this question is in the og and thus well explained by ets . those who exceed : x so x = 10 % + 0,22 x id est x = 12,8 %"
Answer: b
Question (gain): a fruit seller had some oranges . he sells 40 % oranges and still has 480 oranges . how many oranges he had originally ?
Options: a ) 800 , b ) 710 , c ) 720 , d ) 730 , e ) 740
Rationale: "60 % of oranges = 480 100 % of oranges = ( 480 × 100 ) / 6 = 800 total oranges = 700 answer : a"
Answer: a
Question (gain): fresh grapes contain 70 % by weight while dried grapes contain 10 % water by weight . what is the weight of dry grapes available from 100 kg of fresh grapes ?
Options: a ) 18.33 kg , b ) 21.50 kg , c ) 25.00 kg , d ) 33.33 kg , e ) 40.39 kg
Rationale: "from the question we know : 100 kg * 70 % = 70 kg of water in the fresh grapes 100 kg - 70 kg of water = 30 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 10 % of the weight of the dry graps is water and we know that 30 kg is non - water mass we can set up the following equation : x = 1 / 10 ( x ) + 30 kg 9 / 10 ( x ) = 30 kg x = 33.33 kg answer - d"
Answer: d
Question (physics): a hall 20 m long and 15 m broad is surrounded by a verandah of uniform width of 2.5 m . the cost of flooring the verandah at the rate of rs . 3.50 per sq . meter is
Options: a ) 500 , b ) 600 , c ) 650 , d ) 700 , e ) 750
Rationale: area of verandah = [ ( 25 ã ƒ â € ” 20 ) ? ( 20 ã ƒ â € ” 15 ) ] m â ² = 200 m â ² cost of flooring = rs . ( 200 ã ƒ â € ” 3.50 ) = rs . 700 answer : d
Answer: d
Question (physics): a man rows his boat 90 km downstream and 55 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 76 kmph , b ) 6 kmph , c ) 14 kmph , d ) 8 kmph , e ) 4 kmph
Rationale: "speed downstream = d / t = 90 / ( 3 ) = 30 kmph speed upstream = d / t = 55 / ( 3 ) = 18 kmph the speed of the stream = ( 30 - 18 ) / 2 = 6 kmph answer : b"
Answer: b
Question (gain): jim is able to sell a hand - carved statue for $ 540 which was a 35 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 400.00 , b ) $ 412.40 , c ) $ 455.40 , d ) $ 474.90 , e ) $ 488.20
Rationale: 540 = 1.35 * x x = 540 / 1.35 = 400 $ 400 , which is ( a ) .
Answer: a
Question (physics): the speed at which a girl can row a boat in still water is 30 kmph . if she rows downstream , where the speed of current is 6 kmph , what time will he take to cover 240 metres ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 20 , e ) 24
Rationale: speed of the boat downstream = 30 + 6 = 36 kmph = 36 * 5 / 18 = 10 m / s hence time taken to cover 240 m = 240 / 10 = 24 seconds . answer : e
Answer: e
Question (general): the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 45 . what is a possible value for the mean of the distribution ?
Options: a ) 52 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 45 : { mean } - 3 * { sd } > 45 ; { mean } - 6 > 45 ; { mean } > 51 . answer : a ."
Answer: a