regisss/math_qa huggingface dataset:
Problem: a certain taxi company charges $ 2.80 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 16.0 , c ) 18.4 , d ) 18.7 , e ) 19.1
Rationale: "a certain taxi company charges $ 2.80 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.80 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.8 + $ 15.6 = $ 18.4 . answer : c ."
Answer: c
Problem: the average of first five multiples of 4 is
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "solution average = 4 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 60 / 5 . = 12 answer d"
Answer: d
Problem: of the 3 - digit integers greater than 200 , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 90 , b ) 82 , c ) 80 , d ) 45 , e ) 36
Rationale: let the three digit number be represented as x y z . there are 3 cases : case i . [ x = y ] z is not equal to xy : xxzoryyz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , y can be chosen in 1 way after xy are chosen , z can be chosen in 9 ways thus , possible no of digits = ( 3 ways ) * ( 1 way ) * ( 9 ways ) = 27 . . . . ( 1 ) [ example numbers : 774,779 , 882,993 etc ] case ii . [ x = z ] y is not equal to xz : xyxorzyz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , z can be chosen in 1 way after xz are chosen , z can be chosen in 9 ways thus , possible no of digits = ( 3 ways ) * ( 9 ways ) * ( 1 way ) = 27 . . . . ( 2 ) [ example numbers : 747,797 , 828,939 etc ] case iii . [ y = z ] x is not equal to yz : xyyorxzz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , y can be chosen in 9 ways after y is chosen , z can have 1 way thus , possible no of digits = ( 3 ways ) * ( 1 way ) * ( 9 ways ) = 27 . . . . ( 3 ) [ example numbers : 744,799 , 822,933 etc ] therefore , total numbers of possible digits [ sum of case ( 1 ) , ( 2 ) ( 3 ) above ] = 27 + 27 + 27 - 1 = 80 one digit is subtracted from total number of possible digits to eliminate one possibility of xyz = 700 to satisfy the condition that digit > 200 . answer : ( e )
Answer: e
Problem: a rectangular mat has an area of 120 sq . metres and perimeter of 46 m . the length of its diagonal is :
Options: a ) 19 m
b ) 17 m
c ) 15 m
d ) 16 m
e ) 20 m
Rationale: rectangular area = l × b = 120 and perimeter = 2 ( l + b ) = 46 l + b = 23 ( l - b ) power 2 - 4 lb = ( 23 ) power 2 - 4 × 120 = ( 529 - 480 ) = 49 = l - b = 7 l + b = 23 , l - b = 7 , we get l = 15 , b = 8 diagonal = √ 152 + 82 √ 225 + 64 = > √ 289 = 17 m answer is b .
Answer: b
Problem: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many r acres were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn r = 4 * 94 = 376 correct option - c"
Answer: c
Problem: the tax on a commodity is diminished by 40 % but its consumption is increased by 25 % . find the decrease percent in the revenue derived from it ?
Options: a ) 18 % , b ) 72 % , c ) 25 % , d ) 12 % , e ) 52 %
Rationale: "100 * 100 = 10000 60 * 125 = 7500 10000 - - - - - - - 2500 100 - - - - - - - ? = 25 % answer : c"
Answer: c
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: if 13 = 13 w / ( 1 - w ) , then ( 5 w ) 2 =
Options: a ) 1 / 4 , b ) 5 , c ) 1 , d ) 2 , e ) 3
Rationale: "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 5 w = 5 / 2 5 w * 2 = 5 / 2 * 2 = 5 answer : b"
Answer: b
Problem: two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 32 sec , c ) 82 sec , d ) 20 sec , e ) 19 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 280 = 380 m . the time required = d / s = 380 / 20 = 19 sec . answer : e"
Answer: e
Problem: the ratio of radius of a circle and the side of a square is 2 : 9 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 7 , c ) 8 : 77 , d ) 4 : 81 , e ) none
Rationale: "radius / side = 2 / 9 â ‡ ’ area of circle / area of square = 4 / 81 answer : d"
Answer: d
Problem: if 12 men can reap 120 acres of land in 36 days , how many acres of land can 24 men reap in 62 days ?
Options: a ) 266.5 , b ) 413.3 , c ) 425.8 , d ) 189.3 , e ) 249.6
Rationale: "12 men 120 acres 36 days 24 men ? 62 days 120 * 24 / 12 * 62 / 36 120 * 2 * 31 / 18 240 * 1.72 = 413.3 answer : b"
Answer: b
Problem: evaluate : 10010 - 12 * 3 * 2 = ?
Options: a ) 30002 , b ) 70002 , c ) 50002 , d ) 90002 , e ) 10002
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 10010 - 12 * 3 * 2 = 10010 - 8 = 10002 correct answer e"
Answer: e
Problem: a car travels at a speed of 10 miles per hour . how far will it travel in 5 hours ?
Options: a ) 50 miles , b ) 62 miles , c ) 325 miles , d ) 70 miles , e ) 20 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 10 + 10 + 10 + 10 + 10 = 5 * 10 = 50 miles correct answer a"
Answer: a
Problem: if 42 men do a work in 25 days , in how many days will 50 men do it ?
Options: a ) 23 , b ) 22 , c ) 19 , d ) 20 , e ) 21
Rationale: "42 * 25 = 50 * x x = 21 days answer : e"
Answer: e
Problem: find large number from below question the difference of two numbers is 1345 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1611
Rationale: let the smaller number be x . then larger number = ( x + 1345 ) . x + 1345 = 6 x + 15 5 x = 1330 x = 266 large number = 266 + 1345 = 1611 e
Answer: e
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 9 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 9 / 19
Rationale: "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 9 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 9 / 5 = 9 - - > total time for both of them would be 10 + 9 = 19 - - > deluxe / total = 9 / 19 . answer : e ."
Answer: e
Problem: a train 250 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 28 , c ) 29 , d ) 44 , e ) 21
Rationale: "s = ( 250 + 300 ) / 45 = 550 / 45 * 18 / 5 = 44 answer : d"
Answer: d
Problem: the salaries of a and b together amount to $ 500 . a spends 90 % of his salary and b , 80 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 50 , b ) $ 150 , c ) $ 69 , d ) $ 34 , e ) $ 52
Rationale: "let a ' s salary is x b ' s salary = 500 - x ( 100 - 90 ) % of x = ( 100 - 80 ) % of ( 500 - x ) x = $ 34 ( approximately ) answer is d"
Answer: d
Problem: if there are 10 peanuts in a box and mary puts 8 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 18
Rationale: "10 + 8 = 18 correct answer is e ) 18"
Answer: e
Problem: how many positive integers less than 1960 are such that the product of their digits is 10 .
Options: a ) 220 , b ) 230 , c ) 280 , d ) 220 , e ) 240
Rationale: "1960 is divisible by 10 ( or 2 * 5 ) = 196 196 is divisible by 4 = > 49 49 = 7 * 7 hence 1960 is divisible by 2 , 4,5 , 7 , 7 if there were only one 7 , i . e if the problem were 280 c"
Answer: c
Problem: the average runs of a cricket player of 10 innings was 32 . how many runs must he makes ih his next innings so as to increase his average of runs by 4 ?
Options: a ) 2 , b ) 4 , c ) 70 , d ) 76 , e ) none
Rationale: "sol . average after 11 innings = 36 . therefore required numbert of runs = ( 36 × 11 ) – ( 32 × 10 ) = 396 - 320 = 76 . answer d"
Answer: d
Problem: an outlet pipe can empty 2 / 3 of a cistern in 16 minutes . in 4 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 8
Rationale: "4 / 16 * 2 / 3 = 1 / 6 the answer is d ."
Answer: d
Problem: the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is rs . 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is ?
Options: a ) rs . 3000 , b ) rs . 4000 , c ) rs . 5000 , d ) rs . 6000 , e ) rs . 7000
Rationale: "let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 4000 . p ' s monthly income = rs . 4000 . b )"
Answer: b
Problem: a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 60 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?
Options: a ) 160
b ) 240
c ) 330
d ) 440
e ) 560
Rationale: the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 60 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 60 = 270 . total area = 60 + 270 = 330 . answer : c .
Answer: c
Problem: in a group of 26 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 8
Rationale: "c 5 add 7 + 10 + 4 to get 21 . then subtract 21 from the total students ⇒ 26 – 21 = 5 . answer is c"
Answer: c
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 8 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 22 litres , e ) 16 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 8 ) = 4 / 5 20 x = 4 ( 3 x + 8 ) 8 x = 32 x = 4 quantity of alcohol = ( 4 x 4 ) litres = 16 litres . answer is e ."
Answer: e
Problem: what is the sum of the multiples of 4 between 19 and 130 inclusive ?
Options: a ) 2012 , b ) 2044 , c ) 2060 , d ) 2072 , e ) 2080
Rationale: "the fastest way in an ap is to find the average and multiply with total integers . . between 19 and 130 , the smallest multiple of 4 is 20 and largest = 128 . . average = ( 20 + 128 ) / 2 = 148 / 2 = 74 . total numbers = ( 128 - 20 ) / 4 + 1 = 27 + 1 = 28 . . sum = 28 * 74 = 2072 ans d"
Answer: d
Problem: a certain article of clothing was discounted during a special sale to 3 / 4 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 2 / 5 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 33.33 % , c ) 25 % , d ) 46.66 % , e ) 12.5 %
Rationale: say the original retail price of the item was $ 200 . the price after the first sale = 3 / 4 * $ 200 = $ 150 . the price after the second sale = 2 / 5 * $ 200 = $ 80 . the percent change from the first sale to the second = ( 150 - 80 ) / 150 = 1 / 3 = 46.66 % . answer : d .
Answer: d
Problem: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in 3 hours ) solving these 2 equations we can find b as 12 answer : d"
Answer: d
Problem: if p and q are prime numbers , how many divisors does the product p ^ 3 * q ^ 6 have ?
Options: a ) 9 , b ) 12 , c ) 18 , d ) 28 , e ) 363
Rationale: ", p ^ 2 , p ^ 3 and q , q ^ 1 , q ^ 2 . . . . q ^ 6 together essentially there are 18 different combinations you can make ( 3 x 6 ) also you have to include the different combinations the p and q exponents can be a divisor . there are 3 different p exponents and 6 different q exponents : p , p ^ 2 , p ^ 3 , q , q ^ 2 , q ^ 3 . . . q ^ 6 also add 1 since ` ` 1 ' ' can also be a divisor . 18 + 3 + 6 + 1 = 28 , answer : d"
Answer: d
Problem: two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 10 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 6 hours , c ) 8 hours , d ) 10 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 10 = 5 hours answer is a"
Answer: a
Problem: the rate of interest on a sum of money is 3 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occurred on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 1,200 , b ) 1,800 , c ) 2,100 , d ) 2,250 , e ) 2,540
Rationale: "explanation : i 1 = ( p x 3 x 3 ) / 100 = p / 11 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 p / 11 + 4 p / 25 + p / 20 = 540 30 p / 100 = 540 p = 1800 answer : option b"
Answer: b
Problem: in a renowned city , the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 4 persons are added ( 6 - 2 ) . every second 2 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 2 = 172800 option b is the answer ."
Answer: b
Problem: 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 + [ 8.3 ] - 6.6 ?
Options: a ) 12.6 . , b ) 15.8 . , c ) 14.4 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.3 ] - 6.6 = 6 * 0 + 2 * 7.2 + 8 - 6.6 = 0 + 14.4 + 1.4 15.8 answer b"
Answer: b
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 300 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 300 , b ) 320 , c ) 330 , d ) 340 , e ) 290
Rationale: "answer a 300 * t = 1 km = > t = 1 / 360 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 360 + 2 / 3600 ) = 1 = > v = 300 km / h"
Answer: a
Problem: in a group of 25 , 13 can speak latin , 15 can speak french , and 6 do n ' t speak either . how many of these speak both latin and french ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: let no . of persons who speeks booth latin and french = x so , no . of persons who speeks only latin = 13 - x no . of persons who speeks only french = 15 - x no . of persons who speeks dont speek any lag = 6 therefore ( 13 - x ) + ( 15 - x ) + x + 6 = 25 34 - x = 25 x = 9 answer : a
Answer: a
Problem: a train of length 250 m crosses a bridge of length 120 m in 20 seconds . what is the speed of train ?
Options: a ) 33 , b ) 27 , c ) 66.6 , d ) 22 , e ) 72
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 120 ) = 20 x speed speed = 370 / 20 = 18.5 m / s = 66.6 km / h answer = c"
Answer: c
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 150 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 300 , e ) 250
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 150 total = 150 + 150 = 300 answer ( d )"
Answer: d
Problem: in what ratio should a 20 % methyl alcohol solution be mixed with a 50 % methyl alcohol solution so that the resultant solution has 40 % methyl alcohol in it ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 2 : 3 , d ) 2 : 1 , e ) 3 : 1
Rationale: two things to remember : - 1 ) the ratio of quantity mixed to get an average is related to the ratio of each qty ' s distance from average . 2 ) more the qty of x from that of y , more closer will be average to x . . qty of 20 % / qty of 50 % = ( 50 − 40 ) / ( 40 − 20 ) = 1 / 2 = 1 : 2 answer : b
Answer: b
Problem: each of the 42 points is placed either inside or on the surface of a perfect sphere . if 65 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 7 , b ) 11 , c ) 13 , d ) 23 , e ) 38
Rationale: "maximum number of points on the surface is 65 % * 42 = 27.3 . . . or 27 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 27 points , so at best we can form 13 pairs ( 26 ) . so , answer is ( c )"
Answer: c
Problem: rs . 800 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 800 become in 3 years .
Options: a ) rupees 1052 , b ) rs 1152 , c ) rs 1252 , d ) rs 1352 , e ) none of these
Rationale: explanation : s . i . = 956 - 800 = rs 156 r = 156 ∗ 100 / 800 ∗ 3 r = 6 1 / 2 % new rate = 6 1 / 2 + 4 = 21 / 2 % new s . i . = 800 × 21 / 2 × 3100 = 252 now amount will be 800 + 252 = 1052 option a
Answer: a
Problem: in the rectangular coordinate system , if the line x = 8 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "x = 8 y + 5 , and thus y = x / 8 - 5 / 8 the slope is 1 / 8 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 8 and thus p = 1 / 4 the answer is c ."
Answer: c
Problem: a taxi leaves point a 5 hours after a bus left the same spot . the bus is traveling 10 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in three hours .
Options: a ) 20 , b ) 24 , c ) 32 , d ) 16 , e ) 40
Rationale: "let the speed of bus be v - 10 , speed of taxi be v the bus travelled a total of 8 hrs and taxi a total of 3 hrs . hence 8 * ( v - 10 ) = 3 v 8 v - 80 = 3 v 5 v = 80 d"
Answer: d
Problem: the length of a rectangular landscape is 12 times its breadth . there is a playground in it whose area is 1200 square mtr & which is 1 / 4 rd of the total landscape . what is the length of the landscape ?
Options: a ) 90 , b ) 120 , c ) 240 , d ) 180 , e ) 110
Rationale: "sol . x * 12 x = 4 * 1200 x = 20 length = 12 * 20 = 240 c"
Answer: c
Problem: if x , y , and z are positive real numbers such that x + y - z = 62 , y - z + x = 82 , and z - x + y = 100 , then find the x + y + z value ?
Options: a ) 80 , b ) 91 , c ) 62 , d ) 74 , e ) 82
Rationale: "x + y - z = 62 , - - - - - - 1 ) y - z + x = 82 , - - - - - - 2 ) z - x + y = 100 - - - - - - 3 ) from ( 1 ) & ( 2 ) 2 z = 20 z = 10 from ( 2 ) & ( 3 ) 2 y = 182 y = 91 then x = 62 - 81 = - 19 x + y + z = 82 correct option is e"
Answer: e
Problem: how many seconds will a 400 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 24 , b ) 30 , c ) 40 , d ) 45 , e ) 50
Rationale: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 400 * 3 / 50 = 24 sec answer : a"
Answer: a
Problem: a 240 meter long train crosses a man standing on the platform in 4 sec . what is the speed of the train ?
Options: a ) 176 kmph , b ) 108 kmph , c ) 216 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 240 / 4 * 18 / 5 = 216 kmph answer : c"
Answer: c
Problem: the population of a town is 10000 . it decreases annually at the rate of 10 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 4500 , c ) 8100 , d ) 5230 , e ) 5366
Rationale: "10000 × 90 / 100 × 90 / 100 = 8100 answer : c"
Answer: c
Problem: a boat running downstream covers a distance of 10 km in 3 hr while for covering the same distance upstream , it takes 6 hr . what is the speed of the boat ?
Options: a ) 2.5 kmph , b ) 3.5 kmph , c ) 4.5 kmph , d ) 1.5 kmph , e ) 9.5 kmph
Rationale: speed upstream = 10 / 3 speed of boat down stream = 10 / 6 speed of boat = 1 / 2 ( 10 / 3 + 10 / 6 ) = 2.5 kmph answer : a
Answer: a
Problem: a fort had provision of food for 150 men for 45 days . after 15 days , 25 men left the fort . the number of days for which the remaining food will last , is :
Options: a ) 36 , b ) 37 1 / 4 , c ) 42 , d ) 54 , e ) 48
Rationale: "after 15 days : 150 men had food for 30 days . suppose 125 men had food for x days . now , less men , more days ( indirect proportion ) therefore 125 : 150 : : 30 : x < = > 125 x x = 150 x 30 = > x = 150 x 30 / 125 = > x = 36 . correct answer is a"
Answer: a
Problem: the length of a room is 8 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 34200
Rationale: "area = 8 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 8 × 4.75 × 900 = 8 × 4275 = rs . 34200 answer is e ."
Answer: e
Problem: a person distributed 15 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ?
Options: a ) a ) 452000 , b ) b ) 200000 , c ) c ) 800000 , d ) d ) 500000 , e ) e ) 652000
Rationale: "3 children got = 3 * 15 % = 45 % wife got = 30 % orphan house = 5 % total = 45 + 30 + 5 = 80 % remaining = 100 - 80 = 20 % 20 % = 40000 100 % = 40000 * 100 / 20 = $ 200000 answer is b"
Answer: b
Problem: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 81 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 81 ⇔ 9 ( x - y ) = 81 ⇔ x - y = 9 answer e"
Answer: e
Problem: a and b runs around a circular track . a beats b by one round or 10 minutes . in this race , they had completed 4 rounds . if the race was only of one round , find the a ' s time over the course :
Options: a ) 8.5 min
b ) 7.5 min
c ) 1.5 min
d ) 9.5 min
e ) 4.5 min
Rationale: explanation : b runs around the track in 10 min . i . e , speed of b = 10 min per round a beats b by 1 round time taken by a to complete 4 rounds = time taken by b to complete 3 rounds = 30 min a ' s speed = 30 / 4 min per round = 7.5 min per round hence , if the race is only of one round a ' s time over the course = 7 min 30 sec answer : b
Answer: b