regisss/math_qa huggingface dataset:
Problem: the speed at which a man can row a boat in still water is 15 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 100 meters ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: the speed of the boat downstream = 15 + 3 = 18 km / hr 18 km / hr * 5 / 18 = 5 m / s the time taken to cover 100 meters = 100 / 5 = 20 seconds . the answer is d .
Answer: d
Problem: 3 people decided to put a down payment on a car for 3500 dollars . how much money do they each have to pay , given that that they have to pay the same amount , and they can not use any bills below $ 1 ?
Options: a ) $ 1166 , b ) $ 1168 , c ) $ 1166.6 , d ) $ 1167 , e ) none of the above
Rationale: to keep the amount exact when dividing for 3 , we have to work backwards through division . dividing 3500 by 3 will give us 1166.66 then by subtracting . 66 , we get 1166 , and we multiply it by 3 to get 3498 . to get enough for the down payment , we add 3 to 3498 . dividing the result by 3 gives us our answer . correct option : d
Answer: d
Problem: a biker covered half the distance between two towns in 2 hr 30 min . after that he increased his speed by 2 km / hr . he covered the second half of the distance in 2 hr 20 min . find the distance between the two towns and the initial speed of the biker .
Options: a ) 140 , b ) 120 , c ) 130 , d ) 150 , e ) 160
Rationale: let x km / hr be the initial speed of the biker , then his speed during the second part of the trip is x + 2 km / hr . half the distance between two cities equals 23060 ⋅ x km and 22060 ⋅ ( x + 2 ) km . from the equation : 23060 ⋅ x = 22060 ⋅ ( x + 2 ) we get x = 28 km / hr . the intial speed of the biker is 28 km / h . half the distance between the two towns is 2 h 30 min × 28 = 2.5 × 28 = 70 . so the distance is 2 × 70 = 140 km . answer is a .
Answer: a
Problem: the diagonal of a square is 40 m . the area of the square is :
Options: a ) 600
b ) 900
c ) 800
d ) 500
e ) 400
Rationale: arear = 1 / 2 × ( diagonal ) ( power ) 2 = ( 1 / 2 × 40 × 40 ) m ( power ) 2 = 1600 / 2 = 800 m ( power ) 2 answer is c .
Answer: c
Problem: on dividing 16698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 743 , b ) 154 , c ) 187 , d ) 741 , e ) 785
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 16698 - 14 ) / 89 = 187 answer ( c )"
Answer: c
Problem: a box contains 4 black , 3 red and 6 green marbles . 2 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?
Options: a ) 24 / 78 , b ) 24 / 709 , c ) 24 / 76 , d ) 24 / 71 , e ) 24 / 72
Rationale: explanation : total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 2 marbles are drawn from 13 marbles at random . therefore , n ( s ) = 13 c 2 = 78 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 4 c 2 + 3 c 2 + 6 c 2 = 6 + 3 + 15 = 24 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 24 / 78 answer : a
Answer: a
Problem: when an amount was distributed among 14 boys , each of them got rs 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys . what was the amount ?
Options: a ) 5000 , b ) 5030 , c ) 5010 , d ) 5040 , e ) 5020
Rationale: let the total amount be rs . x the , x / 14 - x / 18 = 80 < = > 2 x / 126 = 80 < = > x / 63 = 63 x 80 = 5040 . hence the total amount is 5040 answer is d .
Answer: d
Problem: sum of the squares of 3 no . is 156 and the sum of their products taken two at a time is 50 . find the sum ?
Options: a ) 18 , b ) 16 , c ) 19 , d ) 21 , e ) 15
Rationale: ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 156 + 2 * 50 a + b + c = â ˆ š 256 = 16 answer b
Answer: b
Problem: two trains of length 150 m and 250 m are 150 m apart . they start moving towards each other on parallel tracks , at speeds 36 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 55 / 3 , b ) 55 / 7 , c ) 55 / 6 , d ) 55 / 8 , e ) 55 / 9
Rationale: "relative speed = ( 36 + 72 ) * 5 / 18 = 6 * 5 = 30 mps . the time required = d / s = ( 150 + 150 + 250 ) / 30 = 550 / 30 = 55 / 3 sec . answer : a"
Answer: a
Problem: farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15.502 % , b ) 25.7014 % , c ) 12.502 % , d ) 21.7014 % , e ) none
Rationale: "only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 500 / 3840 ) x 100 = 13.02083 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 13.02083 % x ( 100 / 60 ) = 21.7014 % and the answer is not there in the options . the correct answer is ( d ) ."
Answer: d
Problem: a , b and c started a business with capitals of rs . 6000 , rs . 8000 , and rs . 10000 respectively . at the end of the year , the profit share of b is rs 1000 . the difference between the profit shares of a and c is
Options: a ) rs . 400 , b ) rs . 450 , c ) rs . 500 , d ) rs . 550 , e ) rs . 650
Rationale: ratio of investments of a , b and c is 6000 : 8000 : 10000 = 3 : 4 : 5 . and also given that , profit share of ‘ b ’ is rs . 1000 . now required difference is 5 – 3 = 2 parts . therefore , required difference = 2 / 4 ( 1000 ) = rs . 500 . answer : c
Answer: c
Problem: the probability that a computer company will get a computer hardware contract is 4 / 5 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 5 / 6 , what is the probability that it will get both the contracts ?
Options: a ) 7 / 20 , b ) 9 / 25 , c ) 11 / 30 , d ) 13 / 35 , e ) 17 / 40
Rationale: "let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 4 / 5 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 5 / 6 = ( 4 / 5 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 11 / 30 . hence , the required probability is 11 / 30 . the answer is c ."
Answer: c
Problem: the length of a rectangle is five times of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 16 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 11 units ?
Options: a ) 180 sq . units
b ) 11 sq . units
c ) 110 sq . units
d ) 140 sq . units
e ) 220 sq . units
Rationale: given that the area of the square = 16 sq . units = > side of square = â ˆ š 16 = 4 units the radius of the circle = side of the square = 4 units length of the rectangle = 5 * 4 = 20 units given that breadth = 11 units area of the rectangle = lb = 20 * 11 = 220 sq . units answer : e
Answer: e
Problem: second saturday and every sunday is a holiday . how many working days will be there in a month of 30 days beginning on a saturday ?
Options: a ) 24 , b ) 23 , c ) 18 , d ) 21 , e ) 22
Rationale: explanation : mentioned month begins on a saturday and has 30 days sundays = 2 nd , 9 th , 16 th , 23 rd , 30 th = > total sundays = 5 every second saturday is holiday . 1 second saturday in every month total days in the month = 30 total working days = 30 - ( 5 + 1 ) = 24 . answer : option a
Answer: a
Problem: if 80 % of 90 is greater than 70 % of a number by 30 , what is the number ?
Options: a ) 70 , b ) 60 , c ) 10 , d ) 75 , e ) 85
Rationale: "explanation : 80 / 100 * 90 - 70 / 100 * x = 30 72 - 70 / 100 * x = 30 72 - 30 = 70 / 100 * x 42 = 70 / 100 * x 42 * 100 / 70 = x 60 = x answer : option b"
Answer: b
Problem: a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 40 inches . find b .
Options: a ) 8 , b ) 6 , c ) 24 , d ) 32 , e ) 48
Rationale: "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) andbis 4 ( = 2 ^ 2 ) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) andbis 40 ( 2 ^ 3 * 5 ) , sob = 2 ^ 3 or 2 ^ 3 * 5 ( 8 or 40 ) . combining 2 premises shows the answer is b ( 6 ) ."
Answer: b
Problem: find large number from below question the difference of two numbers is 1000 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1345 , b ) 1197 , c ) 1540 , d ) 1600 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1000 = 6 x + 15 5 x = 985 x = 197 large number = 197 + 1365 = 1197 b"
Answer: b
Problem: a wire can be bent in the form of a circle of radius 56 cm . if it is bent in the form of a square , then its area will be ?
Options: a ) 7744
b ) 8844
c ) 5544
d ) 4444
e ) 3444
Rationale: length of wire = 2 pier = 2 * ( 22 / 7 ) * 56 = 352 cm side of the square = 352 / 4 = 88 cm area of the square = 88 * 88 = 7744 sq cm answer : a
Answer: a
Problem: a rectangular courtyard , the sides of which are in the ratio of 4 : 3 , cost rs . 600 for paving at 50 p per m 2 ; find the length of the diagonal of the courtyard ?
Options: a ) 17 m
b ) 45 m
c ) 54 m
d ) 77 m
e ) 34 m
Rationale: 1 m 2 - - - - 1 / 2 ? - - - - - 600 = > 1200 m 2 4 x * 3 x = 1200 = > x = 10 answer : b
Answer: b
Problem: if the area of a circle decreases by 42 % , then the radius of a circle decreases by
Options: a ) 20 % , b ) 18 % , c ) 24 % , d ) 64 % , e ) none of these
Rationale: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 42 ) % = ( 100 − 10 √ 58 ) % = 100 - 76 = 24 % answer c"
Answer: c
Problem: a batsman makes a score of 83 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 35 , d ) 49 , e ) 59
Rationale: "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 83 = 17 x therefore x = 35 answer : c"
Answer: c
Problem: when x is multiplied by 3 , the result is 20 more than the result of subtracting x from 20 . what is the value of x ?
Options: a ) 10 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 20 = 20 - x or , 4 x = 40 or , x = 10 . answer : a"
Answer: a
Problem: solution for 2.75 + . 003 + . 158
Options: a ) 2.91 , b ) 2.911 , c ) 2.938 , d ) 2.986 , e ) 2.999
Rationale: "2.75 + . 003 + . 158 = 0 0 = 0 - 2.75 - 0.003 - 0.158 0 = - 2.911 answer : b"
Answer: b
Problem: jane makes toy bears . when she works with an assistant , she makes 70 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional values the productivity in 1 st case is 0.5 bears / hour and in the 2 nd case it is 1 bear / hour hence the productivity is double with the assistant i . e . the increase in productivity is 80 % b"
Answer: b
Problem: ravi and sunil are partners in a business . ravi invests rs . 9,000 for 8 months and sunil invested rs . 12000 for 9 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4
Rationale: "= ( 9000 * 8 ) : ( 15000 * 8 ) = 72000 : 108000 = 2 : 3 answer : b"
Answer: b
Problem: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 238 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 22 , b ) 33 , c ) 55 , d ) 42 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 238 = > . 1 x + 3 / 4 x = 238 = > x = 280 280 - 238 = pure gala = 42 . answer d"
Answer: d
Problem: the purchase price of an article is $ 48 . in order to include 25 % of cost for overhead and to provide $ 12 of net profit , the markup should be
Options: a ) 50 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: cost price of article = 48 $ % of overhead cost = 25 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 25 = 50 % answer a
Answer: a
Problem: a car is running at a speed of 90 kmph . what distance will it cover in 15 second ?
Options: a ) 100 m , b ) 255 m , c ) 375 m , d ) can not be determined , e ) none of these
Rationale: "explanation : given : speed = 108 kmph = ( 90 x ( 5 / 18 ) ) m / sec = 25 m / sec distance covered in 15 second = ( 25 x 15 ) m = 375 m . answer : c"
Answer: c
Problem: what should be the least number to be added to the 51234 number to make it divisible by 9 ?
Options: a ) 6 , b ) 4 , c ) 3 , d ) 5 , e ) 2
Rationale: "the least number to be added to the numbers to make them divisible by 9 is equal to the difference of the least multiple of 9 greater than the sum of the digits and sum of the digits . sum of digits = 15 . nearest multiple of 9 greater than sum of digits = 18 . hence 3 has to be added . answer : c"
Answer: c
Problem: in a 120 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 49 , b ) 47 , c ) 25 , d ) 43 , e ) 41
Rationale: "solution simple out of 120 20 % are male i . e 24 and 25 % are female i . e 30 , so total homeowner is 54 . now min number homeowner is 24 and max is 54 so question ask us to find least and 25 has least value among all option . so ans is 25 . answer : c"
Answer: c
Problem: 8 k 8 + k 88 - - - - - - - - 16 t 6 if k and t represent non - zero digits within the integers above , what is t ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 17
Rationale: 8 k 8 k 88 - - - - - - - - 16 t 6 trial and error or just plug - in method might be the shortest way to solve this problem . though you can narrow down the possible values of k to just two : 7 and 8 - - > 8 * * + 7 * * = 16 * * or 8 * * + 8 * * = 16 * * ( k can not be less than 7 or 9 , as the result wo n ' t be 16 * * ) . after that it ' s easy to get that k = 7 and t = 6 . answer : a .
Answer: a
Problem: the distance between delhi and mathura is 110 kms . a starts from delhi with a speed of 20 kmph at 7 a . m . for mathura and b starts from mathura with a speed of 25 kmph at 8 p . m . from delhi . when will they meet ?
Options: a ) 08 a . m . , b ) 09 a . m . , c ) 12 a . m . , d ) 10 a . m . , e ) 07 a . m .
Rationale: "d 10 a . m . d = 110 – 20 = 90 rs = 20 + 25 = 45 t = 90 / 45 = 2 hours 8 a . m . + 2 = 10 a . m ."
Answer: d
Problem: what is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 3 , b ) 27 , c ) 30 , d ) 21 , e ) 18
Rationale: "explanatory answer useful result pertaining to remainders you can solve this problem if you know this rule about remainders . let a number x divide the product of a and b . the remainder will be the product of the remainders when x divides a and when x divides b . using this rule , the remainder when 33 divides 1044 is 21 . the remainder when 33 divides 1047 is 24 . the remainder when 33 divides 1050 is 27 . the remainder when 33 divides 1053 is 30 . ∴ the remainder when 33 divides 1044 * 1047 * 1050 * 1053 is 21 * 24 * 27 * 30 . note : the remainder when a number is divided by a divisor ' d ' will take values from 0 to ( d - 1 ) . it can not be equal to or more than ' d ' . the value of 21 * 24 * 27 * 30 is more than 33 . when the value of the remainder is more than the divisor , final remainder will be the remainder of dividing the product by the divisor . i . e . , the final remainder is the remainder when 33 divides 21 * 24 * 27 * 30 . when 33 divides 21 * 24 * 27 * 30 , the remainder is 30 . choice c"
Answer: c
Problem: how many positive integers less than 100 are neither multiples of 3 or 4 .
Options: a ) a ) 50 , b ) b ) 31 , c ) c ) 32 , d ) d ) 33 , e ) e ) 34
Rationale: "to answer this q we require to know 1 ) multiples of 3 till 100 = 100 / 3 = 33 2 ) multiples of 4 till 100 = 100 / 4 = 25 add the two 25 + 33 = 58 ; subtract common terms that are multiple of both 3 and 4 . . lcm of 4 and 3 = 12 multiples of 6 till 100 = 100 / 12 = 8.3 = 8 so total multiples of 3 and 4 = 58 - 8 = 50 ans = 100 - 50 = 50 a"
Answer: a
Problem: shopkeeper rise price by 31 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 0.215 % , b ) 1.215 % , c ) 3.215 % , d ) 6.215 % , e ) 7.215 %
Rationale: "let d initial price be 100 31 % rise now price = 131 / 100 * 100 = 131 10 % discount then price = 131 * 90 / 100 = 117.9 15 % discount then price = 117.9 * 85 / 100 = 100.215 so gain = 100.215 - 100 = 0.215 gain % = gain * 100 / cp = = > 0.215 * 100 / 100 = 0.215 % answer : a"
Answer: a
Problem: the probability that a computer company will get a computer hardware contract is 4 / 5 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 9 / 10 , what is the probability that it will get both the contracts ?
Options: a ) 1 / 8 , b ) 2 / 9 , c ) 3 / 10 , d ) 4 / 11 , e ) 5 / 12
Rationale: "let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 4 / 5 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 9 / 10 = ( 4 / 5 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 3 / 10 . hence , the required probability is 3 / 10 . the answer is c ."
Answer: c
Problem: in right triangle abc , ac is the hypotenuse . if ac is 20 and ab + bc = 50 , what is the area of the triangle abc ?
Options: a ) 225 , b ) 525 , c ) 25 √ 2 , d ) 200 , e ) 200 √ 2
Rationale: "square ab + bc = 50 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 2500 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 20 ^ 2 = 400 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 400 + 2 * ab * bc = 2500 . 400 + 2 * ab * bc = 2500 . ab * bc = 1050 . the area = 1 / 2 * ab * bc = 525 . answer : b ."
Answer: b
Problem: a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 500 feet . what is its area , in square feet ?
Options: a ) 12,000 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800
Rationale: "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 500 , you can deduce the following a = 300 b = 400 300 x 400 = 120,000 a is the answer ."
Answer: a
Problem: if k and w are the dimensions of a rectangle that has area 21 , and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: "kw = 21 = 21 * 1 = 7 * 3 - - > k can take 2 values , answer : a"
Answer: a
Problem: how many digits are in the number 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 6 ?
Options: a ) 22 , b ) 20 , c ) 19 , d ) 18 , e ) 17
Rationale: "whenever you are asked to find the number of digits , try to bring the number in multiples of 10 . this way , we can wasily calculate the umber of 0 ' s through the powers of 10 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 6 = ( 5 ^ 2 * 2 ) ^ 8 * 2 ^ 9 * 11 ^ 2 x 10 ^ 6 = 5 ^ 16 * 2 ^ 17 * 11 ^ 2 x 10 ^ 6 = 2 * 11 ^ 2 * 10 ^ 16 x 10 ^ 6 = 242 * 10 ^ 22 hence we would have 16 trailing 0 ' s and the three digits from 242 total digits = 3 + 22 = 25 correct option : e"
Answer: e
Problem: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 4 years ?
Options: a ) 3277 , b ) 2977 , c ) 12656 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 * ( 3 / 4 ) ^ 4 answer : c"
Answer: c
Problem: the simple interest on a sum of money will be rs . 400 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 800 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 1732
Rationale: "p - - - 10 - - - - 400 p - - - 5 - - - - - 200 3 p - - - 5 - - - - - 600 - - - - - - = > 800 answer : a"
Answer: a
Problem: the banker â € ™ s gain on a sum due 3 years hence at 10 % per annum is rs . 120 . the banker â € ™ s discount is
Options: a ) rs . 960 , b ) rs . 840 , c ) rs . 520 , d ) rs . 760 , e ) none
Rationale: "solution t . d = ( b . g x 100 / r x t ) = rs . ( 120 x 100 / 10 x 3 ) = rs . 400 . b . d = rs ( 400 + 120 ) = rs . 520 . answer c"
Answer: c
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.90 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 255 , b ) $ 275 , c ) $ 459 , d ) $ 1,250 , e ) $ 2,550
Rationale: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.9 = $ 459 answer c"
Answer: c
Problem: for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 5.0 – 5.0 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 1.0
Rationale: "since y * is defined as the greatest positive even integer less than or equal to y , then 5.0 * = 4 ( the greatest positive even integer less than or equal to 5.0 is 4 ) . hence , 5.0 – 5.0 * = 5.0 - 4 = 1.0 answer : e ."
Answer: e
Problem: the salary of a person was reduced by 10 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 10 % , b ) 11 1 / 9 % , c ) 13 2 / 7 % , d ) 15 3 / 11 % , e ) 12 1 / 3 %
Rationale: "let the original salary be $ 100 new salary = $ 90 increase on 90 = 10 increase on 100 = 10 / 90 * 100 = 11 1 / 9 % answer is b"
Answer: b
Problem: if the average ( arithmetic mean ) of 102 consecutive odd integers is 414 , then the least of these integers is
Options: a ) a ) 160 , b ) b ) 289 , c ) c ) 250 , d ) d ) 313 , e ) e ) 525
Rationale: "a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 102 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 51 st and 52 nd numbers in the set ) . this means that numbers 51 and 52 in this set are 413 and 415 . because we know that number 51 is 413 , we know that the smallest number is 50 odd numbers below this , which means that it is 50 * 2 = 100 below this ( every odd number is every other number ) . therefore 413 - 100 = 313 , answer choice d"
Answer: d
Problem: 10 play kabadi , 40 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 50
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 40 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 40 + 5 = 45 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 45 - 5 = 50 answer : e"
Answer: e
Problem: set s consists of integers { 6 , 8 , 10 , 12 , 14 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 30 % . what is the value of integer n ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 22 , e ) 28
Rationale: "the average of the numbers in set s is 10 . if we increase the mean by 30 % , the new mean is 13 . thus , on average , 5 numbers increase by 3 . therefore n = 13 + 15 = 28 the answer is e ."
Answer: e
Problem: 1 + 2 = 10 2 + 3 = 26 3 + 4 = 50 then 4 + 5 = ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: 1 + 2 = 10 . . . . . ( 1 + 2 ) ^ 2 + 1 = 10 2 + 3 = 26 . . . . . . . ( 2 + 3 ) ^ 2 + 1 = 26 3 + 4 = 50 then . . . ( 3 + 4 ) ^ 2 + 1 = 50 4 + 5 = 82 . . . . . . . . ( 4 + 5 ) ^ 2 + 1 = 82 answer : c
Answer: c
Problem: n is a positive integer . when n + 1 is divided by 4 , the remainder is 3 . what is the remainder when n is divided by 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 0 , e ) 4
Rationale: "n + 1 = 4 a + 3 i . e . n + 1 = 7 , 10 , 13 , 16 , . . . etc . i . e . n = 6 , 9 , 12 , 15 , . . . etc . when n is divided by 3 remainder is always 0 answer : d"
Answer: d
Problem: in the list 3 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ?
Options: a ) 2 / 9 , b ) 1 / 3 , c ) 2 / 5 , d ) 2 / 3 , e ) 7 / 9
Rationale: highest frequent term in the set is 5 ( with frequency 4 ) hence mode = 5 two terms ( 3 , 4 ) out of a total of 9 terms are less than mode of the set . fraction of set that are less than mode of set = 2 / 9 answer : option a
Answer: a
Problem: how many multiples of 8 are less than 4500 , and also multiples of 12 ?
Options: a ) 104.6 , b ) 187.5 , c ) 625.6 , d ) 450.5 , e ) 467.4
Rationale: "lcm of 8 & 12 = 24 tried dividing 4500 by 24 got quotient 187.5 ' so b is answer"
Answer: b
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 84 a week . what is the % increase ?
Options: a ) 16.12 % , b ) 16.66 % , c ) 16.56 % , d ) 40 % , e ) 18.1 %
Rationale: "increase = ( 24 / 60 ) * 100 = ( 4 / 10 ) * 100 = 40 % . d"
Answer: d
Problem: 56 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 33.0 , b ) 37.66 , c ) 32.1 , d ) 31.23 , e ) 19
Rationale: explanation : let the two parts be ( 56 - x ) and x . then , 10 ( 56 - x ) + 22 x = 780 = > 12 x = 220 = > x = 20 . bigger part = ( 56 - x ) = 37.66 . answer : b ) 37.66
Answer: b
Problem: the sides of a cube measures 8 cm . if the surface area of the cube is the same as a ball , what is the radius of the ball ? round to the nearest whole number .
Options: a ) 3 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: first calculate the surface area of the cube . the cube is made of 6 squares with the sides measuring 8 cm each . the surface area of 1 side of the cube is 64 cm . multiply the surface area of the 1 side by 6 will give you the cube ' s total surface area . the cubes total surface area is 384 cm . now we know that the surface area of the ball is 384 cm . to find out the surface area of a sphere you need to square the radius , then multiply by pi , and multiply by the number 4 . going backwards to find the radius - you will need to dived the surface area by 96 . then divide by pi . then determine the square root of the answer . the radius is 5.527 . rounding to the nearest whole number the radius is 6 . the correct answer is ( d ) .
Answer: d
Problem: find the value for x from below equation : x / 2 = - 2 ?
Options: a ) - 6 , b ) 1 , c ) - 2 , d ) - 3 , e ) - 4
Rationale: "1 . multiply both sides by 2 : x * 2 / 2 = - 2 / 2 simplify both sides : x = - 4 e"
Answer: e
Problem: a man sold 18 toys for rs . 18900 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 990
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 18900 . gain = sp â € “ cp 3 x = 18900 â € “ 18 x 21 x = 18900 x = rs . 900 . answer : option d"
Answer: d
Problem: how many of the positive factors of 75 are not factors of 95 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "factors of 75 - 1 , 3 , 5 , 15 , 25 , 75 , factors of 95 - 1 , 5 , 19 , 95 , comparing both , we have three factors of 75 which are not factors of 95 - 3 , 15 , 25 , 75 , the answer is e"
Answer: e
Problem: q is as much younger than r as he is older than t . if the sum of the ages of r and t is 50 years , what is definitely the difference between r and q ’ s age ?
Options: a ) 1 year , b ) 2 years , c ) 25 years , d ) data inadequate , e ) none of these
Rationale: "explanation given that : 1 . the difference of age b / w r and q = the difference of age b / w q and t . 2 . sum of age of r and t is 50 i . e . ( r + t ) = 50 . question : r – q = ? . explanation : r – q = q – t ( r + t ) = 2 q now given that , ( r + t ) = 50 so , 50 = 2 q and therefore q = 25 . question is ( r – q ) = ? here we know the value ( age ) of q ( 25 ) , but we don ’ t know the age of r . therefore , ( r - q ) can not be determined . answer d"
Answer: d
Problem: if it is assumed that 62 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 420 , c ) 480 , d ) 483.8 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 62 % = 300 / 0.62 = 483.8 option d"
Answer: d
Problem: what is the lowest positive integer that is divisible by 1 through 2 , inclusive ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 6 , e ) 1
Rationale: the integer should be divisible by : 1 and 2 . the least common multiple of these integers is lcm = 1 * 2 = 2 answer : a
Answer: a
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 12 % .
Options: a ) 37.5 % , b ) 38.5 % , c ) 42 % , d ) 27.5 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 64 . s . p = rs . 88 . ∴ gain % = [ 24 / 64 * 100 ] % = 37.5 % . answer a"
Answer: a
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 1 : 2 and 3 : 2 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 99 : 61
b ) 1 : 1
c ) 61 : 160
d ) 61 : 99
e ) 99 : 160
Rationale: vessel a = 300 gallons - - > milk = 100 , water = 200 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 400 , water 400 . the ratio = 400 / 400 - - > 1 : 1 answer : b
Answer: b
Problem: 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 30 % profit ?
Options: a ) 220 , b ) 230 , c ) 960 , d ) 832 , e ) 400
Rationale: "c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 130 % of rs . 640 = 130 / 100 * 640 = rs . 832 . d"
Answer: d
Problem: each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 1250 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .
Options: a ) 513 , b ) 512 , c ) 517 , d ) 519 , e ) 521
Rationale: trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , c , d , e the answer to be b again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 512 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 512 = 1250 hence , correct answer = b
Answer: b
Problem: a river boat leaves silver town and travels upstream to gold town at an average speed of 6 kilometers per hour . it returns by the same route at an average speed of 5 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 5.5 , b ) 7.1 , c ) 7.2 , d ) 7.0 , e ) 8.0
Rationale: "pick a number which is lcm of 5 and 6 = 30 . upstream time = 30 / 6 = 5 hrs downstream time = 30 / 5 = 6 hrs total time = 11 hrs total distance = 60 average speed = 60 / 11 = 5.5 km / hr"
Answer: a
Problem: a cistern is normally filled in 10 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 88 , c ) 60 , d ) 99 , e ) 11
Rationale: "1 / 10 - 1 / x = 1 / 12 x = 60 answer : c"
Answer: c
Problem: three numbers are in the ratio 4 : 5 : 6 and their average is 42 . the largest number is :
Options: a ) 28 , b ) 32 , c ) 36 , d ) 50.4 , e ) 45
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 42 15 x = 126 x = 8.4 largest number = 6 x = 50.4 . answer d"
Answer: d
Problem: 6 % of customers that enter a store on any given day must not pay tax . if 1000 people shop every day , how many people pay taxes in the store every week
Options: a ) 6500 , b ) 6580 , c ) 7200 , d ) 7120 , e ) 6800
Rationale: 6 % of customers do not pay taxes . 6 / 100 * 1000 customers do not pay taxes . 6 / 100 * 1000 = 60 therefore 1000 - 60 customers do pay taxes . 1000 - 60 = 940 940 * 7 days per week = 6580 b )
Answer: b
Problem: find the compound ratio of ( 2 : 3 ) , ( 5 : 3 ) and ( 2 : 5 ) is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 9 , e ) 3 : 2
Rationale: "required ratio = 2 / 3 * 5 / 3 * 2 / 5 = 4 / 9 = 4 : 9 answer is d"
Answer: d
Problem: 1 = 5,2 = 10,3 = 253,4 = 254,5 = 255,6 = 256,7 = 257,8 = 258 then 10 = ?
Options: a ) 2 , b ) 255 , c ) 345 , d ) 445 , e ) 235
Rationale: "1 = 5,2 = 10,3 = 253,4 = 254,5 = 255,6 = 256,7 = 257,8 = 258 then 10 = ? 10 = 2 check the first eqn . answer : a"
Answer: a
Problem: p and q started a business investing rs . 85,000 and rs . 30,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 4 , d ) 17 : 2 , e ) 17 : 3
Rationale: "p : q = 85000 : 30000 = 17 : 6 . answer : a"
Answer: a
Problem: a raz ' s company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options: a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3
Rationale: a raz ' s company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . 1996 - x - - - - - y - - - - - - - x + y 1997 - x 1 - - - - y 1 - - x 1 + y 1 x 1 = a * x . . . . . ( p ) y 1 = 1.07 * y . . . ( q ) x 1 + y 1 / x + y = 1.01 solve using p and q and find x / y
Answer: a
Problem: what is the units digit of 23 ^ 3 * 17 ^ 2 * 39 ^ 2 ?
Options: a ) 9 , b ) 7 , c ) 5 , d ) 3 , e ) 1
Rationale: "the units digit of 23 ^ 3 is the units digit of 3 * 3 * 3 = 27 which is 7 . the units digit of 17 ^ 2 is the units digit of 7 * 7 = 49 which is 9 . the units digit of 39 ^ 2 is the units digit of 9 * 9 = 81 which is 1 . the units digit of 7 * 9 * 1 = 63 is 3 . the answer is d ."
Answer: d
Problem: three numbers are in the ratio 4 : 5 : 6 and their average is 20 . the largest number is :
Options: a ) 24 , b ) 32 , c ) 36 , d ) 42 , e ) 45
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 20 15 x = 60 x = 4 largest number = 6 x = 24 . answer a"
Answer: a
Problem: a customer went to a shop and paid a total of $ 25 , out of which 90 cents was for sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) $ 8.50 , b ) $ 8.70 , c ) $ 9.10 , d ) $ 10.00 , e ) $ 10.40
Rationale: "the total cost was $ 25 . the tax was $ 0.90 let the original price of the taxable items = x given that tax rate = 6 % 0.06 x = 0.90 x = $ 15 the cost of the tax free items was $ 25 - $ 15 - $ 0.90 = $ 9.10 the answer is c ."
Answer: c
Problem: 45 x ? = 60 % of 900
Options: a ) 16.2 , b ) 12 , c ) 5 , d ) 500 , e ) none
Rationale: "answer let 45 x a = ( 60 x 900 ) / 100 ∴ a = ( 60 x 9 ) / 45 = 12 correct option : b"
Answer: b
Problem: set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 6 , while all other numbers remain the same , what is the new average of set s ?
Options: a ) 6.6 , b ) 6.7 , c ) 6.8 , d ) 6.85 , e ) 6.9
Rationale: "old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 6 then total increased to 62 + 6 = 68 new avg - 68 / 10 = 6.8 . hence answer is c ."
Answer: c
Problem: a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 3 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) 0.5
Rationale: "b work 1 / 8 * 3 = 3 / 8 remaining work = 1 - 3 / 8 = 5 / 8 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 remaining work is done in = 8 / 5 * 1 / 4 = 2 / 5 = 0.4 answer : d"
Answer: d
Problem: what is the greatest 6 - digit number when divided by 8 , 9 , and 10 leaves a remainder of 6 , 7 , and 8 respectively ?
Options: a ) 456780 , b ) 678918 , c ) 997479 , d ) 997916 , e ) 997920
Rationale: when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 8 when we divide by 10 , so b is the only possible answer .
Answer: b
Problem: a thief is spotted by a policeman from a distance of 160 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 240 m , c ) 440 m , d ) 640 m , e ) none of them
Rationale: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 160 m / 1000 ) x 1 / 2 hr = 2 / 25 hr . in 2 / 25 hr / s , the thief covers a distance of 8 x 2 / 25 km = 16 / 25 km = 640 m answer is d ."
Answer: d
Problem: the average of runs of a cricket player of 20 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 96 , b ) 106 , c ) 122 , d ) 116 , e ) 120
Rationale: "average = total runs / no . of innings = 36 so , total = average x no . of innings = 36 * 20 = 720 now increase in avg = 4 runs . so , new avg = 36 + 4 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 720 = 120 answer : e"
Answer: e
Problem: the product of a and b is equal to 14 more than twice the sum of a and b . if b = 8 , what is the value of b - a ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 24 , e ) 35
Rationale: "ab = 14 + 2 ( a + b ) 8 a = 14 + 2 a + 16 6 a = 30 a = 5 b - a = 8 - 5 = 3 b is the answer"
Answer: b
Problem: excluding stoppages , the speed of a train is 42 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) 7.5 , b ) 8.5 , c ) 9.5 , d ) 4.5 , e ) 6.5
Rationale: t = 6 / 42 * 60 = 8.5 answer : b
Answer: b
Problem: a can do a piece of work in 4 hours . a and c together can do it in just 2 hours , while b and c together need 3 hours to finish the same work . in how many hours b can complete the work ?
Options: a ) 10 hours , b ) 12 hours , c ) 16 hours , d ) 18 hours , e ) 20 hours
Rationale: "explanation : work done by a in 1 hour = 1 / 4 work done by b and c in 1 hour = 1 / 3 work done by a and c in 1 hour = 1 / 2 work done by a , b and c in 1 hour = ( 1 / 4 ) + ( 1 / 3 ) = 7 / 12 work done by b in 1 hour = ( 7 / 12 ) – ( 1 / 2 ) = 1 / 12 = > b alone can complete the work in 12 hour option b"
Answer: b
Problem: a man can row downstream at the rate of 32 kmph and upstream at 17 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 7.5 , b ) 8.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 32 + 17 ) = 24.5 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 32 - 17 ) = 1 / 2 ( 15 ) = 7.5 kmph answer is a ."
Answer: a
Problem: a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 15 minutes , a combustion reaction creates 15,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 1,000 , b ) 500 , c ) 250 , d ) 50 , e ) 0
Rationale: "solution : 15,000 carbon dioxide molecules are created over a period of 15 minutes . therefore 15,000 / 15 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is a ."
Answer: a
Problem: a train speeds past a pole in 15 seconds and a platform 100 m long in 20 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 300 m , e ) 145 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 20 = x / 15 x = 300 m . answer : d"
Answer: d
Problem: the smallest number when increased by ` ` 1 ` ` is exactly divisible by 618 , 3648 , 60 is :
Options: a ) 724 , b ) 721 , c ) 720 , d ) 719 , e ) 700
Rationale: lcm = 720 720 - 1 = 719 answer : d
Answer: d
Problem: a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days g will the work get over ?
Options: a ) 60 , b ) 70 , c ) g = 75 , d ) g = 80 , e ) 100
Rationale: "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
Answer: c
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.96 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 3.00 , b ) $ 3.20 , c ) $ 3.40 , d ) $ 3.60 , e ) $ 3.80
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 96 4 x / 15 = 96 x = $ 3.60 = $ 3.60 the answer is d ."
Answer: d
Problem: how many prime numbers are between 78 / 14 and 55 / 4 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "78 / 14 = 39 / 7 = 6 - 55 / 4 = 14 - prime numbers between 6 and 14 are 7 , 11 and 13 - sign signifies that the number is marginally less . answer b"
Answer: b
Problem: a person can swim in still water at 12 km / h . if the speed of water 10 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 12 s = 10 us = 12 - 10 = 2 d = 12 t = 12 / 2 = 6 answer : d"
Answer: d
Problem: if 15 % of a class averages 100 % on a test , 50 % of the class averages 78 % on the test , and the remainder of the class averages 63 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .
Options: a ) 76 % , b ) 77 % , c ) 78 % , d ) 79 % , e ) 80 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 15 % - 50 % = 35 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.15 x 100 + 0.50 x 78 + 0.35 x 63 = 76.05 the class average ( rounded ) is 76 % final answer a ) 76 %"
Answer: a
Problem: what is x if x + 3 y = 10 and y = 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "substitute y by 3 in x + 3 y = 10 x + 3 ( 3 ) = 10 x + 9 = 10 if we substitute x by 1 in x + 9 = 10 , we have 1 + 9 = 10 . hence x = 1 correct answer a"
Answer: a
Problem: arun borrowed a sum of money from jayant at the rate of 8 % per annum simple interest for the first 4 years , 10 % per annum for the next 6 years and 12 % per annum for the period beyond 10 years . if he pays a total of 12160 as interest only at the end of 15 years , how much money did he borrow ?
Options: a ) 8000 , b ) 10000 , c ) 12000 , d ) 9000 , e ) none of these
Rationale: let the principal = p then p × 8 × 4 / 100 + p × 10 × 6 / 100 + p × 12 × 5 / 100 = 12160 ⇒ 152 p = 12160 × 100 or 12160 × 100 / 152 = 8000 answer a
Answer: a
Problem: what is the largest 4 digit number exactly divisible by 88 ?
Options: a ) 9999 , b ) 9944 , c ) 9988 , d ) 9900 , e ) 9991
Rationale: "largest 4 digit number = 9999 9999 ÷ 88 = 113 , remainder = 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 answer is b"
Answer: b
Problem: a women travels from x to y distance of 1000 miles in 10 hours . she returns to x in 4 hours . find her average speed
Options: a ) 300 mph , b ) 150.2 mph , c ) 142.8 mph , d ) 200 mph , e ) 111.01 mph
Rationale: speed from x to y = 1000 / 10 = 100 mph speed from y to x = 1000 / 4 = 250 mph average speed = 2 * 100 * 250 / 350 = 142.8 mph answer is c
Answer: c
Problem: in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 45 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: "you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 3 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : d . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d"
Answer: d