Cheukting/mathqa huggingface dataset:
Question (other): in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 40 people were made to stand in a column , how many columns could be formed ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "16 * 30 = 40 * n n = 12 the answer is a ."
Answer: a
Question (general): find large number from below question the difference of two numbers is 1200 . on dividing the larger number by the smaller , we get 5 as quotient and the 4 as remainder
Options: a ) 1234 , b ) 1345 , c ) 1456 , d ) 1567 , e ) 1499
Rationale: "let the smaller number be x . then larger number = ( x + 1200 ) . x + 1200 = 5 x + 4 4 x = 1196 x = 299 large number = 299 + 1200 = 1499 e"
Answer: e
Question (geometry): the area of a rectangular field is equal to 50 square meters . its perimeter is equal to 30 meters . find the width of this rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "l * w = 50 : area , l is the length and w is the width . 2 l + 2 w = 30 : perimeter l = 15 - w : solve for l ( 15 - w ) * w = 30 : substitute in the area equation w = 5 and l = 10 correct answer a"
Answer: a
Question (gain): a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 35 % ?
Options: a ) 600 , b ) 887 , c ) 256 , d ) 654 , e ) 675
Rationale: "cost price = rs . 500 profit = 35 % of 500 = rs . 175 selling price = cost price + profit = 500 + 175 = 675 answer : e"
Answer: e
Question (gain): jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 3000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 13,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400
Rationale: "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 3000 ) solving for x , we get the shares as 13000 . ans : ( option a )"
Answer: a
Question (physics): 65 boys can complete a work in 30 days . how many men need to complete twice the work in 20 days
Options: a ) 160 , b ) 170 , c ) 180 , d ) 195 , e ) 200
Rationale: "one man can complete the work in 30 * 65 = 1950 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1950 m = 195 workers answer : d"
Answer: d
Question (general): in a recent election , james received 0.5 percent of the 2000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001
Rationale: james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d
Answer: d
Question (other): the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 12000 , then find the annual income of a ?
Options: a ) rs . 420000 , b ) rs . 403200 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these
Rationale: "b ' s monthly income = 12000 * 112 / 100 = rs . 13440 b ' s monthly income = 2 parts - - - - > rs . 13440 a ' s monthly income = 5 parts = 5 / 2 * 13440 = rs . 33600 a ' s annual income = rs . 33600 * 12 = rs . 403200 answer : b"
Answer: b
Question (gain): a shopkeeper sold an article offering a discount of 5 % and earned a profit of 42.5 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 27.675 , c ) 30 , d ) 50 , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 42.5 ) / ( 100 â ˆ ’ 5 ) = 150 hence , required % profit = 150 â € “ 100 = 50 % answer d"
Answer: d
Question (other): pants , shorts and shirts in a dresser are in the ratio of 7 : 7 : 10 . if there are 14 pants , the number of shirts in the dresser is :
Options: a ) 14 , b ) 7 , c ) 20 , d ) 70 , e ) 35
Rationale: explanation : let pants = 7 x , shorts = 7 x & shirts = 10 x . now , 7 x = 14 hence x = 2 . number of apples = 10 x = 20 . answer : c
Answer: c
Question (general): if x / ( 11 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99
Rationale: "x / ( 11 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 11 * lowest value of p = 2 * 11 * 2 = 44 answer c"
Answer: c
Question (general): list i : { y , 2 , 4 , 7 , 10 , 11 } list ii : { 3 , 3 , 4 , 6 , 7 , 10 } if the median r of list i is equal to the sum of the median of list ii and the mode of list ii , then y equals
Options: a ) 5 , b ) 7 , c ) 8 , d ) r = 9 , e ) 10
Rationale: mode of list ii = 3 median r of list ii = 4 + 6 / 2 = 5 sum of mode + mean = 3 + 5 = 8 now to make 8 as the median we need to find a value of y such that if the no . of terms in list 1 are odd then y = 8 else if even then 7 + y / 2 = 8 here its even so 7 + y / 2 = 8 from this y = 9 ( d )
Answer: d
Question (general): a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 4 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 194
Rationale: "by the question , the equation would be 150 p - 84 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 194 . answer e for me ."
Answer: e
Question (gain): at a special sale , 9 tickets can be purchased for the price of 6 tickets . if 9 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 9 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 60 % , e ) 66.6 %
Rationale: "let the price of a ticket be rs . 100 , so 6 tickets cost 600 & 9 tickets cost 900 9 tickets purchased at price of 6 tickets ie . , for 600 , so amount saved s rs . 300 , % of 9 tickets = ( 300 / 900 ) * 100 = 33.3 % answer : b"
Answer: b
Question (general): how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.35 * 8 = 0.2 ( x + 8 ) - - > x = 12 . answer : b ."
Answer: b
Question (general): a students was asked to find the arithmetic mean of the numbers 3 , 11 , 7 , 9 , 15 , 13 , 8 , 19 , 17 , 21 , 14 and x . he found the mean to be 12 . what should be the number in place of x ?
Options: a ) 3 , b ) 7 , c ) 17 , d ) 31 , e ) 38
Rationale: adding all the numbers we get 137 + x given - ( 137 + x ) / 12 = 12 137 + x = 12 * 12 x = 144 - 137 x = 7 answer : b
Answer: b
Question (gain): harkamal purchased 10 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1190 , b ) b ) 1065 , c ) c ) 1070 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 10 kg grapes = 70 × 10 = 700 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 700 + 490 = 1190 a"
Answer: a
Question (gain): a chemical supply company has 60 liters of a 40 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 40 % hno 3 solution means hno 3 = 24 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 24 + x = 50 % of ( 60 + x ) or x = 12 . hence , a"
Answer: a
Question (general): the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 36 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 24 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: "262.85 ( 36 ) + 3 , 104.35 x = 1 , 399.45 ( 36 + x ) solve the equation . 262.85 ( 36 ) + 3 , 104.35 x = 1 , 399.45 ( 36 + x ) 9 , 462.6 + 3 , 104.35 x = 50 , 380.2 + 1 , 399.45 x 9 , 462.6 + 1 , 704.9 x = 50 , 380.2 1 , 704.9 x = 40 , 917.6 x = 24 answer is b ."
Answer: b
Question (gain): a man spends 35 % of his income on food , 25 % on children education and 80 % of the remaining on house rent . what percent of his income he is left with ?
Options: a ) 1 % , b ) 8 % , c ) 12 % , d ) 5 % , e ) 4 %
Rationale: let the total income be x then , income left = ( 100 - 80 ) % of x - [ 100 - ( 35 + 25 ) ] % of x = 20 % of 40 % of x = 8 % of x answer is b
Answer: b
Question (physics): a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 261 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 408 , b ) 475 , c ) 550 , d ) 625 , e ) 700
Rationale: "let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 261 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 561 a + b + c = 51 per hour so for eight hrs = 51 * 8 = 408 = answer = a"
Answer: a
Question (general): a container contains 20 liters of milk , from this container 2 liters of milk was taken out and replaced by water . this process was repeated further 2 times . how much milk is now contained by the container ?
Options: a ) 14.58 liters , b ) 20.16 liters , c ) 22.45 liters , d ) 26.95 liters , e ) 31.45 liters
Rationale: "amount of milk left after 3 operations = 20 ( 1 - 2 / 20 ) ^ 3 = 20 * 9 / 10 * 9 / 10 * 9 / 10 = 14.58 liters answer is a"
Answer: a
Question (geometry): the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "given that the area of the square = 2025 sq . units = > side of square = √ 2025 = 45 units the radius of the circle = side of the square = 45 units length of the rectangle = 2 / 5 * 45 = 18 units given that breadth = 10 units area of the rectangle = lb = 18 * 10 = 180 sq . units answer : option e"
Answer: e
Question (physics): a train of length 250 m crosses a bridge of length 150 m in 25 seconds . what is the speed of train ?
Options: a ) 57.6 , b ) 27 , c ) 25 , d ) 22 , e ) 72
Rationale: sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 150 ) = 25 x speed speed = 400 / 25 = 16 m / s = 57.6 km / h answer = a
Answer: a
Question (gain): indu gave bindu rs . 500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 0.2 , b ) 1.2 , c ) 3 , d ) 4 , e ) 0.8
Rationale: "500 = d ( 100 / 4 ) 2 d = 0.8 answer : e"
Answer: e
Question (geometry): the product of the squares of two positive integers is 9 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : b - 1 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 9 [ square root both sides ] xy = 3 3 = 1 x 3 , 3 x 1 cancel the repeats this leaves us with exactly 1 options . hence , b"
Answer: b
Question (physics): with both inlets open , a water tank will be filled with water in 52 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 9,000 , b ) 10,500 , c ) 11,750 , d ) 17,500 , e ) 19,500
Rationale: "the work done by inlet a and b together in 1 min = 1 / 52 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 52 ) - ( 1 / 120 ) = 1 / 92 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 92 ) - ( 1 / 120 ) = 50 cubic meter = 19,500 cubic meter answer : option e"
Answer: e
Question (geometry): if each edge of a cube is increased by 50 % , find the percentage increase in its surface area
Options: a ) 125 %
b ) 129 %
c ) 185 %
d ) 725 %
e ) 145 %
Rationale: let the edge = a cm so increase by 50 % = = total surface area of original cube = tsa of new cube = = = increase in area = = increase % = = 125 % answer : a
Answer: a
Question (physics): 12 : 8 seconds : : ? : 4 minutes
Options: a ) 10 , b ) 15 , c ) 6 , d ) 8 , e ) 7
Rationale: "12 * 4 = 8 * x x = 6 answer : c"
Answer: c
Question (general): in the xy - plane the point ( - 2 - 3 ) is the centre of a circle , the point ( - 2 , 0 ) lies inside the circle and the point ( 2 , - 3 ) lies outside the circle . if the radius r of the circle r is an integer then r =
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 2 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 2 , - 3 ) - - - > lesser than 5 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,0 ) - - - - > greater than 3 units . thus the radius is > 3 but < 5 and as it is an integer , the only possible value of radius = 4 units . c is the correct answer ."
Answer: c
Question (physics): a hall 36 m long and 15 m broad is to be paved with stones , each measuring 4 dm by 5 dm . the number of stones required is :
Options: a ) 180 , b ) 2700 , c ) 18 , d ) 18000 , e ) 1.8
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 40 * 50 ) therefore , number of stones = ( 3600 * 1500 / 40 * 50 ) = 2700 answer : b"
Answer: b
Question (physics): jane makes toy bears . when she works with an assistant , she makes 80 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 r ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . r = [ ( 2 - 1 ) / 1 ] * 100 % = 100 % . c"
Answer: c
Question (general): the cost to park a car in a certain parking garage is $ 15.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 1.09 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 3.03
Rationale: total cost of parking for 9 hours = 15 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 15 + 7 * 1.75 = 27.25 thus the average parking price = 27.25 / 9 = 3.03 $ e is the correct answer .
Answer: e
Question (general): cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 4 - 2 ) / ( 10 - 4 ) = 2 / 6 = 1 / 3 so they should be mixed in the ratio 1 : 3 answer - e"
Answer: e
Question (physics): a trader sells 75 meters of cloth for rs . 4950 at the profit of rs . 15 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 51 , b ) 88 , c ) 90 , d ) 42 , e ) 22
Rationale: "sp of 1 m of cloth = 4950 / 75 = rs . 66 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 66 - rs . 15 = rs . 51 answer : a"
Answer: a
Question (general): 587 x 999 = ?
Options: a ) 586413 , b ) 587523 , c ) 614823 , d ) 615173 , e ) none of them
Rationale: "= 587 x 999 = 587 x ( 1000 - 1 ) = 587 x 1000 - 587 - 1 = 587000 - 587 = 586413 answer is a"
Answer: a
Question (general): the contents of a certain box consist of 14 apples and 12 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 12 oranges , so to get to 6 oranges , we should remove 12 - 6 = 6 oranges . answer b"
Answer: b
Question (general): he total marks obtained by a student in physics , chemistry and mathematics is 110 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 110 + p c + m = 110 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 110 / 2 = 55 . answer : a"
Answer: a
Question (geometry): the diagonal of a square is 4 ? 2 cm . what will be the diameter of another square if their area is double that of the first square ?
Options: a ) 8 cm
b ) 9 cm
c ) 10 cm
d ) 11 cm
e ) 12 cm
Rationale: d 1 = 4 ? 2 = > area = 1 / 2 d 12 = 1 / 2 * ( 4 ? 2 ) 2 = 16 cm 2 area of new square = ( 2 * 16 ) cm 2 = 32 cm 2 therefore 1 / 2 * d 22 = 32 = > d 22 = 64 = > d 2 = 8 cm answer a
Answer: a
Question (gain): the sale price sarees listed for rs . 400 after successive discount is 10 % and 5 % is ?
Options: a ) 166 , b ) 178 , c ) 342 , d ) 199 , e ) 112
Rationale: "400 * ( 90 / 100 ) * ( 95 / 100 ) = 342 answer : c"
Answer: c
Question (geometry): a volume of 10936 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812
b ) 8231
c ) 2734
d ) 4222
e ) 4254
Rationale: a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10936 l can be kept in ( 10936 / 4 ) hemispheres ans . 2734 answer : c
Answer: c
Question (general): the average age of 31 students in a group is 16 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 31 , b ) 36 , c ) 48 , d ) 45 , e ) 57
Rationale: "age of the teacher = ( 32 * 17 - 31 * 16 ) = 48 years . answer : c"
Answer: c
Question (physics): venki takes a trip and drives 5 hours from town x to town z at a rate of 80 miles per hour . on her way back , venki drives 45 miles per hour and stops in town y which is midway between town x and town z . how many hours does it take venki to drive from town z to town y ?
Options: a ) 1.01 , b ) 4.44 , c ) 11.5 , d ) 1.75 , e ) 2.14
Rationale: distance from x to z = 5 hr * 80 mph = 400 miles hence distance from y to z = 1 / 2 * 400 = 200 time = 200 / 45 = 4.44 hrs imo : b
Answer: b
Question (geometry): if a rectangle have length 16 cm and diagonal 20 cm . calculate its area .
Options: a ) 185
b ) 132
c ) 165
d ) 192
e ) 212
Rationale: breadth = √ 20 ^ 2 - 16 ^ 2 = √ 144 = 12 cm area = 16 * 12 = 192 sq . cm answer d
Answer: d
Question (general): a qualified worker digs a well in 5 hours . he invites 2 apprentices , both capable of working 3 / 5 as fast and 2 trainees both working 1 / 5 as fast as he . if the 5 - person team digs the same well , how much time does the team need to finish the job ?
Options: a ) 1 : 42 , b ) 1 : 34 , c ) 1 : 44 , d ) 1 : 54 , e ) 2 : 14
Rationale: and answer is correct as you have calculated : 100 / 59 hrs that is 1.71 hrs - 1 hr and 42 minutes , so 1 : 42 , hence , a .
Answer: a
Question (physics): find the cost of fencing around a circular field of diameter 28 m at the rate of rs . 1.50 a meter ?
Options: a ) rs . 150
b ) rs . 132
c ) rs . 100
d ) rs . 125
e ) rs . 225
Rationale: 2 * 22 / 7 * 14 = 88 88 * 1 1 / 2 = rs . 132 answer : b
Answer: b
Question (physics): truck x is 14 miles ahead of truck y , which is traveling the same direction along the same route as truck x . if truck x is traveling at an average speed of 57 miles per hour and truck y is traveling at an average speed of 63 miles per hour , how long will it take truck y to overtake and drive 4 miles ahead of truck x ?
Options: a ) 5 hours , b ) 3 hours 20 minutes , c ) 3 hours , d ) 2 hours 45 minutes , e ) 8 hours
Rationale: "relative speed = 63 - 57 = 6 miles per hour dist required = 14 + 4 = 18 miles time taken to overtake = 18 / 6 = 3 hours . c is the answer ."
Answer: c
Question (gain): a and b ’ s salaries together amount to rs . 2,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is a ’ s salary ?
Options: a ) rs . 500 , b ) rs . 750 , c ) rs . 1250 , d ) rs . 1500 , e ) rs . 1520
Rationale: "explanation : ( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 2000 4 b = 2000 = > b = 500 a = 1500 answer is d"
Answer: d
Question (general): last year , for every 100 million vehicles that traveled on a certain highway , 80 vehicles were involved in accidents . if 4 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 1600 , b ) 3200 , c ) 800 , d ) 400 , e ) 200
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 80 accidents as 4 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 4,000 million rather than 4 billion . creating a proportion we have : 100 / 80 = 4,000 / x cross multiplying gives us : 100 x = 4,000 * 80 x = 40 * 80 = 3200 answer : b"
Answer: b
Question (general): on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 20 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 20 . . 4 x + 12 = 20 . . x = 2 . . ans = x + 4 = 2 + 4 = 6 answer b
Answer: b
Question (general): log root ( 8 ) / log 8 is equal to
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: = > log ( 8 ) ^ 1 / 2 / log 8 = 1 / 2 log 8 / log 8 = 1 / 2 answer a
Answer: a
Question (general): one - third less than 40 % of 180 is equal to :
Options: a ) 15 , b ) 30 , c ) 35 , d ) 40 , e ) 48
Rationale: "lots of ways to tackle this . 40 % of 180 = 72 1 / 3 of 72 = 24 so , 1 / 3 less than 72 is equal to 72 - 24 = 48 answer : e"
Answer: e