Cheukting/mathqa huggingface dataset:
Question (physics): joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 2 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 225 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 2 ) * 270 = 135 gallons total paint used = 225 gallons . option b"
Answer: b
Question (general): a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 5 per unit . further , the manufacturer has costs of $ 16500 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 ) $ 195
Rationale: by the question , the equation would be 150 p - 85 * 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 = $ 195 . answer e for me .
Answer: e
Question (general): set s consists of integers { 7 , 8 , 10 , 12 , 13 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 10 % . what is the value of integer n ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 22 , e ) 24
Rationale: "the average of the numbers in set s is 10 . if we increase the mean by 10 % , the new mean is 11 . thus , on average , 5 numbers increase by 1 . therefore n = 11 + 5 = 16 the answer is c ."
Answer: c
Question (general): the average runs scored by a batsman in 30 matches is 50 . in the next 15 matches the batsman scored an average of 26 runs . find his average in all the 45 matches ?
Options: a ) 31 , b ) 42 , c ) 29 , d ) 97 , e ) 27
Rationale: total score of the batsman in 30 matches = 1500 . total score of the batsman in the next 15 matches = 390 . total score of the batsman in the 30 matches = 1890 . average score of the batsman = 1890 / 45 = 42 . answer : b
Answer: b
Question (gain): the owner of a furniture shop charges his customer 60 % more than the cost price . if a customer paid rs . 2000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 2789 , b ) 2772 , c ) 1250 , d ) 6725 , e ) 2099
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1250 ( 100 / 160 ) = rs . 1250 . answer : c"
Answer: c
Question (other): a shipment of 240 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
Options: a ) 1 / 250 , b ) 9 / 74 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3
Rationale: "probability of chosing one defective phone from a lot of 240 which ontains 84 defective phones is = ( 84 / 240 ) probability of chosing one defective phone from a lot of 239 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 239 ) combined probability of series of events = product of the probabilities = ( 84 / 240 ) * ( 83 / 239 ) 84 / 240 is close to ( 7 / 20 ) and ( 83 / 239 ) = ( 25 / 72 ) so answer is ( 7 / 20 ) * ( 25 / 72 ) ( 9 / 74 ) so , answer will be b"
Answer: b
Question (general): set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 8 ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 8 , e ) e ) 16
Rationale: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d"
Answer: d
Question (physics): the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 600 per sq . metre .
Options: a ) $ 12375 , b ) $ 13575 , c ) $ 16575 , d ) $ 14575 , e ) $ 18575
Rationale: "a area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 600 hence , total cost = 5.5 × 3.75 × 600 = $ 12375 a"
Answer: a
Question (general): if n = 10 ^ 100 and n ^ n = 10 k what is the value of k ?
Options: a ) 200 , b ) 10 ^ 100 , c ) 10 ^ 102 , d ) 100 ^ 100 , e ) 1000 ^ 10
Rationale: "there is a simple logic to this question . ( a ^ m ) ^ n = a ^ mn so , ( 10 ^ 100 ) ^ ( 10 ^ 100 ) = 10 ^ ( 100 * ( 10 ^ 100 ) ) = 10 ^ ( ( 10 ^ 2 ) * ( 10 ^ 100 ) ) = 10 ^ ( 10 ^ 102 ) and this equals 10 ^ k so , k = 10 ^ 102 answer : c"
Answer: c
Question (probability): a bag contains 30 red jellybeans and 30 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 1 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 1 / 20 answer : option d"
Answer: d
Question (general): what is the sum of the multiples of 4 between 63 and 151 inclusive ?
Options: a ) 2240 , b ) 2250 , c ) 2310 , d ) 2330 , e ) 2332
Rationale: "the fastest way in an ap is to find the average and multiply with total integers . . between 63 and 151 , the smallest multiple of 4 is 64 and largest = 148 . . average = ( 64 + 148 ) / 2 = 106 . . total numbers = ( 148 - 64 ) / 4 + 1 = 21 + 1 = 22 . . sum = 22 * 106 = 2332 ans e"
Answer: e
Question (gain): on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 60 % 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 ) 12.5 % , c ) 15 % , d ) 22 % , e ) 25 %
Rationale: "0.1 m = 0.40 e = > e / m = 1 / 4 * 100 = 25 % so answer is e . m - # of motorists e - # of motorists exceeding speed"
Answer: e
Question (other): if the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3 , what is the ratio of apples to cucumbers ?
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 3 : 7 , d ) 2 : 5 , e ) 1 : 6
Rationale: "the ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9 . the ratio of apples to bananas to cucumbers is 4 to 3 to 9 . the answer is a ."
Answer: a
Question (general): car dealership x , the total profit from sales increased by 12 percent over the previous years , while the number of cars sold decreased by 12 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 18 % , b ) 20 % , c ) 22 % , d ) 27.27 % , e ) 35 %
Rationale: "let profit be x and cars sold be y originally profit / car = x / y now it is 1.12 x / 0.88 y = 112 / 88 ( x / y ) increase in profit per car = ( ( 24 / 88 ) ( x / y ) ) / ( x / y ) * 100 = 27.27 % answer = d"
Answer: d
Question (general): a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 46.24 , the number of the member is the group is :
Options: a ) 57 , b ) 68 , c ) 77 , d ) 87 , e ) 97
Rationale: "explanation : money collected = ( 46.24 x 100 ) paise = 4624 paise . ∴ number of members = √ ( 4624 ) = 68 . answer : b"
Answer: b
Question (general): arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 15 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 15 0 = a + d - 14 a + d = 14 a = d ( as they are twin brothers ) a = d = 7 d is the answer"
Answer: d
Question (general): for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 99 true ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "answer c ( a + b ) ( a - b ) = 99 3 cases for ( a + b ) , ( a - b ) 99 , 1 33 , 3 11 , 9 answer b"
Answer: b
Question (general): how many positive integers less than 100 are there such that they are multiples of 8 or multiples of 7 but not both ?
Options: a ) 21 , b ) 22 , c ) 25 , d ) 24 , e ) 31
Rationale: "for 8 : 8 . . . 100 = 8 * 12 for 7 : 7 . . . 98 = 7 * 14 but there is one integer 8 * 7 . so n = ( 12 - 1 ) + ( 14 - 1 ) = 24 d"
Answer: d
Question (general): when x is multiplied by 2 , the result is 19 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 15 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 2 x - 19 = 26 - x or , 3 x = 45 or , x = 15 . c answer ."
Answer: c
Question (general): if - 3 x + 5 y = 48 and 3 x - 2 y = 6 , what is the product of x and y ?
Options: a ) 252 , b ) 428 , c ) 464 . , d ) 200 , e ) 642
Rationale: "given - 3 x + 5 y = 48 - - - eq 1 3 x - 2 y = 6 - - eq 2 sum both eqns we get 3 y = 54 = > y = 18 sub 2 y in eq 2 = > 3 x - 36 = 6 . = > x = 14 now xy = 14 * 18 = 252 option a is correct answer ."
Answer: a
Question (physics): a can give b 60 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 148.94 , b ) 148.13 , c ) 148.22 , d ) 111.0 , e ) 111.12
Rationale: "a runs 1000 m while b runs 940 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 940 = 851.06 m . b can give c = 1000 - 851.06 = 148.94 m . answer : a"
Answer: a
Question (physics): kim finds a 6 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ?
Options: a ) 7 / 5 , b ) 1 / 2 , c ) 8 / 15 , d ) 2 / 5 , e ) 3 / 5
Rationale: "3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is e"
Answer: e
Question (other): how many prime numbers between 1 and 100 are factors of 143 ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 2 , e ) 3
Rationale: "factor of 143 = 11 * 13 - - - 2 prime numbers d"
Answer: d
Question (other): a jar contains a mixture of ab in the ratio 3 : 2 . when 20 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 12 , b ) 15 , c ) 16 , d ) 20 , e ) 36
Rationale: "20 litres of mixture that is replaced will contain 12 litres of a and 8 litres of b ( as a : b = 3 : 2 ) let the initial volume of the mixture be 3 k + 2 k = 5 k so by condition , [ 3 k - 12 ] / [ 2 k - 8 + 20 ] = 2 / 3 = > 9 k - 36 = 4 k - 16 + 40 = > 5 k = 60 solve for k which is k = 12 so initial volume of liquid a = 3 k = 36 litres answer : e"
Answer: e
Question (general): alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 3,600 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?
Options: a ) 850 , b ) 1,100 , c ) 1,800 , d ) 2,550 , e ) 3,400
Rationale: "assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 3600 therefore x = 2400 / 4 = 600 price of 28 inch + 30 inch = 800 + 1000 = 1800 option c"
Answer: c
Question (general): the average of marks obtained by 120 boys was 38 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 115 , d ) 125 , e ) 140
Rationale: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 38 24 x = 4560 - 1800 = > x = 2760 / 24 x = 115 . hence , the number of boys passed = 115 . answer : c"
Answer: c
Question (general): if x , y , and z are positive integers , and 2 x = 5 y = 8 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 28 , c ) 33 , d ) 42 , e ) 60
Rationale: "take lcm of 2,5 and 8 = 40 now 2 x = 40 = > x = 20 5 y = 40 = > y = 8 8 z = 40 = > z = 5 20 + 8 + 5 = 33 . option c ."
Answer: c
Question (physics): john and beth each drove from smallville to crown city by different routes . john drove an an average speed of 40 miles per hour and completed the trip in 30 minutes . beth ' s route was 5 miles longer , and it took her 20 minutes more than john to complete the trip . how many miles per hour was beth ' s average speed on this trip ?
Options: a ) 24 , b ) 30 , c ) 48 , d ) 54 , e ) 75
Rationale: speed = distance / time distance for john = speed * time = 40 * 1 / 2 = 20 miles distance for beth = distance for john + 5 = 20 + 5 = 25 miles time taken by beth = time taken by john + ( 1 / 3 hour ) = 1 / 2 + 1 / 3 = 5 / 6 speed of beth = d / t = 25 / ( 5 / 6 ) = 25 * 6 / 5 = 30 miles per hour hence , b is the answer .
Answer: b
Question (other): what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 100 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "prime factorization out is the way to go here ! 36 ^ 100 3 ^ 2 times 2 ^ 2 and both to the power of 100 [ ( 3 ^ 2 ) * ( 2 ^ 2 ) ] ^ 100 giving you the beautifully simplistic answer of 3 ^ 200 and 2 ^ 200 ans is 200 answer : b"
Answer: b
Question (general): the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 17 positive perfect squares ?
Options: a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 1,316 , e ) 1,785
Rationale: "first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 17 and c = 1 / 2 into the equation and simplify to get the answer 1785 . option e ."
Answer: e
Question (general): 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 180 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 12 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 180 rs . 5 m + 5 m + 5 m - - - - - 180 rs . 15 m - - - - - - 180 rs . = > 1 m = 12 rs . answer : e"
Answer: e
Question (physics): a train is 250 meter long is running at a speed of 36 km / hour . in what time will it pass a station of 200 meter length ?
Options: a ) 28 seconds , b ) 27 seconds , c ) 45 seconds , d ) 26 seconds , e ) 18 seconds
Rationale: "speed = 36 km / hr = 36 * ( 5 / 18 ) m / sec = 10 m / sec total distance = 250 + 200 = 450 meter time = distance / speed = 450 * ( 10 ) = 45 seconds answer : c"
Answer: c
Question (general): a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 72.25 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 85 , e ) 97
Rationale: "explanation : money collected = ( 72.25 x 100 ) paise = 7225 paise . ∴ number of members = √ ( 7225 ) = 85 . answer : d"
Answer: d
Question (geometry): triangle atriangle b are similar triangles with areas 2023 units square and 1792 units square respectively . the ratio of there corresponding height would be
Options: a ) 9 : 10 , b ) 17 : 16 , c ) 23 : 27 , d ) 13 : 17 , e ) 15 : 23
Rationale: "let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 2023 / 1792 ( x ^ 2 / y ^ 2 ) = ( 17 * 17 * 7 ) / ( 16 * 16 * 7 ) ( x ^ 2 / y ^ 2 ) = 17 ^ 2 / 16 ^ 2 x / y = 17 / 16 ans = b you need to take a hint from given options to find factors of 2013 and 2527 ."
Answer: b
Question (physics): two trains each 120 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 85 km / h while the other travels at 65 km / h . how long will it take for them to pass each other completely .
Options: a ) 11.07 sec , b ) 10.07 sec , c ) 13.07 sec , d ) 12.07 sec , e ) 14.07 sec
Rationale: "explanation : d = 120 m + 120 m = 240 m rs = 85 + 65 = 150 * 5 / 18 = 417 / 10 t = 420 * 10 / 417 = 10.07 sec answer : option b"
Answer: b
Question (gain): john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 15,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 20000 , b ) 30000 , c ) 40000 , d ) 30301.5 , e ) 50000
Rationale: "a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 15,000 ( 1 + 0.04 / 4 ) ^ 4 - 15,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 15,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 15,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 15,000 ( 1.0201 + 1 ) = 30301.5 hence answer is d ."
Answer: d
Question (geometry): the length of a rectangle is reduced by 20 % . by what % would the width have to be increased to maintainthe original area ?
Options: a ) 14 % , b ) 15 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "sol . required change = ( 20 * 100 ) / ( 100 - 20 ) = 25 % c"
Answer: c
Question (geometry): find the area of a parallelogram with base 10 cm and height 20 cm .
Options: a ) 200 , b ) 384 , c ) 200 , d ) 244 , e ) 242
Rationale: "area of a parallelogram = base * height = 10 * 20 = 200 cm 2 answer : option c"
Answer: c
Question (physics): a train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the train must run to reduce the time of journey to 40 min will be .
Options: a ) 60 kmph , b ) 63 kmph , c ) 57 kmph , d ) 70 kmph , e ) 61 kmph
Rationale: time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph answer is a .
Answer: a
Question (general): if y > 0 , ( 2 y ) / 10 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to y / 5 + 3 y / 10 = 2 y / 5 = 50 % b"
Answer: b
Question (other): 200 pupil total , out of 125 like pizza , 115 like burger , then how many like both ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: n ( a u b ) = n ( a ) + n ( b ) - n ( a intersection b ) 200 = 125 + 115 - both both = 240 - 200 = 40 . answer : a
Answer: a
Question (geometry): the area of a rectangular plot is 15 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 10 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 15 × b ∴ l = 15 m and l – b = 10 ∴ b = 15 – 10 = 5 m answer b"
Answer: b
Question (general): what could be the range of a set consisting of odd multiples of 9 ?
Options: a ) 21 , b ) 24 , c ) 35 , d ) 72 , e ) 70
Rationale: "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 9 * ( 2 n + 1 ) where n is any positive integer . range = 9 * ( 2 m + 1 ) - 9 * ( 2 n + 1 ) = 9 * 2 * ( m - n ) = 18 * ( m - n ) . m , n - any positive integers the answer must be divisible by 18 , which is only 72 . the correct answer is d"
Answer: d
Question (gain): the compound interest earned by sunil on a certain amount at the end of two years at the rate of 10 % p . a . was rs . 420 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 2530 , b ) rs . 2430 , c ) rs . 2420 , d ) rs . 2410 , e ) rs . 2440
Rationale: "let the sum be rs . p p { [ 1 + 10 / 100 ] 2 - 1 } = 420 p ( 10 / 100 ) ( 2 + 10 / 100 ) = 420 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 420 / ( 0.1 ) ( 2.1 ) = 2000 . amount = 2000 + 420 = rs . 2420 answer : c"
Answer: c
Question (physics): sandy walked 20 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 25 meters . what distance is she from the starting point and in which direction ?
Options: a ) 35 m east , b ) 35 m north , c ) 30 m west , d ) 45 m west , e ) 45 m east
Rationale: the net distance is 20 + 25 = 45 meters to the east . the answer is e .
Answer: e
Question (general): the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 4 type b widgets , and the weight of 3 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 5 : 4 , b ) 7 : 6 , c ) 9 : 8 , d ) 11 : 10 , e ) 13 : 12
Rationale: "3 b = 7 c and so b = 7 c / 3 7 a = 4 b and so a = 4 b / 7 = 4 c / 3 a + b = 4 c / 3 + 7 c / 3 = 11 c / 3 b + c = 7 c / 3 + c = 10 c / 3 the ratio of a + b : b + c = 11 : 10 the answer is d ."
Answer: d
Question (general): a man can swim in still water at 3 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 1.4 , c ) 1.1 , d ) 1.5 , e ) 1
Rationale: "m = 3 s = x ds = 3 + x us = 3 + x 3 + x = ( 3 - x ) 2 3 + x = 6 - 2 x 3 x = 3 x = 1 answer : e"
Answer: e
Question (gain): a man gains 30 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 140 % , c ) 150 % , d ) 260 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 130 / 100 ) x = 13 x / 10 new s . p . = 2 ( 13 x / 10 ) = 26 x / 10 profit = 26 x / 10 - x = 26 x / 10 profit % = ( profit / c . p . ) * 100 = > ( 26 x / 10 ) * ( 1 / x ) * 100 = 260 % option d"
Answer: d
Question (physics): a train traveled the first d miles of its journey it an average speed of 50 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 96 miles per hour , what is the value of y ?
Options: a ) 68 , b ) 84 , c ) 90 , d ) 120 , e ) 160
Rationale: "average speed = total distance traveled / total time taken 3 d / d / 50 + d / y + d / 160 = 96 solving for d and y , 15 y = 11 y + 480 3 y = 480 y = 160 answer e"
Answer: e