regisss/math_qa huggingface dataset:
Problem: ( 12 ) ^ 3 x 6 ^ 4 ÷ 432 = ?
Options: a ) 5184 , b ) 5060 , c ) 5148 , d ) 5084 , e ) none of them
Rationale: = ( 12 ) ^ 3 x 6 ^ 4 / 432 = ( 12 ) ^ 3 x 6 ^ 4 / 12 x 6 ^ 2 = ( 12 ) ^ 2 x 6 ^ 2 = ( 72 ) ^ 2 = 70 answer is e
Answer: e
Problem: two cylinders are of the same height . their radii are in the ratio 1 : 3 . if the volume of the first cylinder is 40 cc . find the volume of the second cylinder ?
Options: a ) 360 cc
b ) 60 cc
c ) 300 cc
d ) 36 cc
e ) 39 cc
Rationale: r 1 = x r 2 = 3 x π * x 2 * h = 40 π 9 x 2 h = 40 * 9 = 360 answer : a
Answer: a
Problem: a grocer has a sale of rs . 2500 , rs . 4000 , rs . 3540 for 3 consecutive months . how much sale must he have in the fourth month so that he gets an average sale of rs . 2890 ?
Options: a ) rs . 3500 , b ) rs . 1520 , c ) rs . 4996 , d ) rs . 4000 , e ) rs . 900
Rationale: total sale for 5 months = rs . ( 2500 + 4000 + 3540 ) = rs . 10040 . required sale = rs . [ ( 2890 x 4 ) - 10040 ] = rs . ( 11560 - 10040 ) = rs . 1520 . b )
Answer: b
Problem: if 3 ^ x * 4 ^ y = 4 , 782,969 and x – y = 14 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 4 , 782,969 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 14 and y = 0 , then x = 14 . the answer is e ."
Answer: e
Problem: if x , y , and z are positive real numbers such that x + y - z = 100 , y - z + x = 120 , and z - x + y = 50 , then find the x + y + z value ?
Options: a ) 100 , b ) 120 , c ) 150 , d ) 200 , e ) 160
Rationale: "x + y - z = 100 , - - - - - - 1 ) y - z + x = 120 , - - - - - - 2 ) z - x + y = 50 - - - - - - 3 ) from ( 1 ) & ( 2 ) 2 z = 20 z = 10 from ( 2 ) & ( 3 ) 2 y = 170 y = 85 then x = 100 - 75 = 25 x + y + z = 120 correct option is b"
Answer: b
Problem: the volume of a cube is 3375 cc . find its surface .
Options: a ) 1350 , b ) 1150 , c ) 1456 , d ) 1254 , e ) 1489
Rationale: a 3 = 3375 = > a = 15 6 a 2 = 6 * 15 * 15 = 1350 answer : a
Answer: a
Problem: if the cost price of 10 articles is equal to the selling price of 20 articles , what is the % profit or loss made by the merchant ?
Options: a ) 25 % loss , b ) 25 % profit , c ) 20 % loss , d ) 20 % profit , e ) 50 % loss
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 10 articles = 10 * 1 = $ 10 the selling price of 20 articles = cost price of 10 articles = $ 10 . now , we know the selling price of 20 articles . let us find the cost price of 20 articles . cost price of 20 articles = 20 * 1 = $ 20 . therefore , profit made on sale of 20 articles = selling price of 20 articles - cost price of 20 articles = 10 - 20 = - $ 10 . as the profit is in the negative , the merchant has made a loss of $ 10 . therefore , % loss = loss / cp * 100 % loss = - 10 / 20 * 100 = 50 % loss . e"
Answer: e
Problem: ( 0.76 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.76 ) ( power 2 ) + 0.076 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.66 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.76
Rationale: "given expression = ( 0.76 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.76 ) ( power 2 ) + ( 0.76 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.76 - 0.1 ) = 0.66 answer is a ."
Answer: a
Problem: one - third of 1206 is what percent of 134 ?
Options: a ) 3 , b ) 30 , c ) 300 , d ) none of these , e ) can not be determined
Rationale: "answer let one - third of 1206 is n % of 134 . ∵ 1206 / 3 = ( n x 134 ) / 100 ∴ n = ( 402 x 100 ) / 134 = 300 correct option : c"
Answer: c
Problem: the digit sum of the year 2007 is 2 + 0 + 0 + 7 = 9 , which is a square number . how many years during the 20 - first century have a square digital sum ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: the twenty - first century runs from the year 2001 to 2100 inclusive , so with the exception of the year 2100 , for which the digital sum is three anyway , the first two digits of all the other years are fixed as 20 . hence for the sum of all the digits to be square the sum of the last two digits number be two less than a perfect square . as the maximum sum of the last two digits is 18 , the greatest sum will be 20 . therefore we can obtain digital sums of 4 , 9 , or 16 , with the last two digits adding to 2 , 7 , or 14 respectively . 4 : 2002 , 2011 , 2020 9 : 2007 , 2016 , 2025 , 2034 , 2043 , 2052 , 2061 , 2070 16 : 2059 , 2068 , 2077 , 2086 , 2095 that is , there are sixteen years during the twenty - first century for which the digital sum is square . answer : d
Answer: d
Problem: a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 40 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 30 , b ) 64 , c ) 60 , d ) 70 , e ) 90
Rationale: total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 40 vehicles . hence 2 / 3 constitutes 80 speedster convertibls = 80 * 4 / 5 = 64 b
Answer: b
Problem: earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 180 envelopes
Options: a ) 6 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envelopes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 180 envelopes they will take 180 / 60 mins . i . e . , 3 mins . answer : d
Answer: d
Problem: boy sells a book for rs . 810 he gets a loss of 10 % , to gain 10 % , what should be the sp ?
Options: a ) 430 , b ) 990 , c ) 550 , d ) 590 , e ) 600
Rationale: "cost price = 810 / 90 x 100 = 900 to gain 10 % = 900 x 10 / 100 = 90 sp = cp + gain = 900 + 90 = 990 answer : b"
Answer: b
Problem: a discount electronics store normally sells all merchandise at a discount of 2 percent to 50 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 100 before any discount ?
Options: a ) $ 100.00 , b ) $ 40.00 , c ) $ 50.00 , d ) $ 30.00 , e ) $ 10.00
Rationale: "original price : 100 $ max first discount = - 50 % thus : 100 â ˆ — ( 1 â ˆ ’ 50 / 100 ) = 50 second discount on the discounted price = - 20 % thus : 50 â ˆ — ( 1 â ˆ ’ 20 / 100 ) = 40 answer b ."
Answer: b
Problem: how many pieces of 85 cm length can be cut from a rod of 34 meters long ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: "number of pieces = 3400 / 85 = 40 the answer is b ."
Answer: b
Problem: if 525 / 999 = 0.525 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?
Options: a ) - 1 , b ) 0 , c ) 3 , d ) 4 , e ) 5
Rationale: "0 . [ u ] 125 [ / u = 0.525525525 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e"
Answer: e
Problem: p and q invested in a business . the profit earned was divided in the ratio 4 : 5 . if p invested rs 52000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 40000 , d ) 20000 , e ) 65000
Rationale: "let the amount invested by q = q 52000 : q = 4 : 5 ⇒ 52000 × 5 = 4 q ⇒ q = ( 52000 × 5 ) / 4 = 65000 answer is e ."
Answer: e
Problem: the number 152 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 15 , c ) 21 , d ) 27 , e ) 39
Rationale: "actually , decomposition into factors can easily give you the answer here . you should just do the decomposition of the right thing i . e . the options since they represent the product of those integers . since the sum of cubes is 152 , the numbers can not be larger than 5 since 6 ^ 3 itself is 216 . 21 , 27 , 39 - the factors are too large so ignore 8 - ( 2 , 4 ) does not satisfy 15 - ( 3 , 5 ) yes . 3 ^ 3 + 5 ^ 3 = 152 - answer answer : b"
Answer: b
Problem: a goods train runs at the speed of 72 km / hr and crosses a 280 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 240 , b ) 277 , c ) 276 , d ) 270 , e ) 281
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 280 ) / 26 = 20 x = 240 m . answer : a"
Answer: a
Problem: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 13 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276 , b ) 1560 , c ) 2832 , d ) 1299 , e ) 1236
Rationale: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 13 = 1560 answer : option b"
Answer: b
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 50 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 25 , d ) 88 , e ) 78
Rationale: "we have : l = 20 ft and lb = 50 sq . ft . so , b = 2.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 5 ) ft = 25 ft . answer : c"
Answer: c
Problem: the average weight of 24 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 48.975 , b ) 42.255 , c ) 50 , d ) 51.255 , e ) 52.253
Rationale: "explanation : average weight of 24 boys = 50.25 total weight of 24 boys = 50.25 × 24 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 24 ) + ( 45.15 × 8 ) total boys = 24 + 8 = 32 average weight of all the boys = ( 50.25 × 24 ) + ( 45.15 × 8 ) / 32 = 48.975 answer : option a"
Answer: a
Problem: if ' y ' is a positive integer exactly divisible by 4 or 5 but not divisible by 8 . what could possibly be the value of ' y ' ?
Options: a ) 40 , b ) 80 , c ) 20 , d ) 24 , e ) 36
Rationale: 40 and 80 are both divisible by 4 and 5 but also by 8 . so they are not the right answer . 24 and 36 are both clearly not divisible by 5 ( not correct ) 20 is both divisible by 4 and 5 but not by 8 . answer : ( c )
Answer: c
Problem: two goods trains each 625 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 40 , b ) 45 , c ) 48 , d ) 60 , e ) 44
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 625 + 625 = 1250 m . required time = 1250 * 6 / 125 = 60 sec . answer : option d"
Answer: d
Problem: how many figures are required to number the pages the pages of a book containing 1000 pages ?
Options: a ) 2793 , b ) 2333 , c ) 2993 , d ) 2893 , e ) 2693
Rationale: 1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 999 = 900 * 3 = 2700 1000 = 4 - - - - - - - - - - - 2893 answer : d
Answer: d
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 50 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 87.5 % , d ) 60 % , e ) 75 %
Rationale: "original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.5 c ( 50 % profit ) x = 1.5 / . 8 * c x = 15 / 8 c original selling price is 1.875 c which is 87.5 % profit answer c"
Answer: c
Problem: the diagonal of a rhombus are 65 m and 60 m . its area is :
Options: a ) 1940 , b ) 1950 , c ) 1960 , d ) 1990 , e ) 1980
Rationale: "area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 × 65 × 60 ) cm ( power ) 2 = 65 × 30 = 1950 cm ( power ) 2 answer is b ."
Answer: b
Problem: a taxi company charges $ 1.40 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 1.40 for the first quarter - mile , we will have $ 3.50 left to spend on quarter - mile intervals . since $ 3.50 / $ 0.15 = 23.33 , we can buy 23.33 more quarter - miles , and will travel 24.33 quarter miles in all : 24.33 × 1 / 4 = 6 miles . the correct answer is choice ( e ) ."
Answer: e
Problem: the difference between a number and its three - fifths is 50 . what is the number ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) can not be determined , e ) none of these
Rationale: "suppose the number is n . then n - 3 ⁄ 5 n = 50 ⇒ 2 n ⁄ 5 = 50 ∴ n = 50 × 52 = 125 answer . c"
Answer: c
Problem: john and david can finish a job together in 6 hours . if john can do the job by himself in 8 hours , what percent of the job does david do ?
Options: a ) 35 % , b ) 45 % , c ) 25 % , d ) 30 % , e ) 20 %
Rationale: "you can also plug in numbers . for example , bob and alice work at a donut factory and make 24 donuts which is the job ( i picked this as a smart number ) . john on his own works 24 / 8 = 3 donuts per hour . john and david work 24 / 6 = 4 donuts per hour so david works 1 donuts / hour to find out the percentage , david works 1 donuts / hr x 6 hours = 6 donuts per hour . therefore 6 donuts / 24 donuts = 1 / 4 = 25 % answer : c"
Answer: c
Problem: a and b finish the job in 15 days . while a , b and c can finish it in 10 days . c alone will finish the job in
Options: a ) 40 days , b ) 30 days , c ) 60 days , d ) 70 days , e ) 50 days
Rationale: "explanation : 10 = ( 15 * x ) / ( 15 + x ) 150 + 10 x = 15 x 5 x = 150 x = 30 answer : option b"
Answer: b
Problem: in what ratio should a variety of rice costing rs . 10 per kg be mixed with another variety of rice costing rs . 13.25 per kg to obtain a mixture costing rs . 10.75 per kg ?
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 5 : 1 , d ) 4 : 1 , e ) 3 : 1
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 13.25 - 10.75 ) / ( 10.75 - 10 ) = 6 / 3 = 2 / 1 answer : a"
Answer: a
Problem: a 9 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 9 , d ) 3 / 10 , e ) 4 / 11
Rationale: "the longer wire will form a square with an area more than 4 if the wire is cut at a point within one meter of either end . the probability of this is 2 / 9 . the answer is c ."
Answer: c
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 1 year ?
Options: a ) 3277 , b ) 2977 , c ) 30000 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 * ( 3 / 4 ) ^ 1 answer : c"
Answer: c
Problem: the greatest number by which the product of 3 consecutive multiples of 4 is always divisible is
Options: a ) 54 , b ) 76 , c ) 152 , d ) 384 , e ) none of these
Rationale: solution required number = product of first three multiplies of 3 = ( 4 ã — 8 ã — 12 ) = 384 . answer d
Answer: d
Problem: if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ^ 2 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ? .
Options: a ) 25 , b ) 27 , c ) 45 , d ) 75 , e ) 125
Rationale: if both 5 ^ 2 & 3 ^ 3 are factors , then they must be present in the number . leaving rest of the prime factors and splitting 6 ^ 2 into 3 ^ 2 * 2 ^ 3 . the number is lacking 5 ^ 2 & a 3 , so that 5 ^ 2 and 3 ^ 3 is a factor . hence the smallest number is 5 ^ 2 * 3 = 75 answer : d
Answer: d
Problem: rajesh spends 40 % of his monthly salary on food , 20 % of the medicines and saves 60 % of the remaining amount . if his monthly salary is rs . 15000 , how much money does he save every month ?
Options: a ) rs . 1000 , b ) rs . 2596 , c ) rs . 4320 , d ) rs . 6489 , e ) rs . 4789
Rationale: explanation : ramesh ' s monthly income = rs . 15000 he spends 40 % on food . the total money spent on food = 40 / 100 * 15000 = rs . 6000 now , his monthly remaining income = rs . 15000 – rs . 6000 = rs . 9000 out of rs . 9000 , he spends 20 % on medicines . the total money spent on medicines = 20 / 100 * 9000 = rs . 1800 now , his monthly remaining income = rs . 9000 – rs . 1800 = rs . 7200 out of rs . 7200 , he saves 600 % . amount saved = 60 / 100 * 7200 = rs . 4320 answer : c
Answer: c
Problem: the average ( arithmetic mean ) of 14 , 32 , and 53 is 3 more than the average of 21 , 47 , and x . what is x ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "the average of 14 , 32 , and 53 is 33 . the average of 21 , 47 and x is 30 . then 21 + 47 + x = 90 . x = 22 . the answer is c ."
Answer: c
Problem: how long does a train 165 meters long running at the rate of 36 kmph take to cross a bridge 660 meters in length ?
Options: a ) 33 , b ) 72 , c ) 55 , d ) 82.5 , e ) 62
Rationale: "explanation : t = ( 660 + 165 ) / 36 * 18 / 5 t = 82.5 answer : option d"
Answer: d
Problem: if √ 2 n = 64 , then the value of n is :
Options: a ) 6 , b ) 12 , c ) 24 , d ) 48 , e ) none
Rationale: sol . √ 2 n = 64 ⇔ ( 2 n ) 1 / 2 ⇔ 2 n / 2 = 26 ⇔ n / 2 = 6 ⇔ n = 12 . answer b
Answer: b
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 4500 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 31500 , d ) 34000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 4500 = > total profit = 4500 * 7 = 31500 . answer : option c"
Answer: c
Problem: robert ' s salary was decreased by 30 % and subsequently increased by 30 % . how much percentage does he lose ?
Options: a ) 10 % , b ) 9 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: "let original salary be $ 100 salary after decreasing 30 % = 100 - 100 x 30 / 100 = $ 70 salary after increasing 30 % on $ 70 = 70 + 70 x 30 / 100 = $ 91 percentage of loss = 100 - 91 = 9 % answer : b"
Answer: b
Problem: 4 + 4
Options: a ) 8 , b ) 2 , c ) 1 , d ) 5 , e ) 2
Rationale: c
Answer: c
Problem: the total age of a and b is 20 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 20 , b ) 12 , c ) 15 , d ) 16 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 20 a - c = 20 answer is a"
Answer: a
Problem: if 6 cats can kill 6 rats in 6 minutes , how long will it take 100 cats to kill 100 rats ?
Options: a ) 1 minutes , b ) 2 minutes , c ) 3 minutes , d ) 4 minutes , e ) 6 minutes
Rationale: "it will take 6 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 6 minutes , so 100 cats can kill 100 rats in 6 minutes answer e"
Answer: e
Problem: what is the smallest integer that is multiple of 5 , 7,20
Options: a ) 70 , b ) 35 , c ) 200 , d ) 280 , e ) 140
Rationale: "it is the lcm of 5 , 7 and 20 which is 140 . the answer is e ."
Answer: e
Problem: in the xy - coordinate system , what is the slope of the line that goes through the point ( 7 , 3 ) and is equidistant from the two points p = ( 5 , 5 ) and q = ( 13 , 7 ) ?
Options: a ) 0.5 , b ) 0.75 , c ) 1.0 , d ) 1.25 , e ) 1.5
Rationale: "first , get the middle coordinate between ( 5,5 ) and ( 13,7 ) . . . x = 5 + ( 13 - 5 ) / 2 = 9 y = 5 + ( 7 - 5 ) / 2 = 6 second , get the slope of ( 9,6 ) and ( 7,3 ) . m = 6 - 3 / 9 - 7 = 3 / 2 = 1.5 answer : e"
Answer: e
Problem: if x is to be chosen at random from the integers between 1 to 7 , inclusive , and y is to be chosen at random from the integers between 8 and 12 , inclusive , what is the probability that x + y will be even ?
Options: a ) 2 / 5 , b ) 3 / 7 , c ) 5 / 7 , d ) 17 / 35 , e ) 24 / 35
Rationale: "x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 3 / 7 * 3 / 5 = 9 / 35 p ( x and y are both odd ) = 4 / 7 * 2 / 5 = 8 / 35 p ( x + y is even ) = 9 / 35 + 8 / 35 = 17 / 35 the answer is d ."
Answer: d
Problem: hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of 1 hammers and three wrenches is one - third that of 8 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 , d ) 5 / 4 , e ) 2
Rationale: "x be the weight of a hammer and y be the weight of a wrench . ( 1 x + 3 y ) = 1 / 3 * ( 8 x + 5 y ) 3 ( 1 x + 3 y ) = ( 8 x + 5 y ) 3 x + 9 y = 8 x + 5 y 4 y = 5 x y = 5 x / 4 ans - d"
Answer: d
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 175 kg then find the average weight of all the 7 rounds ?
Options: a ) 100 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 175 / 7 = 100 kgs answer : a"
Answer: a
Problem: a jogger running at 9 km / hr along side a railway track is 360 m ahead of the engine of a 90 m long train running at 63 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 76 sec , b ) 67 sec , c ) 30 sec , d ) 36 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 63 - 9 = 54 km / hr . = 54 * 5 / 18 = 15 m / sec . distance to be covered = 360 + 90 = 450 m . time taken = 450 / 15 = 30 sec . answer : c"
Answer: c
Problem: if price of t . v set is reduced by 18 % , then its sale increases by 72 % , find net effect on sale value
Options: a ) 41 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 18 + 72 + ( - 18 * 72 ) / 100 = - 18 + 72 - 13 = 41 answer : a"
Answer: a
Problem: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 155 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 177.50 , d ) rs . 258.50 , e ) none of these
Rationale: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 155 ) / \ x â ˆ ’ 155 22.50 = > x â ˆ ’ ( 155 / 22.50 ) = 1 . = > x â ˆ ’ 155 = 22.50 . = > x = 177.50 rs . answer : c"
Answer: c
Problem: solution for 4.75 + . 303 + . 432
Options: a ) 2.91 , b ) 5.911 , c ) 5.485 , d ) 5.986 , e ) 2.999
Rationale: "4.75 + . 303 + . 432 = 0 0 = 0 - 4.75 - 0.303 - 0.432 0 = - 5.485 answer : c"
Answer: c
Problem: what number is 70 more than one - fourth of itself ?
Options: a ) 93 , b ) 225 , c ) 288 , d ) 324 , e ) 336
Rationale: 1 / 4 x + 70 = x that means 70 = 3 / 4 x x = ( 70 * 4 ) / 3 = 280 / 3 = 93 a is the answer .
Answer: a
Problem: 2 / 3 rd of the boys and 3 / 4 th of the girls of a school participate in a function . if the no . of participating students is 550 , out of which 150 are girls , what is the total no . of students in the school ?
Options: a ) 500 , b ) 600 , c ) 800 , d ) 900 , e ) 1200
Rationale: let total number of boys be x and total number of girls be y . y = 400 = > x = 600 and ^ = i 50 = > y = 200 now , x + y = 800 c
Answer: c
Problem: length of a rectangular plot is 30 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 46 m , b ) 60 m , c ) 65 m , d ) 78 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 30 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 30 ) + x ] = 200 2 x + 30 = 100 2 x = 70 x = 35 . hence , length = x + 30 = 65 m c"
Answer: c
Problem: a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 5 hours , then the distance covered at 40 kmph is
Options: a ) 130 km , b ) 120 km , c ) 100 km , d ) 140 km , e ) none of these
Rationale: "let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 5 or , x / 40 + ( 250 - x ) / 60 = 5 or , ( 3 x + 500 - 2 x ) / / 120 = 5 or 500 + x = 600 x = 100 answer : c"
Answer: c
Problem: how many litres of pure acid are there in 5 litres of a 30 % solution
Options: a ) 1.5 , b ) 1.6 , c ) 1.7 , d ) 1.8 , e ) 1.9
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 5 * 30 / 100 = 1.5 answer : option a
Answer: a
Problem: in a college students can play cricket or basketball . 500 play cricket . 220 played both and 600 played basketball . what is the total strength of college ?
Options: a ) 800 , b ) 880 , c ) 920 , d ) 950 , e ) 980
Rationale: p ( c ) = 500 p ( b ) = 600 p ( c n b ) = 220 p ( c u b ) = p ( c ) + p ( b ) - p ( c n b ) = 500 + 600 - 220 = 880 answer : b
Answer: b
Problem: if an average hard drive had a capacity of 0.2 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 5122 , c ) 768 , d ) 2048 , e ) 1536
Rationale: "0.2 * 2 ^ 10 = 0.2 * 1024 = 204.8 the answer is d ."
Answer: d
Problem: the cricket team of 11 members is 24 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28
Rationale: "let the average age of the whole team be x years . 11 x - ( 24 + 27 ) = 9 ( x - 1 ) = > 11 x - 9 x = 42 = > 2 x = 42 = > x = 21 . so , average age of the team is 21 years . a"
Answer: a
Problem: what is the least number . which should be added to 0.0320 to make it a perfect square ?
Options: a ) 0.0005 , b ) 0.0004 , c ) 0.0006 , d ) 0.0002 , e ) 0.0001
Rationale: 0.0320 + 0.0004 = 0.0324 ( 0.18 ) ^ 2 answer : b
Answer: b
Problem: a 21 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 6 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 21 = 6 answer : b"
Answer: b
Problem: a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 340 . how much does c have ?
Options: a ) 50 , b ) 40 , c ) 267 , d ) 29 , e ) 27
Rationale: "a + b + c = 500 a + c = 200 b + c = 340 - - - - - - - - - - - - - - a + b + 2 c = 540 a + b + c = 500 - - - - - - - - - - - - - - - - c = 40 answer : b"
Answer: b
Problem: light glows for every 15 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 381 , b ) 332 , c ) 383 , d ) 334 , e ) 385
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 13 = 331 . so total 332 times light ll glow answer : b"
Answer: b
Problem: the average age of 29 students in a group is 15 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 ) 29 , d ) 53 , e ) 57
Rationale: age of the teacher = ( 29 * 16 - 29 * 15 ) = 29 years . answer : c
Answer: c
Problem: find the perimeter of a triangle with sides measuring 5 centimeters , 20 centimeters and 30 centimeters .
Options: a ) 30 cm , b ) 40 cm , c ) 50 cm , d ) 55 cm , e ) 60 cm
Rationale: "perimeter of triangle = a + b + c perimeter = 5 cm + 20 cm + 30 cm = 55 cm answer : d ."
Answer: d
Problem: in may mrs lee ' s earnings were 30 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 34 , b ) 67 , c ) 85 , d ) 25 , e ) 38
Rationale: "lets say the family income is 100 in may , lee earned 30 family income is 70 in june , lee earned 20 % more than may , so it is ( 30 + 20 * 30 / 100 = 36 ) family income is same 70 in june lee ' s income percent is 36 * 100 / 106 ~ 34 ans is a"
Answer: a
Problem: a and b invests rs . 6000 and rs . 9000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 99 , b ) 82 : 31 , c ) 24 : 45 , d ) 34 : 89 , e ) 35 : 21
Rationale: "a : b ( 6000 * 4 ) + ( 3000 * 8 ) : ( 9000 * 6 ) + ( 6000 * 6 ) 48000 : 90000 24 : 45 answer : c"
Answer: c
Problem: what is the remainder when 8 ^ 1 + 8 ^ 2 + 8 ^ 3 + . . . + 8 ^ 9 is divided by 8 ?
Options: a ) 4 , b ) 0 , c ) 2 , d ) 5 , e ) none of the above
Rationale: "notice that in the brackets we have the sum of 9 even multiples of 8 , which yields remainder of 0 upon division by 8 . answer : b"
Answer: b
Problem: if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 2 ] ] ?
Options: a ) 3 , b ) 9 , c ) 12 , d ) 19 , e ) 25
Rationale: these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 2 ] ] = 2 ^ 2 + 2 * 2 + 4 = 12 . option c
Answer: c
Problem: the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 13 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 11.81 % , e ) 11.50 %
Rationale: 13 = 1.1 * x x = 11.81 % answer d )
Answer: d
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 62000 ?
Options: a ) 81000 , b ) 78468.75 , c ) 81008 , d ) 81066 , e ) 81022
Rationale: "62000 * 9 / 8 * 9 / 8 = 78468.75 answer : b"
Answer: b
Problem: if p ( a ) = 2 / 15 , p ( b ) = 7 / 15 , and p ( a â ˆ ª b ) = 16 / 15 find p ( a | b )
Options: a ) 1 / 2 , b ) 16 / 7 , c ) 3 / 2 , d ) 4 / 5 , e ) 4 / 7
Rationale: "p ( a | b ) = p ( a â ˆ ª b ) / p ( b ) p ( a | b ) = ( 16 / 15 ) / ( 7 / 15 ) = 16 / 7 . b"
Answer: b
Problem: tanks m and b are each in the shape of a right circular cylinder . the interior of tank m has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank m is what percent of the capacity of tank b ?
Options: a ) 75 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: b . for m , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi m / b = 160 pi / 200 pi = 0.8
Answer: b
Problem: in a class , 20 % of the students were absent for an exam . 30 % failed by 20 marks and 10 % just passed . find the average score of the class if the remaining students scored an average of 65 marks and the cut off for passing the exam is 40 .
Options: a ) 36 , b ) 302 , c ) 272 , d ) 292 , e ) 271
Rationale: explanation : let total students be 100 . hence , marks of 20 students is 0 as they were absent . 30 students scored 20 marks ( as they failed by 20 marks ) 10 students scored 40 marks ( just passed ) 40 students scored 65 marks ( average of 65 ) therefore , average score of the class is : ( 0 + 600 + 400 + 2600 ) / 100 = 3600 / 100 = 36 answer : a
Answer: a
Problem: a library has an average of 510 visitors on sundays and 240 on other days . the avearge number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 150 , b ) 225 , c ) 285 , d ) 315 , e ) 374
Rationale: "since the month begin with sunday , so there will be five sundays in the month required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 answer is c"
Answer: c
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 40 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 85 , d ) 95 , e ) 60
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 40 = > 20 = x - 40 = > x = 20 + 40 = 60 answer is e ."
Answer: e
Problem: how long does a train 110 m long traveling at 72 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 16.5 , b ) 16.0 , c ) 16.4 , d ) 14 , e ) 16.1
Rationale: "d = 110 + 170 = 280 m s = 72 * 5 / 18 = 20 t = 280 * 1 / 20 = 14 sec answer : d"
Answer: d
Problem: find large number from below question the difference of two numbers is 250 . on dividing the larger number by the smaller , we get 5 as quotient and the 14 as remainder
Options: a ) 120 , b ) 135 , c ) 140 , d ) 309 , e ) 369
Rationale: "let the smaller number be x . then larger number = ( x + 250 ) . x + 250 = 5 x + 14 4 x = 236 x = 59 large number = 59 + 250 = 309 d"
Answer: d
Problem: what is the probability of drawn an ace or a space or both from a dew of cards .
Options: a ) 14 / 52 , b ) 15 / 52 , c ) 16 / 52 , d ) 17 / 52 , e ) 18 / 52
Rationale: "there are 13 spades in a standard deck of cards . there are four aces in a standard deck of cards . one of the aces is a spade . so , 13 + 4 - 1 = 16 spades or aces to choose from . since we have a total of 52 cards , the probability of selecting an ace or a spade is 16 / 52 answer : c"
Answer: c
Problem: the water level in a reservoir has been dropping at the rate of 14 inches per day . exactly 4 days ago , the water level was at w inches . what will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same ?
Options: a ) w − 126 , b ) w − 112 , c ) w − 14 , d ) w + 14 , e ) w + 126
Rationale: "drop = 14 inches / day 4 days ago = w , means now it ' s equal w - 56 and in 4 days = w - 56 - 56 = w - 112 answer b"
Answer: b
Problem: thirty percent of the women in a college class are science majors , and the non - science majors make up 80 % of the class . what percentage of the men are non - science majors if 40 % of the class are men ?
Options: a ) 2 % , b ) 5 % , c ) 28 % , d ) 30 % , e ) 95 %
Rationale: "3 / k + 2 / m = 6 / t assuming total # is 100 : [ science - women ] will have - 0.3 * 60 = 18 [ non - science - women ] will have - 42 [ science - men ] will have = 20 - 18 = 2 [ non - science - men ] will have - 38 s 0 38 / 40 * 100 = 95 % answer - e"
Answer: e
Problem: an amount of rs . 1000 is to be distributed amongst p , q , r and s such that “ p ” gets twice as that of “ q ” and “ s ” gets 4 times as that of “ r ” . if “ q ” and “ r ” are to receive equal amount , what is the difference between the amounts received by s and p ?
Options: a ) 2378 , b ) 2697 , c ) 250 , d ) 5000 , e ) 6971
Rationale: explanation : we have , p = 2 q & s = 4 r further q = r & p + q + r + s = 1,000 thus we get , 2 q + q + q + 4 q = 1,000 8 q = 1,000 or q = rs . 125 thus , r = rs . 125 , p = 250 & s = rs . 500 hence , the required difference = ( s – p ) = ( 500 – 250 ) = rs . 250 answer : c
Answer: c
Problem: a certain galaxy is known to comprise approximately 4 x 10 ^ 10 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 8,000 , d ) 12,000 , e ) 80,000
Rationale: "total no . of stars on galaxy = 4 * 10 ^ 10 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 4 * 10 ^ 10 / 50 * 10 ^ 6 = 40 * 10 ^ 2 / 5 = 800 therefore answer is a"
Answer: a
Problem: ajay can walk 6 km in 1 hour . in how many hours he can walk 45 km ?
Options: a ) 5 hrs , b ) 10 hrs , c ) 7.5 hrs , d ) 20 hrs , e ) 30 hrs
Rationale: "1 hour he walk 6 km he walk 45 km in = 45 / 6 * 1 = 7.5 hours answer is c"
Answer: c
Problem: a man sells a car to his friend at 13 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 21724.14 , b ) rs . 31724.14 , c ) rs . 51724.14 , d ) rs . 61724.14 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 13 % . now s . p = rs . 45000 and loss = 13 % c . p . rs . [ 100 / 87 ã — 45000 ] = rs . 51724.14 . correct option : c"
Answer: c
Problem: n 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b the present age of b is
Options: a ) 22 , b ) 897 , c ) 268 , d ) 20 , e ) 48
Rationale: a + 10 = 2 ( b - 10 ) . . . . . . . . ( 1 ) a = b + 9 . . . . . . . . . ( 2 ) from equations . 1 & 2 we get b = 39 a will be 39 + 9 = 48 years old . answer : e
Answer: e
Problem: rs . 700 is divided among a , b , c so that a receives half as much as b and b half as much as c . then c ' s share is
Options: a ) rs 429 , b ) rs 412 , c ) rs 400 , d ) rs 129 , e ) rs 122
Rationale: "let c = x . then b = x / 2 and a = x / 4 a : b : c = 1 : 2 : 4 . c ' s share rs . [ ( 4 / 7 ) * 700 ) = 400 answer : c"
Answer: c
Problem: if the height of a cone is increased by 130 % then its volume is increased by ?
Options: a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 130
Rationale: "100 % answer : e"
Answer: e
Problem: the decimal 0.1 is how many times greater than the decimal ( 0.01 ) ^ 5 ?
Options: a ) 10 ^ 6 , b ) 10 ^ 7 , c ) 10 ^ 8 , d ) 10 ^ 9 , e ) 10 ^ 10
Rationale: "0.1 = 10 ^ - 1 ( 0.01 ) ^ 5 = ( 10 ^ - 2 ) ^ 5 = 10 ^ - 10 10 ^ 9 * 10 ^ - 10 = 10 ^ - 1 the answer is d ."
Answer: d
Problem: a number exceeds by 15 from its 3 / 8 part . then the number is ?
Options: a ) a ) 32 , b ) b ) 24 , c ) c ) 39 , d ) d ) 40 , e ) e ) 45
Rationale: x – 3 / 8 x = 15 x = 24 answer : b
Answer: b
Problem: yearly subscription to professional magazines cost a company $ 940.00 . to make a 20 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 752 , c ) 656 , d ) 657 , e ) 658
Rationale: "total cost 940 940 * 20 / 100 = 188 so the cut in amount is 188 the less amount to be spend is 940 - 188 = 752 answer : b"
Answer: b
Problem: a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are
Options: a ) 600 , b ) 500 , c ) 400 , d ) 300 , e ) none of these
Rationale: explanation : given that the student got 125 marks and still he failed by 40 marks = > the minimum pass mark = 125 + 40 = 165 given that minimum pass mark = 33 % of the total mark = > total mark × ( 33 / 100 ) = 165 = > total mark = 16500 / 33 = 500 answer : option b
Answer: b
Problem: find the number of shares that can be bought for rs . 8800 if the market value is rs . 20 each with brokerage being 2.5 % .
Options: a ) 429.3 , b ) 270 , c ) 177 , d ) 166 , e ) 111
Rationale: explanation : cost of each share = ( 20 + 2.5 % of 20 ) = rs . 20.5 therefore , number of shares = 8800 / 20.5 = 429.3 answer : a
Answer: a
Problem: 1 / 0.08 is equal to
Options: a ) 25.5 , b ) 2.5 , c ) 12.5 , d ) . 25 , e ) none of these
Rationale: "explanation : 1 / 0.08 = ( 1 * 100 ) / 8 = 100 / 8 = 12.5 option c"
Answer: c
Problem: when a certain number x is divided by 52 , the remainder is 19 . what is the remainder when x is divided by 7 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: when a certain number x is divided by 52 , the remainder is 19 . what is the remainder when x is divided by 7 ? putting a value say x = 19 we get remainder as 19 when divided by 52 . when 19 divided by 7 we get 5 as remainder . d is the answer .
Answer: d
Problem: the simple form of the ratio 5 / 8 : 3 / 2 is ?
Options: a ) 5 : 8 , b ) 5 : 5 , c ) 5 : 9 , d ) 5 : 3 , e ) 5 : 1
Rationale: "5 / 8 : 3 / 2 = 5 : 8 answer : a"
Answer: a
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 50 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.34 , b ) 2.84 , c ) 3.84 , d ) 4.34 , e ) 5
Rationale: "40 * ( 40 / 100 ) = 16 - - - 50 ? - - - 12 = > rs . 3.84 answer : c"
Answer: c
Problem: two unbiased coins are tossed . find the probability of getting two heads ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 3 / 5
Rationale: "s = { hh , ht , th , tt } e = event of getting two heads e = { tt } p ( e ) = 1 / 4 answer is c"
Answer: c
Problem: a student traveled 30 percent of the distance of the trip alone , continued another 20 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 240 , b ) 200 , c ) 160 , d ) 100 , e ) 50
Rationale: "let x be the total length of the trip . 0.3 x + 20 miles + 0.5 x = x 20 miles = 0.2 x x = 100 miles the answer is d ."
Answer: d
Problem: two pipes a and b can fill a tank in 12 and 24 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 6 minutes , b ) 8 minutes , c ) 5 minutes , d ) 2 minutes , e ) 7 minutes
Rationale: "required time = 12 * 24 / 12 + 12 = 12 * 24 / 36 = 24 / 3 = 8 minutes answer : b"
Answer: b
Problem: the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 10 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 35 , c ) 48 , d ) 65 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 67.5 . 4 ) now 67.5 has to be added by x % in order to equal the original price . 67.5 + ( x % ) 67.5 = 100 . solving this eq for x , we get x = 48.1 answer is c ."
Answer: c
Problem: a man whose speed is 3.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 2.0 , b ) 2.5 , c ) 3.0 , d ) 2.1 , e ) 4.0
Rationale: "m = 3.5 s = 1.5 ds = 5 us = 2 as = ( 2 * 5 * 2 ) / 5 = 4 answer : e"
Answer: e
Problem: if a , b , c , and d are integers ; w , x , y , and z are prime numbers ; w < x < y < z ; and ( wa ) ( xb ) ( yc ) ( zd ) = 660 ( wa ) ( xb ) ( yc ) ( zd ) = 660 , what is the value of ( a + b ) – ( c + d ) ?
Options: a ) – 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: 660660 = 2 ^ 2 x 3 ^ 1 x 5 ^ 1 x 11 ^ 1 w < x < y < z = 2 < 3 < 5 < 11 so , can can say - w = 2 x = 3 y = 5 z = 11 hence a = 2 , b = c = d = 1 ( a + b ) – ( c + d ) will be ( 2 + 1 ) – ( 1 + 1 ) = 1 answer will be ( c )
Answer: c
Problem: a man gains 50 % 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 ) 300 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: explanation : let the c . p . = x , then s . p . = ( 150 / 100 ) x = 3 x / 2 new s . p . = 2 ( 3 x / 2 ) = 3 x / 1 profit = 3 x / 1 - x = 3 x / 1 profit % = ( profit / c . p . ) * 100 = > ( 3 x / 1 ) * ( 1 / x ) * 100 = 300 % option b
Answer: b
Problem: | 14 - 5 | - | 8 - 12 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 5 , e ) 4
Rationale: | 14 - 5 | - | 8 - 12 | = | 9 | - | - 4 | = 9 - 4 = 5 correct answer d
Answer: d
Problem: in kaya ' s teacher ' s desk there are 3 pink highlighters , 7 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 15 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 3 + 7 + 5 = 15 . answer is b ."
Answer: b
Problem: the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum w of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just w = 900 : the answer is c ."
Answer: c
Problem: the difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4 % per annum is rs 1 . find the sum
Options: a ) rs 600 , b ) rs 625 , c ) rs 650 , d ) rs 675 , e ) none of these
Rationale: explanation : let the sum be p s . i . = p ∗ 4 ∗ 2 / 100 = 2 p / 25 c . i . = p ( 1 + 4 / 100 ) 2 − p = 676 p / 625 − p = 51 p / 625 as , c . i . - s . i = 1 = > 51 p / 625 − 2 p / 25 = 1 = > 51 p − 50 p / 625 = 1 p = 625 option b
Answer: b
Problem: the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 8.4 . the true discount is
Options: a ) rs . 70 , b ) rs . 36 , c ) rs . 54 , d ) rs . 50 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 8.4 x 100 / 12 x 1 ) = rs . 70 . answer a"
Answer: a
Problem: in a basketball game , tim scored 20 points more than joe , but only half as many points as ken . if the 3 players scored a combined total of 100 points , how many points did tim score ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 45
Rationale: let joe scored point = x then tim scored = x + 20 ken scored = 2 * ( x + 20 ) = 2 x + 40 as given , x + x + 20 + 2 x + 40 = 100 points 4 x + 60 = 100 x = 100 - 60 / 4 = 10 so tim scored = x + 20 i . e ) 10 + 20 = 30 answer : d
Answer: d
Problem: if taxi fares were $ 2.00 for the first 1 / 5 mile and $ 0.60 for each 1 / 5 mile there after , then the taxi fare for a 8 - mile ride was
Options: a ) $ 2.40 , b ) $ 25.20 , c ) $ 25.40 , d ) $ 25.60 , e ) $ 25.50
Rationale: "in 8 miles , initial 1 / 5 mile charge is $ 2 rest of the distance = 8 - ( 1 / 5 ) = 39 / 5 rest of the distance charge = 39 ( 0.6 ) = $ 23.4 ( as the charge is 0.6 for every 1 / 5 mile ) = > total charge for 4 miles = 2 + 23.4 = 25.4 answer is c"
Answer: c
Problem: ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 670 then loss of pyarelal ?
Options: a ) 603 , b ) 703 , c ) 800 , d ) 903 , e ) 1000
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 670 , loss of pyarelal = 670 * 9 x / 10 x = 603 answer : a"
Answer: a
Problem: 40 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 57600 , b ) 44000 , c ) 34936 , d ) 25640 , e ) none
Rationale: "answer ∵ 40 % of p = 23040 ∴ p = ( 23040 x 100 ) / 40 = 57600 correct option : a"
Answer: a
Problem: what distance will be covered by a bus moving at 54 kmph in 30 seconds ?
Options: a ) 287 , b ) 900 , c ) 289 , d ) 276 , e ) 207
Rationale: "54 kmph = 54 * 5 / 18 = 30 mps d = speed * time = 30 * 30 = 900 m . answer : b"
Answer: b
Problem: if ( 1 / 2 ) ^ 22 ( 1 / 81 ) ^ k = 1 / 18 ^ 22 , then k =
Options: a ) 8 , b ) 12 , c ) 16 , d ) 24 , e ) 11
Rationale: i ' m going to focus on denominator only . . ( 2 ^ 22 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 22 ( 2 ^ 22 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 22 ( 2 ^ 22 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 22 hence 4 k = 44 k = 11 answer e i hope it ' s quite clear
Answer: e