regisss/math_qa huggingface dataset:
Problem: a small pool filled only with water will require an additional 600 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 600 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 2000
Rationale: "since pumping in additional 600 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 600 = 0.8 * { total } - - > { total } = 2,000 . answer : e ."
Answer: e
Problem: the compound ratio of 2 : 3 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 4 : 5 , e ) 1 : 4
Rationale: "2 / 3 * 3 / 2 * 4 / 5 = 4 / 5 = 4 : 5 answer : d"
Answer: d
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the numbers is 720 , then the other is :
Options: a ) 8 , b ) 10 , c ) 12 , d ) 4 , e ) 6
Rationale: "other number = ( 12 x 600 ) / 720 = 10 . answer : c"
Answer: c
Problem: david obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) none of these , e ) can not be determined
Rationale: "solution : average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . hence , average = 75 . answer : option c"
Answer: c
Problem: if the ratio of s . i earned on certain amount on same rate is 4 : 5 . what is the ratio of time ?
Options: a ) 1 : 2 , b ) 6 : 9 , c ) 4 : 5 , d ) 2 : 3 , e ) not possible to calculate
Rationale: s . i 1 / s . i 2 = [ ( p * r * t 1 ) / 100 ] / [ ( p * r * t 2 ) / 100 ] 4 / 5 = t 1 / t 2 ratio = 4 : 5 answer c
Answer: c
Problem: dick and jane each saved $ 2,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 4,000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "1990 dick saved = $ 2200 jane saved = $ 1800 ( jane saved $ 200 less than she did the prior year ) jane saved approximately $ 200 / 2000 $ ( 10 % ) less in 1990 answer : a"
Answer: a
Problem: tough and tricky questions : exponents . if 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y , then x + y =
Options: a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 5
Rationale: here is my solution . 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y here rhs 49 ^ x * 27 ^ y = 7 ^ ( 2 x ) * 3 ^ ( 3 y ) equating powers on both sides - - > 3 x - 1 = 2 x , thus x = 1 and 4 y - 3 = 3 y giving y = 3 so , x + y = 4 option : b
Answer: b
Problem: a candidate got 35 % of the votes polled and he lost to his rival by 2250 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 2665 , d ) 2888 , e ) 2661
Rationale: 35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2250 100 % - - - - - - - - - ? = > 7500 answer : a
Answer: a
Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg .
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 3 : 5 , e ) 4 : 5
Rationale: "req = 60 : 90 = 2 : 3 answer b"
Answer: b
Problem: a volume of 11248 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 11248 l can be kept in ( 11248 / 4 ) hemispheres ans . 2812 answer : a"
Answer: a
Problem: b completes a work in 6 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.33 days , b ) 4.33 days , c ) 5.33 days , d ) 6.33 days , e ) 7.33 days
Rationale: "1 / 5 + 1 / 10 = 3 / 10 10 / 3 = 3.33 days answer : a"
Answer: a
Problem: a man can row upstream at 20 kmph and downstream at 28 kmph , and then find the speed of the man in still water ?
Options: a ) 24 , b ) 37 , c ) 30 , d ) 27 , e ) 18
Rationale: "us = 20 ds = 28 m = ( 28 + 20 ) / 2 = 24 answer : a"
Answer: a
Problem: if x and y are integers such that x ^ 2 = 2 y and xy = 256 , then x – y = ?
Options: a ) - 30 , b ) - 24 , c ) - 5 , d ) 5 , e ) 20
Rationale: "here x and y are integers . x ^ 2 = 2 y , xy = 256 . substitute ( x ^ 2 ) / 2 = y in xy = > x ^ 3 = 256 * 2 = > x ^ 3 = 512 . here x ^ 3 is positive , x is also positive . x = 8 then y = 32 . x - y = - 24 so option b is correct"
Answer: b
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 144 km / h , what is the circumference of the tire ?
Options: a ) 2 meters , b ) 6 meters , c ) 5 meters , d ) 3 meters , e ) 7 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 144,000 m : c is the circumference c = 6 meters correct answer b"
Answer: b
Problem: the average of runs of a cricket player of 10 innings was 18 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 16 , c ) 62 , d ) 76 , e ) 17
Rationale: "average after 11 innings = 22 required number of runs = ( 33 * 11 ) - ( 18 * 10 ) = 242 - 180 = 62 . answer : c"
Answer: c
Problem: if a = 105 and a ^ 3 = 21 * 25 * 15 * b , what is the value of b ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 147 , e ) 54
Rationale: "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 15 = 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 2 * 5 ^ 3 * 7 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 2 * 5 ^ 3 * 7 b = 3 * 7 ^ 2 = 3 * 49 = 147 correct answer d ."
Answer: d
Problem: if the difference of two numbers is 3 and the difference of their square is 39 , then the larger number is :
Options: a ) 9 , b ) 2 , c ) 12 , d ) 14 , e ) 8
Rationale: let the numbers be x and y then x 2 - y 2 = 39 and x - y = 3 we get x + y = 13 solving x - y = 3 , x + y = 13 x = 8 , y = 5 larger number 8 answer e
Answer: e
Problem: the ratio of two numbers is 3 : 4 and their sum is 21 . the greater of the two numbers is ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 17 , e ) 19
Rationale: 3 : 4 total parts = 7 = 7 parts - - > 21 ( 7 ã — 3 = 21 ) = 1 part - - - - > 3 ( 1 ã — 3 = 4 ) = the greater of the two number is = 4 = 4 parts - - - - > 12 ( 4 ã — 3 = 12 ) a
Answer: a
Problem: working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 6 x boxes ?
Options: a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 6 minutes , e ) 12 minutes
Rationale: "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 6 x / 5 x * 10 = 12 min ans : e"
Answer: e
Problem: a light flashes every 15 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 600 , c ) 240 , d ) 700 , e ) 750
Rationale: "1 flash = 15 sec for 1 min = 4 flashes so for 1 hour = 4 * 60 = 240 flashes . answer : c"
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 7 seconds . find the length of the train .
Options: a ) 116.67 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 7 = 116.67 meter . answer : a"
Answer: a
Problem: in what time will a train 40 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 1.0 sec , c ) 7.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 40 / 40 = 1.0 sec . answer : b"
Answer: b
Problem: a certain country had a total annual expenditure of $ 1.2 x 10 ^ 12 . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1000 , c ) $ 2000 , d ) $ 3000 , e ) $ 5000
Rationale: "explanation : in scientific notation 240 million is 2.4 x 10 ^ 8 . so the per capita expenditure was : ( $ 1.2 x 10 ^ 12 ) / ( 2.4 x 10 ^ 8 ) = ( $ 1.2 ) / ( 2.4 ) x 10 ^ 12 - 8 = $ 0.5 x 10 ^ 4 = $ 5000 answer : option e"
Answer: e
Problem: in a dairy farm , 50 cows eat 50 bags of husk in 50 days . in how many days one cow will eat one bag of husk ?
Options: a ) 34 days , b ) 40 days , c ) 46 days , d ) 50 days , e ) none of these
Rationale: "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 50 bags 50 1 ] : : 50 : x = > x ∗ 50 ∗ 1 = 50 ∗ 1 ∗ 50 = > x = 50 option d"
Answer: d
Problem: what is the range of all the roots of | x ^ 2 - 1 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 1 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 1 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 2 or x = 1 i guess range is 2 - 1 = 1 d
Answer: d
Problem: one - third of rahul ’ s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 2 , 50000 as total savings , how much has he saved in public provident fund ?
Options: a ) rs . 30,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 100,000 , e ) none
Rationale: explanation let savings in n . s . c and p . p . f . be rs . x and rs . ( 250000 – x ) respectively . then , 1 / 3 x = 1 / 2 ( 250000 - x ) = > x / 3 + x / 2 = 125000 = > 5 x / 6 = 125000 = > x = 125000 x 6 / 5 = 150000 savings in public provident fund = rs . ( 250000 – 150000 ) = rs . 100000 answer d
Answer: d
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 2 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 11 , b ) 20 , c ) 77 , d ) 26 , e ) 12
Rationale: "distance = relative speed * time = ( 2 + 3 ) * 4 = 20 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : b"
Answer: b
Problem: the proportion of water to alcohol in solution a is 4 : 1 and the proportion of water to alcohol in solution b is 3 : 1 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 16.5 % , b ) 18.5 % , c ) 20.5 % , d ) 22.5 % , e ) 24.5 %
Rationale: "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 5 ) ( v / 2 ) + ( 1 / 4 ) ( v / 2 ) = v / 10 + v / 8 = 9 v / 40 . the concentration of alcohol is 9 / 40 = 22.5 % the answer is d ."
Answer: d
Problem: find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm ?
Options: a ) 188 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2
Rationale: "1 / 2 * 20 ( 9 + 6 ) = 150 cm 2 answer : b"
Answer: b
Problem: how many integers between 0 and 1000 do not contain the integer 1
Options: a ) 727 , b ) 728 , c ) 758 , d ) 748 , e ) 792
Rationale: from 1 to 99 = 19 integers having 1 from 101 to 199 = all are having 1 similarly 201 - 299 , 301 - 399 , 401 - 499 , . . . . . so on , will have 19 integers having 1 answer = 1000 - ( 19 * 9 + 99 + 2 ) / / 2 is added for 100 and 1000 = 728 answer : b
Answer: b
Problem: working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 6 days ?
Options: a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: "4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 4 x units in 6 days therefore , we need to get to 4 x / 6 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 6 days . 3 x / 6 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 3 x / 6 y = 3 x / 6 * 24 / x cancel 6 with 24 , and x with x and get - > 12 . answer choice d"
Answer: d
Problem: how many factors of 270 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "prime factors of 810 are 2 ^ 1,3 ^ 4,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 4 + 1 ) ( 1 + 1 ) = 10 since we need odd divisors other than 1 = > 10 - 1 = 9 odd divisors e is the answer"
Answer: e
Problem: a batsman in his 12 th innings makes a score of 65 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 65 ∴ x = 43 answer b"
Answer: b
Problem: what is the unit digit in 7 ^ 105
Options: a ) 7 , b ) 0 , c ) 2 , d ) 3 , e ) 5
Rationale: "explanation : unit digit in 7 ^ 105 = unit digit in [ ( 7 ^ 4 ) 26 x 7 ] but , unit digit in ( 7 ^ 4 ) 26 = 1 unit digit in 7105 = ( 1 x 7 ) = 7 a"
Answer: a
Problem: if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 14 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 14 ) / 10 = ( 54 - 14 ) / 10 = 4 answer : option a"
Answer: a
Problem: when the number 1 y 92355 is exactly divisible by 11 , then the smallest whole number in place of y is ?
Options: a ) 1 , b ) 3 , c ) 7 , d ) 9 , e ) 0
Rationale: the given number = 1 y 92355 sum of the odd places = 5 + 3 + 9 + 1 = 18 sum of the even places = 5 + 2 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 18 - ( 7 + y ) = divisible by 11 11 � y = divisible by 11 . y must be 0 , to make given number divisible by 11 . e
Answer: e
Problem: how many liters of oil at rs . 40 per liter should be mixed with 240 liters of a second variety of oil at rs . 60 per liter so as to get a mixture whose cost is rs . 52 per liter ?
Options: a ) 120 , b ) 150 , c ) 160 , d ) 180 , e ) 200
Rationale: 8 : 12 = 2 : 3 if 240 lrs of the 2 nd variety taken then the 1 st variety should be taken as 160 lr answer c
Answer: c
Problem: if w / x = 1 / 3 and w / y = 2 / 3 , then ( x + y ) / y =
Options: a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 7
Rationale: "ratio 1 : 3 w = x ratio 2 : 3 w = 2 y x = 2 y ( x + y ) / y = ( 2 y + y ) / y = y ( 2 + 1 ) / y = 3 answer is d"
Answer: d
Problem: two trains running in opposite directions cross a man standing on the platform in 25 seconds and 18 seconds respectively and they cross each other in 20 seconds . the ratio of their speeds is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 8 , d ) 2 : 5 , e ) 3 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 25 x meters , and length of the second train = 18 y meters . ( 25 x + 18 y ) / ( x + y ) = 20 = = > 25 x + 18 y = 20 x + 20 y = = > 5 x = 2 y = = > x / y = 2 / 5 answer : option d"
Answer: d
Problem: in how many no . between 100 and 1000 at least one of their digits is 7 ?
Options: a ) 900 , b ) 648 , c ) 720 , d ) 252 , e ) 729
Rationale: "let ' s count the number of occurrences with only one 7 : ( 1 ) 7 xx : 1 * 9 * 9 = 81 ( 2 ) x 7 x : 8 * 1 * 9 = 72 ( 3 ) xx 7 : 8 * 9 * 1 = 72 81 + 72 + 72 = 225 at this point we can already see that the answer must be d since the choice are very dispersed . anyways , let ' s count number of occurrences with two 7 s : ( 1 ) 77 x : 1 * 1 * 9 = 9 ( 2 ) x 77 : 8 * 1 * 1 = 8 ( 3 ) 7 x 7 : 1 * 9 * 1 = 9 9 + 8 + 9 = 26 number 777 is missing . so the total becomes 225 + 26 + 1 = 252 d is the correct answer ."
Answer: d
Problem: the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 150 %
Rationale: "let rate in r = 100 x then p = 75 x g = 100 y p = 90 y thus 75 x = 90 y or x = 1.20 y ans r = 120 y so increase = 20 % answer : b ."
Answer: b
Problem: farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 4000 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 12.5 % , d ) 20.83 % , e ) none
Rationale: "only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 500 / 4000 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 60 ) = 20.833 % and the answer is not there in the options . the correct answer is ( d ) ."
Answer: d
Problem: the s . i . on a certain sum of money for 2 years at 6 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 2197 , b ) 1267 , c ) 3500 , d ) 2267 , e ) 1262
Rationale: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 2 * 6 ) = rs . 3500 answer : c"
Answer: c
Problem: the avg weight of a , b & c is 60 kg . if d joins the group , the avg weight of the group becomes 65 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 64 kg . what is the weight of a ?
Options: a ) 56 , b ) 65 , c ) 75 , d ) 89 , e ) 87
Rationale: "a + b + c = 3 * 60 = 180 a + b + c + d = 4 * 65 = 260 - - - - ( i ) so , d = 80 & e = 80 + 3 = 83 b + c + d + e = 64 * 4 = 256 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 260 – 256 = 4 a = e + 4 = 83 + 4 = 87 answer : e"
Answer: e
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 66 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.91 , b ) 2.91 , c ) 4.91 , d ) 3.91 , e ) 5.91
Rationale: "40 * ( 40 / 100 ) = 16 - - - 66 ? - - - 12 = > rs . 2.91 answer : b"
Answer: b
Problem: a car travels uphill at 30 km / hr and downhill at 80 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 38 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 80 = 5 / 8 ; avg speed = 150 / ( 10 / 3 + 5 / 8 ) = 38 kmph answer : a"
Answer: a
Problem: convert the 8 / 26 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.1 kmph . , e ) 1.9 kmph .
Rationale: "8 / 26 m / s = 8 / 26 * 18 / 5 = 1 ( 1 / 10 ) = 1.1 kmph . answer : d"
Answer: d
Problem: jane and thomas are among the 7 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ?
Options: a ) 30 , b ) 45 , c ) 55 , d ) 65 , e ) 70
Rationale: "the total number of ways to choose 4 people from 7 is 7 c 4 = 35 . the number of committees without jane or thomas is 5 c 4 = 5 . there are 35 - 5 = 30 possible committees which include jane and / or thomas . the answer is a ."
Answer: a
Problem: jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jack and jill will make a basket but sandy will miss ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 48 , d ) 1 / 96 , e ) 1 / 168
Rationale: "the probability that jack and jill will make a basket but sandy will miss is 1 / 6 * 1 / 7 * 7 / 8 = 1 / 48 . the answer is c ."
Answer: c
Problem: you hold some gold in a vault as an investment . over the past year the price of gold increases by 42 % . in order to keep your gold in the vault , you must pay 4 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 38 % , b ) 46 % , c ) 47.68 % , d ) 44.32 % , e ) 36.32 %
Rationale: "( 100 % + 42 % ) * ( 100 % - 4 % ) = 1.42 * 0.96 = 136.32 % an increase of 36.32 % your gold holdings have increased in value by 36.32 % . the answer is e"
Answer: e
Problem: calculate how many seconds it eill take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 2 , 5 , 8 and 11 seconds . ?
Options: a ) 440 , b ) 420 , c ) 410 , d ) 442 , e ) 422
Rationale: "lcm of 2 , 5 , 8 and 11 is 440 lcm = 440 answer : a"
Answer: a
Problem: the sum of the ages of 5 children born at the intervals of 1 year each is 50 years . what is the age of the youngest child ?
Options: a ) 22 , b ) 8 , c ) 10 , d ) 99 , e ) 38
Rationale: "let x = the youngest child . each of the other four children will then be x + 1 , x + 2 , x + 3 , x + 4 . we know that the sum of their ages is 50 . so , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) = 50 therefore the youngest child is 8 years old answer : b"
Answer: b
Problem: if 15 machine can finish a job in 36 days , then how many more machines would be needed to finish the job in one - fourth less time ?
Options: a ) a . 5 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 15 machines ( identical ones , i assume ) work simultaneously for 36 days , they will do a total of 15 * 36 machine - days of work . so the job requires 15 * 36 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 27 days . so we ' ll need 15 * 36 / 27 = 20 machines , or 5 additional machines . a"
Answer: a
Problem: if a randomly selected non - negative single digit integer is added to { 2 , 3 , 6 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6
Rationale: "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 6 ) / 2 = 4.5 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c ."
Answer: c
Problem: in what time will a train 140 m long cross an electric pole , it its speed be 108 km / hr ?
Options: a ) 2.5 , b ) 4.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 108 * 5 / 18 = 30 m / sec time taken = 140 / 30 = 4.7 sec . answer : b"
Answer: b
Problem: a small water pump would take 2 hours to fill an empty tank . a larger pump would take 1 / 3 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
Options: a ) 3 / 7 , b ) 2 / 7 , c ) 1 / 4 , d ) 2 / 3 , e ) 5 / 7
Rationale: "rate of the small pump is 1 / 2 tank / hour rate of the larger pump is 1 / ( 1 / 3 ) or 3 tank / hour ; combined rate of the two pumps is 1 / 2 + 3 = 7 / 2 tank / hour , together they will fill the empty tank in 1 / ( 7 / 2 ) = 2 / 7 hours ( time = job / rate ) . answer : b"
Answer: b
Problem: in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 45 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 31 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 45 % means total women in company 55 % ( assume total people in company 100 % ) no of men employees attended picnic = 45 x ( 20 / 100 ) = 9 no of women employees attend picnic = 55 x ( 40 / 100 ) = 22 total percentage of employees attend the picnic = 9 + 22 = 31 % answer : a"
Answer: a
Problem: the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 5 : 4 : 2 . someone removes 7 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 7 pounds of clothes doubles the ratio of books to clothes , then 7 pounds represents half the weight of the clothes . 2 k = 7 pounds and then k = 3.5 pounds . the electronics weigh 2 ( 3.5 ) = 7 pounds . the answer is b ."
Answer: b
Problem: martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 17.20 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 17.2 0.4 x = 1.2 = > x = 3 discounted tickets = 10 - x = 7 ans : e"
Answer: e
Problem: if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 10 , what is the value of x ?
Options: a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4
Rationale: "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . c"
Answer: c
Problem: if a # b = ab – b + b ^ 2 , then 2 # 3 =
Options: a ) 2 , b ) 8 , c ) 12 , d ) 21 , e ) 35
Rationale: "solution - simply substitute 2 and 3 in equation in the place of a and b respectively . 2 # 3 = 2 * 3 - 3 + 3 ^ 2 = 6 - 3 + 9 = 12 . ans c"
Answer: c
Problem: andy solves problems 70 to 125 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 56 , b ) 52 , c ) 51 , d ) 50 , e ) 49
Rationale: 125 - 70 + 1 = 56 ' a ' is the answer
Answer: a
Problem: share rs . 4200 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400
Rationale: "amount received by sanjay . 4 / 12 x 4200 = 1400 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1400 . e"
Answer: e
Problem: if k is a non - negative integer and 21 ^ k is a divisor of 435,961 then 7 ^ k - k ^ 7 =
Options: a ) 0 , b ) 1 , c ) 42 , d ) 118 , e ) 242
Rationale: "4 + 3 + 5 + 9 + 6 + 1 = 28 , so this number is not divisible by 3 and thus not divisible by 21 . therefore , k = 0 7 ^ k - k ^ 7 = 1 - 0 = 1 the answer is b ."
Answer: b
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 60 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 36 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 60 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 60 / 10 = 6 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 6 = 36 kms . . . answer - b"
Answer: b
Problem: a train 90 meters long completely crosses a 200 meters long bridge in 36 seconds . what is the speed of the train is ?
Options: a ) 29 , b ) 40 , c ) 25 , d ) 66 , e ) 09
Rationale: "s = ( 90 + 200 ) / 36 = 290 / 36 * 18 / 5 = 29 answer : a"
Answer: a
Problem: a circular plate with a diameter of 10 inches is kept on another plate of 12 inches diameter . what fraction of the big plate ' s surface is not covered by the small plate ?
Options: a ) 11 / 36
b ) 23 / 10
c ) 5 / 14
d ) 22 / 11
e ) 3 / 4
Rationale: the questions asks us to find the surface which is not covered by the plate i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the big plate = pi * r ^ 2 , where r = 6 = > pi * 36 area of the small plate = pi * 25 surface not covered by the plate = pi * 36 - pi * 25 = pi * 11 fraction of big plate ' s surface is not covered by small plate = pi * 11 / total area of the big plate = > pi * 11 / pi * 36 answer a
Answer: a
Problem: a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days b will the work get over ?
Options: a ) 60 , b ) 70 , c ) b = 75 , d ) b = 80 , e ) 100
Rationale: "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
Answer: c
Problem: if the cost price is 25 % of selling price . then what is the profit percent
Options: a ) 238 , b ) 278 , c ) 300 , d ) 166 , e ) 129
Rationale: "explanation : let the s . p = 100 then c . p . = 25 profit = 75 profit % = ( 75 / 25 ) * 100 = 300 % answer : c"
Answer: c
Problem: a man rows downstream 32 km and 14 km upstream . if he takes 6 hours to cover each distance , then the velocity ( in kmph ) of the current is :
Options: a ) 1.5 kmph , b ) 1.75 kmph , c ) 2 kmph , d ) 3 kmph , e ) none
Rationale: sol . rate downstream = [ 32 / 6 ] kmph ; rate upstream = [ 14 / 6 ] kmph . ∴ velocity of current = 1 / 2 [ 32 / 6 - 14 / 6 ] kmph = 3 / 2 kmph = 1.5 kmph . answer a
Answer: a
Problem: the average weight of 10 person ' s increases by 4 kg when a new person comes in place of one of them weighing 70 kg . what is the weight of the new person ?
Options: a ) 85 , b ) 86.5 , c ) 90 , d ) 88.5 , e ) 110
Rationale: "total increase in weight = 10 x 4 = 40 if x is the weight of the new person , total increase in weight = x − 70 = > 40 = x - 70 = > x = 40 + 70 = 110 answer : e"
Answer: e
Problem: the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 20 = rs . 4 per kg . rice can bought now at = 100 / 4 = 25 kg . answer : option c"
Answer: c
Problem: a boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream . if the speed of the boat in still water is 10 mph , the speed of the stream is
Options: a ) 2 mph , b ) 2.5 mph , c ) 3 mph , d ) 4 mph , e ) none
Rationale: "solution speed downstreams = ( 10 + x ) mph . speed upstreams = ( 10 - x ) mph . = 18 kmph . 36 / ( 10 - x ) - 36 / ( 10 + x ) = 90 / 60 = 72 x × 60 = 90 ( 100 - x ² ) x ² + 48 x + 100 = 0 . x = 2 mph . answer a"
Answer: a
Problem: if 2 + 3 = 10 ; 2 + 5 = 27 ; 2 + 7 = 53 then 2 + 11 = ?
Options: a ) 124 , b ) 129 , c ) 128 , d ) 125 , e ) 120
Rationale: "2 ^ 0 + 3 ^ 2 = 1 + 9 = 10 2 ^ 1 + 5 ^ 2 = 2 + 25 = 27 2 ^ 2 + 7 ^ 2 = 4 + 49 = 53 and 2 ^ 3 + 11 ^ 2 = 8 + 121 = 129 answer : b"
Answer: b
Problem: if the sides of a cube are in the ratio 7 : 3 . what is the ratio of their diagonals ?
Options: a ) 9 : 4 , b ) 8 : 4 , c ) 7 : 4 , d ) 7 : 3 , e ) 6 : 4
Rationale: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 7 : 3 d 1 : d 2 = 7 : 3 where √ 3 cancelled both side answer : d"
Answer: d
Problem: the sum of two consecutive integers is 31 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 15 , 16 , d ) 1 , 2 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 31 2 n + 1 = 31 2 n = 30 n = 15 answer : c"
Answer: c
Problem: the average of 4 consecutive odd numbers is 24 . find the largest number
Options: a ) 25 , b ) 27 , c ) 29 , d ) 31 , e ) 32
Rationale: explanation : let the numbers are x , x + 2 , x + 4 , x + 6 , then = > x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) / 4 = 24 = > 4 x + 12 ) / 4 = 24 = > x + 3 = 24 = > x = 21 so largest number is 21 + 6 = 27 option b
Answer: b
Problem: what is the smallest integer that is multiple of 8,7 and 20
Options: a ) 141 , b ) 180 , c ) 130 , d ) 122 , e ) 280
Rationale: correct answer : e it is the lcm of 8,7 and 20 which is 280
Answer: e
Problem: by travelling at 40 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 20 kmph , b ) 17 kmph , c ) 15 kmph , d ) 14 kmph , e ) 13 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 40 * 3 x = 120 x km he covered 2 / 3 * 120 x = 80 x km in 1 / 3 * 3 x = x hours so , the remaining 40 x km , he has to cover in 2 x hours . required speed = 40 x / 2 x = 20 kmph . answer : a"
Answer: a
Problem: the present population of a town is 260 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 226 , e ) 286
Rationale: "p = 260 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 260 * ( 1 + 10 / 100 ) = 260 * ( 11 / 10 ) = 286 answer is e"
Answer: e
Problem: 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 . 3025 . , the number of the member is the group is :
Options: a ) 55 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 30.25 x 100 ) paise = 3025 paise . number of members = square root of 3025 = 55 . answer : option a"
Answer: a
Problem: in 1996 , the property tax of a community is increased by 6 % over the 1995 tax . an additional surcharge of $ 200 is also added for a special project . if the petersons ' 1996 tax totals $ 2108 , find their property tax for the year 1995
Options: a ) 1600 , b ) 1800 , c ) 1900 , d ) 2000 , e ) 2500
Rationale: tax for the year 1996 = 2108 surcharge add : 200 ie 2000 - 200 = 1800 1800 * 6 % = 108 + 2000 = 2108 so the answer is b
Answer: b
Problem: in an election , candidate douglas won 64 percent of the total vote in counties x and y . he won 76 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 10 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 76 % voted means 76 * 200 = 152 votes combined for xy has 300 voters and voted 64 % so total votes = 192 balance votes = 192 - 152 = 40 as y has 100 voters so 40 votes means 40 % of votes required ans e"
Answer: e
Problem: how many seconds will a 900 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 287 , b ) 288 , c ) 500 , d ) 400 , e ) 121
Rationale: "let length of tunnel is x meter distance = 900 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 900 + x = ( 65 / 3 ) * 60 900 + x = 20 * 65 = 1300 x = 1300 - 900 = 400 meters answer : d"
Answer: d
Problem: 16 * 16 * 16 * 16 * 16 = 4 ^ ?
Options: a ) 8 , b ) 6 , c ) 10 , d ) 4 , e ) 3
Rationale: 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 = 4 ^ ( 2 + 2 + 2 + 2 + 2 ) = 4 ^ 10 answer : 10 option : c
Answer: c
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.82 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.82 9.9 - 45 x + 36 x = 8.82 9 x = 1.08 x = 0.12 the answer is d ."
Answer: d
Problem: when average age of 25 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 24 , c ) 21 , d ) 23 , e ) 25
Rationale: "average of 25 numbers = 0 . sum of 25 numbers ( 0 x 25 ) = 0 . it is quite possible that 24 of these numbers may be positive and if their sum is a then 25 th number is ( - a ) answer is 24 ( b )"
Answer: b
Problem: the length of the bridge , which a train 130 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 200 meters , b ) 225 meters , c ) 245 meters , d ) 250 meters , e ) 300 meters
Rationale: "given , length of the train = 130 meters speed of the train = 45 km / hr = 45 * 518 m / sec = 252 m / sec time = 30 secs let the length of the bridge be x meters . the distance travelled by the train while crossing the bridge will be sum of the length of train and length of the bridge = ( x + 130 ) meters so , 252 = x + 13030 = 30 * 25 = 2 x + 260 = 750 - 260 = 2 x = 490 = 2 x = x = 245 meters . answer c"
Answer: c
Problem: sakshi can do a piece of work in 10 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 8 , b ) 16 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 10 : x ⇒ x = ( 10 x 4 / 5 ) ⇒ x = 8 days . hence , tanya takes 8 days is complete the work . answer a"
Answer: a
Problem: there were two candidates in an election . winner candidate received 65 % of votes and won the election by 300 votes . find the number of votes casted to the winning candidate ?
Options: a ) 228 , b ) 744 , c ) 255 , d ) 650 , e ) 231
Rationale: "w = 65 % l = 35 % 65 % - 35 % = 30 % 30 % - - - - - - - - 300 65 % - - - - - - - - ? = > 650 answer : d"
Answer: d
Problem: a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 6.00 ?
Options: a ) 72 , b ) 60 , c ) 90 , d ) 120 , e ) 240
Rationale: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 6 ( 1 / 12 ) * x = 6 x = 72 answer : a"
Answer: a
Problem: in a recent election , geoff received 1 percent of the 6,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3,571 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 54 , c ) 56 , d ) 60 , e ) 60.5
Rationale: "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 60 votes he needs 3571 more votes so : 60 + 3571 = 3631 now what ' s the problem wants ? ? a x % . . . . . . . . 3631 is what % of total votes 6000 . . . . . . . . translating : 3631 = x / 100 * 6000 - - - > x = 60.51666666 x = 60.5 % . . . . . . . . . . e"
Answer: e
Problem: what is the value of 3 x ^ 2 − 1.8 x + 0.4 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.4 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.4 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.4 = 0 + 0.4 = 0.4 answer : c"
Answer: c
Problem: 2500 - ( 1002 / 20.04 ) = ?
Options: a ) 2984 , b ) 2983 , c ) 2982 , d ) 2450 , e ) none of these
Rationale: "2500 - 50 = 2450 answer : d"
Answer: d
Problem: what is the probability of getting equilateral triangles from the vertices of regular hexagon ?
Options: a ) 1 / 10 , b ) 2 / 10 , c ) 3 / 10 , d ) 4 / 10 , e ) 5 / 10
Rationale: total no . of triangles that can b made with the vetices hexagon = 6 c 3 = 20 no . of possible outcomes i . e . no . of equality triangles = 2 . . ' . probability = 2 / 20 = 1 / 10 answer : a
Answer: a
Problem: solomon taken a loan rs . 15000 / - from co - operative society with an interest @ 11.5 % per month . at the same time he deposited rs . 10000 / - as fixed deposit with an interest @ 9.5 % per month . after one week sam asked the manager to calculate the interest to be paid . what is the interest amount for 7 days ?
Options: a ) a ) 165 , b ) b ) 220 , c ) c ) 310 , d ) d ) 185 , e ) e ) 181
Rationale: loan amount : rs . 15000 / - @ 11.5 % interest per month = 15000 / - * 11.5 % = rs . 1725 interest for one day = 1725 / 30 = 57.50 interest for 7 days is = 57.50 * 7 = 403 fd amount is = rs . 10000 / - @ 9.5 % interest per month = 10000 * 9.5 % = 950 / - interest for 7 days = 950 / 30 * 7 = 222 interest amount to be paid by solomon = 403 - 222 = 181 / - for 7 days answer is e
Answer: e
Problem: the sum of the first 50 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 50 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 5000 + 2500 = 7500 b is the answer ."
Answer: b
Problem: johnny makes $ 2.35 per hour at his work . if he works 5 hours , how much money will he earn ?
Options: a ) $ 30 , b ) $ 54 , c ) $ 28.50 , d ) $ 12 , e ) $ 11.75
Rationale: 2.35 * 5 = 11.75 . answer is e .
Answer: e
Problem: a and b together can plough a field in 10 hours but by himself a requires 15 hours . how long would b take to plough the same field ?
Options: a ) 10 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: if a and b together can do a piece of work in x days and a alone can do the same work in y days , then b alone can do the same work in x y / y – x days . therefore , the no . of hours required by b = 10 × 15 / 15 – 10 = 150 / 5 = 30 hours . answer : c
Answer: c
Problem: the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 576 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 36 . , d ) 44 . , e ) 46 .
Rationale: "let the width = x x * 4 x = 576 x ^ 2 = 144 x = 12 length = 4 * 12 = 48 difference = 48 - 12 = 36 c is the answer"
Answer: c
Problem: if two girls starting from same point , walking in the opposite directions with 7 km / hr and 3 km / hr as average speeds respectively . then the distance between them after 12 hours is ?
Options: a ) 120 , b ) 121 , c ) 122 , d ) 123 , e ) 124
Rationale: explanation : total distance = distance traveled by person a + distance traveled by person b = ( 7 ã — 12 ) + ( 3 ã — 12 ) = 84 + 36 = 120 km answer : a
Answer: a
Problem: two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 7 days ?
Options: a ) 2 / 5 , b ) 7 / 18 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 6
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 7 days = 7 ( 1 / 18 ) = 7 / 18 . answer b"
Answer: b
Problem: how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 32 percent alcohol ?
Options: a ) 7 / 2 , b ) 5 , c ) 20 / 3 , d ) 8 , e ) 300 / 17
Rationale: "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 32 % of ( 100 + x ) or 20 + x = ( 100 + x ) 8 / 25 500 + 25 x = 800 + 8 x 17 x = 300 x = 300 / 17 ans : e"
Answer: e
Problem: 24 men working 8 hours a day can finish a work in 10 days . working at the rate of 10 hours a day , the number of men required to finish the same work in 6 days is
Options: a ) 30 , b ) 36 , c ) 34 , d ) 32 , e ) none of these
Rationale: m 1 × d 1 × t 1 × w 2 = m 2 × d 2 × t 2 × w 1 24 × 10 × 8 × 1 = m 2 × 6 × 10 × 1 ⇒ m 2 = 24 × 10 × 8 / 6 × 10 = 32 men answer d
Answer: d