regisss/math_qa huggingface dataset:
Problem: what is the range of all the roots of | x ^ 2 - 5 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 5 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 5 = 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 = 5 or x = 1 i guess range is 5 - 1 = 4 a"
Answer: a
Problem: a man can swim in still water at 15 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 3.9 , b ) 5 , c ) 5.3 , d ) 1.5 , e ) 5.2
Rationale: "m = 15 s = x ds = 15 + x us = 15 - x 15 + x = ( 15 - x ) 2 15 + x = 30 - 2 x 3 x = 15 x = 5 answer : b"
Answer: b
Problem: there are 134 toys coloured red and white in a box . two red toys are removed from the lot and now there are twice as many red ones as white ones . how many of red colour toys are there now ?
Options: a ) 76 , b ) 86 , c ) 90 , d ) 88 , e ) 78
Rationale: r + w = 134 two red toys are removed from the lot and now there are twice red ones as white ones r - 2 = 2 w sub 1 st one we get 134 - w - 2 = 2 w 132 = 3 w w = 44 r = 88 actually red will be 90 now 88 answer : d
Answer: d
Problem: 2224 × 9997 = ?
Options: a ) 22244428 , b ) 22255538 , c ) 22233328 , d ) 22266628 , e ) 22233327
Rationale: "c 22233328 2224 × 9997 = 2224 × ( 10000 - 3 ) = 2224 × 10000 - 2224 × 3 = 22240000 - 6672 = 22233328"
Answer: c
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 340 m long platform ?
Options: a ) 19 , b ) 27 , c ) 29 , d ) 46 , e ) 28
Rationale: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 340 ) / 36 * 5 / 18 = 46 min . answer : d"
Answer: d
Problem: a shopkeeper sells 20 % of his stock at 20 % profit ans sells the remaining at a loss of 10 % . he incurred an overall loss of rs . 500 . find the total worth of the stock ?
Options: a ) 13500 , b ) 12000 , c ) 12500 , d ) 15000 , e ) 15500
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 6 / 5 = 6 x / 25 the sp of 80 % of the stock = 4 / 5 * x * 0.9 = 24 x / 25 total sp = 6 x / 25 + 18 x / 25 = 49 x / 50 overall loss = x - 24 x / 50 = x / 25 x / 25 = 500 = > x = 12500 answer : c"
Answer: c
Problem: triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 25 , what is the measure of side xy ?
Options: a ) 10 , b ) 4 √ 2 , c ) 8 , d ) 8 √ 2 , e ) can not be determined from the information provided
Rationale: "ans a . . 10 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 25 or yz = 5 * \ sqrt { 2 } . . therefore hyp = xy = 10"
Answer: a
Problem: a pharmaceutical company received $ 2 million in royalties on the first $ 12 ; million in sales of generic equivalent of one of its products and then $ 4 million in royalties on the next $ 48 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 12 million in sales to the next $ 48 million in sales ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 50 % , e ) 55 %
Rationale: change in ratio of royalties to sales = 2 / 12 - 4 / 48 = 1 / 12 % decrease = ( 1 / 12 ) / ( 2 / 12 ) * 100 = 50 % ( approx ) answer : d )
Answer: d
Problem: an ore contains 25 % of an alloy that has 90 % iron . other than this , in remaining 75 % of the ore , there is no iron . how many kgs of the ore are needed to obtain 60 kg . of pure iron . ?
Options: a ) 266.69 , b ) 266.67 , c ) 266.66 , d ) 263.66 , e ) 266.61
Rationale: "explanation : let us take 100 x kgs of ore . now it contains 25 x kgs of alloy and it contains 90 % ( 25 x ) kgs of iron . 90 % ( 25 x ) = 60 kg ⇒ x = 60 × 10090 × 12560 × 10090 × 125 = 8383 so iron ore required = 100 × 8383 = 266.66 answer : d"
Answer: d
Problem: what is 15 % of 2 / 3 of 0.4 ?
Options: a ) 0.09 , b ) 0.9 , c ) 9 , d ) 90 , e ) none of the above
Rationale: "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 4 / 10 ) = 120 / 3000 = 0.04 option a"
Answer: a
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 43 degrees . find the temperature on friday ?
Options: a ) 65 degrees , b ) 73 degrees , c ) 37 degrees , d ) 35 degrees , e ) 74 degrees
Rationale: m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 43 tu + w + th = 192 - 43 = 149 f = 184 – 149 = 35 answer : d
Answer: d
Problem: what is the probability that the sum of two dice will yield a 4 , and then when both are thrown again , their sum will again yield a 4 ? assume that each die has 3 sides with faces numbered 1 to 3 .
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "solution - rolling dices is an independent event . the combinations to get 4 are ( 1,3 ) , ( 3,1 ) , ( 2,2 ) , and total combinations of both dices is 9 . the probability of getting 4 in first attempt is 3 / 9 = 1 / 3 . probability of getting 4 again in second attempt = ( 1 / 3 ) * ( 1 / 3 ) = 1 / 9 . ans c"
Answer: c
Problem: in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 232 = 31 greatest - smallest is 144 - 31 = 113 so answer must be c . 113"
Answer: c
Problem: albert father was 48 years of age when she was born while her mother was 46 years old when her brother 2 years younger to her was born . what is the difference between the ages of her parents ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: mother ' s age when albert ' s brother was born = 46 years father ' s age when albert ' s brother was born = 48 + 2 = 50 years required difference = 50 - 46 = 4 years answer is b
Answer: b
Problem: what was the principal , if at 12 % per annum the interest after 3 years amounted to rs . 5888 less than the sum lent ?
Options: a ) 9000 , b ) 3000 , c ) 5000 , d ) 1300 , e ) 9200
Rationale: p - 2336 = ( p * 12 * 3 ) / 100 p = 9200 answer : e
Answer: e
Problem: what is the 14 th digit to the right of the decimal point in the decimal equivalent of 82 / 11 ?
Options: a ) 4 , b ) 3 , c ) 1 , d ) 5 , e ) 7
Rationale: "82 / 11 = 7.4545 . . . . 45 is non - repeating terminating decimal . the 14 th digit to the right of decimal point will be 5 . answer d"
Answer: d
Problem: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 14 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 14 more transactions than cal . jade = 66 + 14 = 80 jade handled = 80 transactions . answer : a"
Answer: a
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 12 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 19 : 2 , b ) 18 : 3 , c ) 11 : 1 , d ) 11 : 5 , e ) 11 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 2 = 15 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 15 / 2 + 7 / 2 = 11 litres as 16 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 11 : 5 answer : d"
Answer: d
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.9 km and 2.1 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 99 , b ) 277 , c ) 48 , d ) 96 , e ) 22
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.9 + 2.1 = 4 km = 4000 m . required time = 4000 * 3 / 125 = 96 sec . answer : d"
Answer: d
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price r per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
Answer: d
Problem: two numbers are in the ratio of 2 : 3 . if 4 is added in both numbers the ratio becomes 5 : 7 . find the difference between numbers .
Options: a ) 8 , b ) 6 , c ) 4 , d ) 2 , e ) 10
Rationale: we ' re told that two numbers are in the ratio of 2 : 3 . thus , the two numbers could be . . . 2 and 3 4 and 6 6 and 9 8 and 12 10 and 15 etc . we ' re told that adding 4 to each number changes the ratio of the numbers to 5 : 7 . we ' re asked for the difference between the original numbers . since adding 4 makes the first number a multiple of 5 , this limits the possibilities . . . . 2 + 4 = 6 not possible 4 + 4 = 8 not possible 6 + 4 = 10 this is possible . . . using this example , we would have . . . 6 and 9 , after adding 4 to each , becomes 10 and 13 . . . this is not a ratio of 5 to 7 though ( even though it ' s pretty close ) , so we have to keep looking . . . . the next value that becomes a multiple of 5 when you add 4 to it is . . . 16 . . . 16 + 4 = 20 with 16 and 24 , after adding 4 to each , we have 20 and 28 . this is a ratio of 5 to 7 , so we have our pair of original numbers . the difference between them is 8 . final answer : a
Answer: a
Problem: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6600 . find the actual price of the good .
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9649 , e ) s . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6600 1 = 6600 / 68.4 100 = ( 6600 * 100 ) / 68.4 = rs . 9649 . answer : option d"
Answer: d
Problem: in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 55 % , and the students on the make - up date had an average score of 95 % , what was the average score for the entire class ?
Options: a ) 60 % , b ) 65 % , c ) 67 % , d ) 70 % , e ) 75 %
Rationale: "70 % of the class scored 55 % and 30 % of the class scored 95 % . the difference between 55 % and 95 % is 40 % . the average will be 55 % + 0.3 ( 40 % ) = 67 % . the answer is c ."
Answer: c
Problem: the length of the bridge , which a train 110 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 265 , b ) 288 , c ) 245 , d ) 776 , e ) 232
Rationale: speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 110 + x ) / 30 = 25 / 2 = = > 2 ( 110 + x ) = 750 = = > x = 265 m . answer : a
Answer: a
Problem: excluding stoppages , the speed of a bus is 64 kmph and including stoppages , it is 50 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 15.5 , b ) 12.3 , c ) 10.5 , d ) 10.12 , e ) 13.12
Rationale: "due to stoppages , it covers 14 km less . time taken to cover 14 km = ( ( 14 / 64 ) ã — 60 ) = 13.12 min . option ( e ) is correct"
Answer: e
Problem: a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 8 hours , b ) 10 hours , c ) 12 hours , d ) 24 hours , e ) none of the above
Rationale: "a ' s 1 hour ' s work = 1 / 4 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( b + c ) ' s 1 hour ' s work = 1 / 2 ( a + b + c ) ' s 1 hour ' s work = ( 1 / 4 + 1 / 3 ) = 7 / 12 b ' s 1 hour ' s work = ( 7 / 12 - 1 / 2 ) = 1 / 12 b alone will take 12 hours to do the work . answer = c"
Answer: c
Problem: the moon revolves around the earth at a speed of approximately 1.02 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 62.5 , d ) 3,600 , e ) 3,672
Rationale: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.02 * 3600 = 3672 kilometers per hour . option e is correct"
Answer: e
Problem: the ratio of football players , baseball players , soccer players , and basketball players in a school is 10 : 7 : 5 : 4 . how many athletes are in the school if 16 players are on the basketball team ?
Options: a ) 40 , b ) 92 , c ) 104 , d ) 208 , e ) 80
Rationale: the ratio is 10 football players : 7 baseball players : 5 soccer players : 4 basketball players . divide 16 by 4 to find 1 ` ` part ' ' of the ratio . 16 / 4 = 4 multiply 4 by 5 to find the number of soccer players . 4 * 5 = 20 multiply 4 by 7 to find the number of baseball players . 4 * 7 = 28 multiply 4 by 10 to find the number of football players . 4 * 10 = 40 . add them all up to find total athletes . 16 + 20 + 28 + 40 = 104 the answer is c .
Answer: c
Problem: 7386038 is divisible by
Options: a ) 3 , b ) 4 , c ) 9 , d ) 11 , e ) 13
Rationale: "explanation : the given number is 7386038 . the sum of the digits at even places is = 3 + 6 + 3 = 12 . the sum of the digits at odd places is = 7 + 8 + 0 + 8 = 23 . the difference is given by 23 - 12 = 11 answer : d"
Answer: d
Problem: 40 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 299 , b ) 277 , c ) 800 , d ) 289 , e ) 271
Rationale: "( 40 / 100 ) * x – ( 20 / 100 ) * 650 = 190 2 / 5 x = 320 x = 800 answer : c"
Answer: c
Problem: what is the sum of the digits of integer k , if k = ( 10 ^ 30 - 36 )
Options: a ) 251 , b ) 260 , c ) 263 , d ) 269 , e ) 262
Rationale: there are 31 digits in 10 ^ 30 when we subtract 36 from it , there will be 30 digits left . 10 ^ 30 can be written as 9999999 . . . . ( 30 times ) + 1 so , 10 ^ 30 - 36 = 9999999 . . . . ( 30 times ) + 1 - 36 = 9999999 . . . . ( 30 times ) - 35 consider the last 2 digits , 99 - 35 = 64 the last 2 digits will be 64 . and our number would be 99999 . . . . . . 99964 with 2 less 9 s after subtraction . number of 9 s left are 28 and the last two digits are 64 the sum of the digits will be ( 28 * 9 ) + 6 + 4 = 262 answer : - e
Answer: e
Problem: if a # b = ab – b + b ^ 2 , then 3 # 7 =
Options: a ) 2 , b ) 63 , c ) 15 , d ) 21 , e ) 35
Rationale: solution - simply substitute 3 and 7 in equation in the place of a and b respectively . 3 # 7 = 3 * 7 - 7 + 7 ^ 2 = 21 - 7 + 49 = 63 . ans b
Answer: b
Problem: a train covers a distance of 12 km in 10 min . if it takes 4 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 20 , b ) 110 , c ) 120 , d ) 80 , e ) 60
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 4 = 80 m . answer : option d"
Answer: d
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction w of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction w of n to the total would be 4 a / 24 a or 1 / 6 answer b"
Answer: b
Problem: the average salary of 16 people in the shipping department at a certain firm is $ 20000 . the salary of 5 of the employees is $ 25000 each and the salary of 4 of the employees is $ 16000 each . what is the average salary of the remaining employees ?
Options: a ) $ 18,714 , b ) $ 18,500 , c ) $ 18,000 , d ) $ 15,850 , e ) $ 12,300
Rationale: total salary . . . 16 * 20 k = 320 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 7 emp sal = 320 k - 125 k - 64 k = 131 k average = 131 k / 7 = 18714 ans : a
Answer: a
Problem: jerry went to a shop and bought things worth rs . 40 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19 , b ) 19.7 , c ) 21.3 , d ) 31.5 , e ) 34.7
Rationale: "total cost of the items he purchased = rs . 40 given that out of this rs . 40 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 40 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 40 − 0.3 − x ) = 30 ⇒ ( 40 − 0.3 − x ) = 5 ⇒ x = 40 − 0.3 − 5 = 34.7 e )"
Answer: e
Problem: a no . when divided by 142 gives a remainder 110 , what remainder will be obtainedby dividingthe same no . 14 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: 142 + 110 = 252 / 14 = 18 ( remainder ) c
Answer: c
Problem: two stations a and b are 110 km apart on a straight line . one train starts from a at 6 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 12 , e ) 15
Rationale: "suppose they meet x hours after 6 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 9 a . m . answer : c"
Answer: c
Problem: one pipe can fill a tank four times as fast as another pipe . if together the two pipes can fill the tank in 40 minutes , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 100 min , b ) 150 min , c ) 200 min , d ) 250 min , e ) 300 min
Rationale: "let the slower pipe alone fill the tank in x minutes then , faster pipe will fill it in x / 4 minutes 1 / x + 4 / x = 1 / 40 5 / x = 1 / 40 x = 200 min answer is c"
Answer: c
Problem: a scale 6 ft . 8 inches long is divided into 5 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 16 inches , d ) 97 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 5 parts = 80 / 5 = 16 inches answer : c"
Answer: c
Problem: the area of rhombus is 150 cm square . the length of one of the its diagonals is 10 cm . the length of the other diagonal is :
Options: a ) 15 cm
b ) 20 cm
c ) 25 cm
d ) 30 cm
e ) none of these
Rationale: explanation : we know the product of diagonals is 1 / 2 * ( product of diagonals ) let one diagonal be d 1 and d 2 so as per question 1 / 2 ∗ d 1 ∗ d 2 = 150 1 / 2 ∗ 10 ∗ d 2 = 150 d 2 = 150 / 5 = 30 option d
Answer: d
Problem: machine a can finish a job in 4 hours , machine в can finish the job in 3 hours , and machine с can finish the job in 6 hours . how many hours will it take for a , b , and с together to finish the job ?
Options: a ) 3 / 2 , b ) 4 / 3 , c ) 5 / 4 , d ) 6 / 5 , e ) 8 / 7
Rationale: "the combined rate is 1 / 4 + 1 / 3 + 1 / 6 = 9 / 12 of the job per hour . the time to complete the job is 12 / 9 = 4 / 3 hours . the answer is b ."
Answer: b
Problem: if 10 litres of an oil of rs . 55 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 51.03 , c ) rs . 58.66 , d ) rs . 55.33 , e ) none of the above
Rationale: 55 * 10 = 550 66 * 5 = 330 880 / 15 = 58.66 answer : c
Answer: c
Problem: a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , a receives :
Options: a ) rs . 8400 , b ) rs . 11,900 , c ) rs . 13,600 , d ) rs . 14,700 , e ) none of these
Rationale: explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 35000 x 21 / 50 ) = rs . 14,700 . answer is d
Answer: d
Problem: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 700 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) 1800
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 700 = 16200 exp in % = 100 - 10 = 90 % , 16200 = 90 % saving = 10 % = 16200 x 10 / 90 = rs . 1800 answer : e"
Answer: e
Problem: if the radius of a circle decreased by 50 % its area is decreased by :
Options: a ) 75
b ) 79
c ) 72
d ) 70
e ) 80
Rationale: original area = π r ( power ) 2 new area = π ( r / 2 ) ( power ) 2 = ( π r ( power ) 2 ) / 4 reduction in area = [ ( π r ( power ) 2 - ( π r ( power ) 2 ) / 4 ] 2 = ( 3 π r ( power ) 2 ) / 4 reduction percent = ( ( 3 π r ( power ) 2 ) / 4 × 1 / ( π r ( power ) 2 × 100 ) % = 75 % answer is a .
Answer: a
Problem: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction e of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
Options: a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14
Rationale: if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus e = 11 / 14 of the remaining votes must be against . answer : a .
Answer: a
Problem: a is thrice as good a work man as b and together they finish a piece of work in 16 days . the number of days taken by b alone to finish the work is :
Options: a ) 64 days . , b ) 24 days . , c ) 52 days . , d ) 35 days . , e ) 28 days .
Rationale: "solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 3 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 16 divide 1 / 14 in the ratio 3 : 1 . ∴ b ’ s 1 day ’ s work = ( 1 / 16 x 1 / 4 ) = 1 / 64 hence , b alone can finish the work in 64 days . answer a"
Answer: a
Problem: if a large pizza has a radius that is 50 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 125 % , e ) 150 %
Rationale: "let the radius of medium pizza be r . then the radius of large pizza is 1.5 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.5 * r ) ^ 2 = 2.25 * pi * r ^ 2 , an increase of 125 % . the answer is d ."
Answer: d
Problem: if it takes 10 kids 6 hours to wear out their teacher , how long would it take 15 kids ?
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) 1 hour
Rationale: 10 * 6 = 15 * x x = 4 answer : b
Answer: b
Problem: the mass of 1 cubic meter of a substance is 500 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 0.1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "500 kg - 1 cubic meter ; 500,000 g - 1 cubic meter ; 500,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 500,000 = 10 / 5 = 2 cubic centimeters . answer : d ."
Answer: d
Problem: john found that the average of 15 numbers is 40 . if 13 is added to each number then the mean of number is ?
Options: a ) 53 , b ) 45 , c ) 65 , d ) 78 , e ) 64
Rationale: "( x + x 1 + . . . x 14 ) / 15 = 40 53 option a"
Answer: a
Problem: a straight line in the xy - plane has y - intercept of 10 . on this line the x - coordinate of the point is 100 and y - coordinate is 1000 then what is the slope of the line ?
Options: a ) 2 , b ) 5.5 , c ) 6.5 , d ) 3.2 , e ) 9.9
Rationale: eq of line = y = mx + c c = 10 x = 100 y = 100 m + 10 , substitute y by 1000 as given in question . 1000 = 100 m + 10 , m = 9.9 . correct option is e
Answer: e
Problem: a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( - 1 , 4 ) . what is the smallest possible area of that circle ?
Options: a ) 13 π , b ) 26 π , c ) 10 π , d ) 52 π , e ) 64 π
Rationale: "the distance between the two points is sqrt ( 40 ) . radius = sqrt ( 40 ) / 2 area = pi * ( sqrt ( 40 ) / 2 ) ^ 2 c . 10 π"
Answer: c
Problem: a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . what is the length of the bridge ( in metres ) ?
Options: a ) 1280 , b ) 1250 , c ) 1320 , d ) 1340 , e ) 1350
Rationale: speed = 5 km / hr time = 15 minutes = 1 / 4 hour length of the bridge = distance travelled by the man = speed × time = 5 × 1 / 4 km = 5 × ( 1 / 4 ) × 1000 metre = 1250 metre answer is b
Answer: b
Problem: the length of the bridge , which a train 160 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 215 m , c ) 245 m , d ) 250 m , e ) 270 m
Rationale: "let the length of the bridge : l the equation now is l + 160 / 12.5 m / s ( 45 km / hr or 12.5 m / s ) = 30 solving , l = 215 m answer : b"
Answer: b
Problem: a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 40 % , what should be the sale price of the mixed tea ?
Options: a ) 22.4 , b ) 22 , c ) 20 , d ) 19.2 , e ) none of these
Rationale: c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 40 ) / 100 × 16 = 22.4 answer a
Answer: a
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability z that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability z is 2 / 3 . d"
Answer: d
Problem: if the price of a book is first decreased by 30 % and then increased by 40 % , then the net change in the price will be :
Options: a ) 10 , b ) 388 , c ) 37 , d ) 29 , e ) 2
Rationale: "explanation : let the original price be rs . 100 . decreased by 30 % = 70 then increased 40 % on rs 70 = 70 + 28 = 98 net change in price = 100 - 98 = 2 answer : e"
Answer: e
Problem: two pipes a and b can fill a cistern in 37 ½ min and 45 minutes respectively . both the pipes are opened . the cistern will be filled in just half an hour , if the pipe b is turned off after
Options: a ) 6 minutes , b ) 9 minutes , c ) 45 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: if pipe b is turned off after x mins , then ( 2 * 30 ) / 75 + x / 45 = 1 x / 45 = 1 - 60 / 75 = 1 / 5 x = 45 / 5 = 9 mins answer : b
Answer: b
Problem: all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 158 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1264 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 158 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 158 = 3 k + 158 = > 2 k = 316 = > k = 158 the initial quantity of milk in a = 8 k = 8 * 158 = 1264 liters ."
Answer: a
Problem: two spies agreed to meet at a gas station between noon and 1 pm , but they have both forgotten the arranged time . each arrives at a random time between noon and 1 pm and stays for 6 minutes unless the other is there before the 6 minutes are up . assuming all random times are equally likely , what is the probability that they will meet within the hour ( noon to 1 pm ) ?
Options: a ) 0.12 , b ) 0.15 , c ) 0.17 , d ) 0.19 , e ) 0.25
Rationale: the probability that they do not meet is represented by the total of the areas of the two outer triangles in the figure below , which is 0.81 . so the probability of a meeting is 1 - 0.81 = 0 . 19 . correct answer d
Answer: d
Problem: the average of 45 results is 12 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 480 , c ) 750 , d ) 650 , e ) 560
Rationale: "23 th result = sum of 45 results - sum of 44 results 12 * 45 - 15 * 22 + 20 * 22 = 540 - 330 + 440 = 650 answer is d"
Answer: d
Problem: how many digits are in ( 8 × 10 ^ 8 ) ( 10 × 10 ^ 10 ) ?
Options: a ) 20 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "the question simplfies to ( 8 × 10 ^ 8 ) ( 10 ^ 11 ) = > 8 * 10 ^ 19 = > will contain 19 zeros + 1 digit 8 = > 20 ans a"
Answer: a
Problem: the water level in a rectangular swimming pool measuring 50 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 1200 , e ) 4687.5
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 50 * 25 * 1 / 2 = 625 feet ^ 3 of water must be removed , which equals to 625 * 7.5 = 4687.5 gallons . answer : e ."
Answer: e
Problem: if 34 men do a work in 40 days , in how many days will 20 men do it ?
Options: a ) 65 , b ) 68 , c ) 61 , d ) 55 , e ) 74
Rationale: "34 * 40 = 20 * x x = 68 days answer : b"
Answer: b
Problem: susan finds that she spends her free time during summer vacation between swimming , reading , and hanging out with friends in a ratio of 1 : 4 : 10 . how many hours did she spend reading if she hung out with her friends for 20 hours ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 10
Rationale: the ratio is 1 hour swimming : 4 hours reading : 10 hours hanging out with friends . divide 20 by 10 to find 1 ` ` part ' ' of the ratio . 20 / 10 = 2 multiply this by 4 to find the hours spent reading . 2 * 4 = 8 the answer is d .
Answer: d
Problem: 3 ltr of water is added with 11 ltr of a solution containing 42 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 23 % , b ) 35 % , c ) 33 % , d ) 40 % , e ) 45 %
Rationale: "we have a 11 litre solution containing 42 % of alcohol in the water . = > quantity of alcohol in the solution = 11 × 42 / 100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 11 + 3 = 14 percentage of alcohol in the new solution = 11 × 42 / 100 14 × 100 = 11 × 4210014 × 100 = 11 × 3 / 100 = 33 % c"
Answer: c
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 30 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 255 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 30 ) = 21 + 234 = > 255 hence answer will be ( b )"
Answer: b
Problem: when positive integer x is divided by positive integer y , the remainder is 1.44 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 1.44 - - > x = qy + 1.44 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 1.44 - - > y = 12 . answer : e ."
Answer: e
Problem: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many e hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in e = 3 hours ) solving these 2 equations we can find b as 12 so , d
Answer: d
Problem: sophia finished 23 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?
Options: a ) 180 , b ) 200 , c ) 250 , d ) 270 , e ) 300
Rationale: "let x be the total number of pages in the book , then she finished 23 ⋅ x pages . then she has x − 23 ⋅ x = 13 ⋅ x pages left . 23 ⋅ x − 13 ⋅ x = 90 13 ⋅ x = 90 x = 270 . so answer is d ."
Answer: d
Problem: on dividing a n by 9 , remainder is 8 . the quotient obtained when divided by 11 , leaves remainder 9 . now the quotient when divided by 13 , leaves remainder 8 . find the remainder when when the n is divided by 1287
Options: a ) 871 , b ) 881 , c ) 891 , d ) 904 , e ) 987
Rationale: take from the last step division suppose no . is n which is divided by 13 and remainder 8 = 13 n + 8 now 13 n + 8 will be the no . which is divided by 11 and remainder is 9 = [ 11 * ( 13 n + 8 ) ] + 9 now this no . is used for the very first step which is divider is 9 and remainder is 8 = { 9 * [ 11 * ( 13 n + 8 ) ] + 9 } + 8 solve and ans is 881 answer : b
Answer: b
Problem: a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 7 / 11 . how many tennis balls did the retailer order originally .
Options: a ) 17.5 , b ) 130 , c ) 175 , d ) 195 , e ) 220
Rationale: "white : yellow = x : ( x + 50 ) = 7 : 11 - - > 11 x = 7 x + 350 - - > x = 87.5 . the total # of balls originally x + x = 87.5 + 87.5 = 175 . answer : c ."
Answer: c
Problem: two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 10 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 20 miles ahead of the black car , how many hours will it take the black car to overtake the red car ?
Options: a ) 0.1 , b ) 0.5 , c ) 1 , d ) 1.2 , e ) 2
Rationale: "option b 20 + 10 t = 50 t t = 0.5"
Answer: b
Problem: an equilateral triangle and three squares are combined as shown above , forming a shape of area 48 + 4 √ 3 . what is the perimeter of the shape formed by the triangle and squares ?
Options: a ) 18
b ) 27
c ) 36
d ) 48
e ) 64
Rationale: triangle area = root ( 3 ) s ^ 2 / 4 area of 3 squares together = 3 s ^ 2 root ( 3 ) s ^ 2 / 4 + 3 s ^ 2 = 48 + 4 root ( 3 ) root ( 3 ) / 4 s ^ 2 = 4 root ( 3 ) s ^ 2 = 16 = > s = 4 there are 3 sides of each square = 3 ( 4 ) ( 3 ) = 36 option c
Answer: c
Problem: if 10 litres of an oil of rs . 54 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 58 , c ) rs . 54.17 , d ) rs . 55.33 , e ) none of the above
Rationale: "54 * 10 = 540 66 * 5 = 330 870 / 15 = 58 answer : b"
Answer: b
Problem: a tank is filled by 3 pipes a , b , c in 10 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 20 hr , b ) 52 hr , c ) 70 hr , d ) 66 hr , e ) 48 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 10 7 / x = 1 / 10 x = 70 hours answer is c"
Answer: c
Problem: the difference between a positive proper fraction and its reciprocal is 9 / 20 . the fraction is
Options: a ) 4 / 5 , b ) 7 / 11 , c ) 7 / 13 , d ) 7 / 15 , e ) 8 / 11
Rationale: let the required fraction be x . then 1 - x = 9 x 20 1 - x 2 = 9 x 20 20 - 20 x 2 = 9 x 20 x 2 + 9 x - 20 = 0 20 x 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 a )
Answer: a
Problem: rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 2250 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 900
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 2250 * 2 / 5 = $ 900 answer is e"
Answer: e
Problem: a can complete the job in 3 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: 1 / 6 = a
Answer: a
Problem: hcf and lcm two numbers are 20 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 132 , d ) 264 , e ) 220
Rationale: 20 * 396 = 36 * x x = 220 answer : e
Answer: e
Problem: a bag has 1 , 3 , 5 , 7 , 9,11 and 13 cm sticks . find the probability that they they will form a triangle if 3 sticks are drawn ?
Options: a ) 13 / 35 , b ) 14 / 35 , c ) 1 / 2 , d ) 5 / 6 , e ) 5 / 5
Rationale: explanation : total cases : = 7 c 3 = 35 favourable cases : ( 3 , 5,7 ) , ( 3 , 7,9 ) , ( 3 , 9,11 ) , ( 3 , 11,13 ) , ( 5 , 7,9 ) , ( 5 , 7,11 ) , ( 5 , 9,11 ) , ( 5 , 9,13 ) , ( 5 , 11,13 ) , ( 7 , 9,11 ) , ( 7 , 9,13 ) , ( 7 , 11,13 ) , ( 9 , 11,13 ) = total 13 . [ others are rejected because to form a triangle it is necessary that the sum of 2 small sides must be greater than the third greatest side . ] hence ( a ) is correct answer . answer : a
Answer: a
Problem: a number whose fifth part increased by 5 is equal to its fourth part diminished by 5 , is
Options: a ) 160 , b ) 180 , c ) 200 , d ) 220 , e ) none of these
Rationale: "x / 5 + 5 = x / 4 - 5 = > x / 5 - x / 4 = 10 x / 20 = 10 = > x = 200 answer : c ."
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 15 seconds . what is the length of the train ?
Options: a ) 187 m , b ) 250 m , c ) 876 m , d ) 150 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 15 ) m = 250 m . answer : b"
Answer: b
Problem: what is the least number which should be added to 2982 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ?
Options: a ) 14 , b ) 18 , c ) 22 , d ) 26 , e ) 30
Rationale: "l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 2982 by 60 , the remainder is 42 . the number to be added = 60 - 42 = 18 . the answer is b ."
Answer: b
Problem: the ratio of toddlers to infants at a day care center is 7 to 3 . if 12 more infants join the day care to change the ratio to 7 to 5 , how many toddlers are there at this day care center ?
Options: a ) 24 , b ) 36 , c ) 42 , d ) 72 , e ) 120
Rationale: 5 x - 3 x = 12 so , 2 x = 6 hence no of toddlers is 6 * 7 = 42 answer will be ( c ) 42
Answer: c
Problem: if x and y are integers such that | y + 3 | ≤ 3 and 2 y – 3 x + 6 = 0 , what is the least possible value e of the product xy ?
Options: a ) - 12 , b ) - 3 , c ) 0 , d ) 2 , e ) none of the above
Rationale: how to deal with inequalities involving absolute values ? first example shows us the so callednumber case in this case we have | y + 3 | ≤ 3 which is generalized | something | ≤ some number . first we solve as if there were no absolute value brackets : y + 3 ≤ 3 y ≤ 0 so y is 0 or negative second scenario - remove the absolute value brackets . put a negative sign around the other side of the inequality , andflip the sign : y + 3 > = - 3 y > = - 6 therefore we have a possible range for y : - 6 = < y < = 0 ok , so far so good , we ' re half way through . what about x ? here ' s the formula : 2 y – 3 x + 6 = 0 , rewrite it as 2 y + 6 = 3 x . you can say that 2 y + 6 is a multiple of 3 ( = 3 x ) . so all values which must be integer must also satisfy this constraint . i ' m just saying that , so it ' s easier to evaluate all the possible numbers ( - 6 , - 3 , 0 ) . if you plug in y = 0 , x will be 2 and xy = 0 as the lowest possible value e . hence , answer choice c is the one to go .
Answer: c
Problem: without stoppages , a train travels certain distance with an average speed of 400 km / h , and with stoppages , it covers the same distance with an average speed of 360 km / h . how many minutes per hour the train stops ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "due to stoppages , it covers 40 km less . time taken to cover 40 km = 40 â  „ 400 h = 1 â  „ 10 h = 1 â  „ 10 ã — 60 min = 6 min answer d"
Answer: d
Problem: express a speed of 18 kmph in meters per second ?
Options: a ) 10 mps , b ) 06 mps , c ) 09 mps , d ) 05 mps , e ) 11 mps
Rationale: d 5 mps 18 * 5 / 18 = 5 mps
Answer: d
Problem: two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 16 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 6 hours , c ) 8 hours , d ) 16 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 16 = 8 hours answer is c"
Answer: c
Problem: each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 20 , e ) 24
Rationale: "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 30 boxes , 6 are 10 - pound boxes and 24 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 15 , the ratio of 10 - pound boxes : 20 - pound boxes should be 1 : 1 . the number of 10 pound boxes remain the same so we still have 6 of them . to get a ratio of 1 : 1 , the number of 20 - pound boxes must be 6 . we need to remove 18 of the 20 - pound boxes . the answer is c ."
Answer: c
Problem: a train 280 m long , running with a speed of 72 km / hr will pass a tree in ?
Options: a ) 17 sec , b ) 16 sec , c ) 18 sec , d ) 14 sec , e ) 12 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec time taken = 280 * 1 / 20 = 14 sec answer : d"
Answer: d
Problem: in a coconut grove , ( x + 4 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x – 4 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 8 , d ) 9 , e ) none of the above
Rationale: ( x + 4 ) × 60 + x × 120 + ( x − 4 ) × 180 / ( x + 4 ) + x + ( x − 4 ) = 100 ⇒ 360 x − 480 / 3 x = 100 ⇒ 60 x = 480 ⇒ x = 8 answer c
Answer: c
Problem: what is the sum of the greatest common factor and the lowest common multiple of 12 and 36 ?
Options: a ) 48 , b ) 22 , c ) 32 , d ) 36 , e ) 38
Rationale: "prime factorization of 12 = 2 x 2 x 3 prime factorization of 36 = 2 x 2 x 3 x 3 gcf = 12 lcm = 36 sum = 48 . answer a ."
Answer: a
Problem: what is the sum of all the prime numbers greater than 30 but less than 50 ?
Options: a ) 126 , b ) 199 , c ) 198 , d ) 188 , e ) 122
Rationale: "required sum = ( 31 + 37 + 41 + 43 + 47 ) = 199 note : 1 is not a prime number answer b"
Answer: b
Problem: in one hour , a boat goes 16 km along the stream and 6 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 11 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 16 + 6 ) kmph . = 11 kmph . answer b"
Answer: b
Problem: what is the sum of the integers from - 150 to 155 , inclusive ?
Options: a ) 865 , b ) 955 , c ) 1050 , d ) 765 , e ) 750
Rationale: "in an arithmetic progression , the nth term is given by tn = a + ( n - 1 ) d here tn = 155 , a = - 150 , d = 1 hence , 155 = - 150 + ( n - 1 ) or n = 306 sum of n terms can be calculated by sn = n / 2 ( a + l ) a = first term , l = last term , n = no . of terms sn = 306 * ( - 150 + 155 ) / 2 sn = 306 * 5 / 2 = 765 answer : d"
Answer: d
Problem: how long does a train 120 m long running at the speed of 70 km / hr takes to cross a bridge 150 m length ?
Options: a ) 12.7 sec , b ) 13.9 sec , c ) 18.1 sec , d ) 17.1 sec , e ) 19.7 sec
Rationale: "speed = 70 * 5 / 18 = 19.4 m / sec total distance covered = 120 + 150 = 270 m . required time = 270 / 19.4 ' = 13.9 sec . answer : b"
Answer: b
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of two metres is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 2 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 2 + 2 = 26 meter answer is c ."
Answer: c
Problem: a palindrome is a number that reads the same forward and backward , such as 121 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 90 , e ) 2500
Rationale: first recognize you only need to consider the first two digits ( because the second two are just the first two flipped ) there are 90 possibilities for the first two digits of a 4 digit number , 10 - 99 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 90 = 50 answer : c
Answer: c
Problem: in an aquarium there is 14 purple fish , 8 orange fish , 12 pink fish , 3 golden fish . how many fish are there in an aquarium ?
Options: a ) 27 , b ) 37 , c ) 17 , d ) 47 , e ) 07
Rationale: 14 + 8 + 12 + 3 = 37 . answer is b
Answer: b