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Question: in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b the present age of b is
A.37.
B.38.
C.39.
D.40.
e ) 41C.
"let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 9 = > 2 b - b - 9 = 30 b = 39 so the present age of b is 39 years answer : c" | null |
Question: a reduction of 15 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
A.2.8.
B.2.3.
C.1.8.
D.2.1.
e ) 2.9C.
"100 * ( 15 / 100 ) = 15 - - - 10 ? - - - 1 = > rs . 1.5 100 - - - 85 ? - - - 1.5 = > rs . 1.8 answer : c" | null |
Question: on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.5 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
A.22.04 %.
B.16.12 %.
C.8 %.
D.18.25 %.
e ) 10.5 %E.
per quarter , interest = 2.5 % so for a year , interest = 10 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 10 % answer = 10.5 % = answer : e | null |
Question: a train which has 250 m long , is running 40 kmph . in what time will it cross a person moving at 4 kmph in same direction ?
A.30 sec.
B.28 sec.
C.29 sec.
D.35 sec.
e ) 25 secE.
"time taken to cross a moving person = length of train / relative speed time taken = 250 / ( ( 40 - 4 ) ( 5 / 18 ) = 250 / 36 * ( 5 / 18 ) = 250 / 10 = 25 sec answer : e" | null |
Question: two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
A.12.
B.14.
C.16.
D.20.
e ) 18A.
"sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 15 ] m / sec = 8 m / sec . relative speed = ( 12 + 8 ) = m / sec = 20 m / sec . ∴ required time = ( 120 + 120 ) / 20 secc = 12 sec . answer a" | null |
Question: if x is a positive number and 2 the square root of x is equal to x / 2 , then x =
A.1 / 16.
B.4.
C.1.
D.2.
e ) 8C.
"2 of sqrt ( x ) = x / 2 , which means that sqrt ( x ) = x or x = x ^ 2 - > divide by x 1 = x x = 1 c ." | null |
Question: two trains of length 100 m and 200 m are 100.00001 m apart . they start moving towards each other on parallel tracks , at speeds 108 kmph and 72 kmph . in how much time will the trains cross each other ?
A.8.
B.7.
C.9.
D.2.
e ) 1A.
"relative speed = ( 108 + 72 ) * 5 / 18 = 50 mps . the time required = d / s = ( 100 + 100 + 200 ) / 50 = 400 / 50 = 8 sec . answer : a" | null |
Question: in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 82 per kg ?
A.5 : 8.
B.4 : 7.
C.3 : 7.
D.1 : 1.
e ) 9 : 8D.
"( 96 - 82 ) / ( 82 - 68 ) = 14 / 14 = 1 / 1 answer : d" | null |
Question: if a ( a + 2 ) = 48 and b ( b + 2 ) = 48 , where a ≠ b , then a + b =
A.- 10.
B.- 9.
C.- 5.
D.- 4.
e ) - 2B.
"i . e . if a = 6 then b = - 8 or if a = - 8 then b = 6 but in each case a + b = - 8 + 6 = - 2 answer : b" | null |
Question: an article with cost price of 240 is sold at 20 % profit . what is the selling price ?
A.288.
B.200.
C.204.
D.207.
e ) 210A.
"sp = 1.20 * 240 = 288 answer : a" | null |
Question: how many seconds will it take for a car that is traveling at a constant rate of 120 miles per hour to travel a distance of 77 yards ? ( 1 mile = 1,160 yards )
A.1.25.
B.1.31.
C.1.58.
D.1.87.
e ) 2.3B.
"speed = 120 miles / hr = 58.67 yard / s distance = 77 yards time = distance / speed = 77 / 58.67 = 1.31 sec ans - b" | null |
Question: 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 r that the first ball picked up is odd numbered ?
A.0.
B.1 / 3.
C.1 / 2.
D.2 / 3.
e ) 1D.
"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 r is 2 / 3 . d" | null |
Question: a store reported total sales of $ 460 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
A.2 %.
B.17 %.
C.44 %.
D.65 %.
e ) 83 %C.
"new value – old value ) / old value x 100 we are given : february sales this year = 460 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 460 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 460 – 320 ) / 320 ] x 100 ≈ 44 % . the answer is c ." | null |
Question: water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 55 ° c , what is the temperature of the pot of water in ° f ?
A.116 ° f.
B.125 ° f.
C.131 ° f.
D.138 ° f.
e ) 145 ° fC.
"let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 55 ) / 5 + 32 = 131 ° f the answer is c ." | null |
Question: what distance will be covered by a bus moving at 126 kmph in 10 seconds ?
A.287.
B.600.
C.350.
D.276.
e ) 207C.
"126 kmph = 126 * 5 / 18 = 35 mps d = speed * time = 35 * 10 = 350 m . answer : c" | null |
Question: the dimensions of a room are 10 m x 7 m x 5 m . there are 2 doors and 3 windows in the room . the dimensions of the doors are 1 m x 3 m . one window is of size 2 m x 1.5 m and the other 2 windows are of size 1 m x 1.5 m . the cost of painting the walls at rs . 3 per sq m is
A.2488.
B.378.
C.739.
D.474.
e ) 291D.
explanation : area of 4 walls = 2 ( l + b ) h = 2 ( 10 + 7 ) x 5 = 170 sq m area of 2 doors and 3 windows = 2 ( 1 x 3 ) + ( 2 x 1.5 ) + 2 ( 1 x 1.5 ) = 12 sq m area to be planted = 170 - 12 = 158 sq m cost of painting = rs . 158 x 3 = rs . 474 answer : d | null |
Question: o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 5.3 ) + e ( – 6.7 ) + o ( – 7.3 ) + e ( 6.6 ) is :
A.- 4.
B.- 2.
C.0.
D.2.
e ) 4B.
o ( 5.3 ) + e ( – 6.7 ) + o ( – 7.3 ) + e ( 6.6 ) = 7 + ( - 6 ) + ( - 9 ) + 6 = - 2 the answer is b . | null |
Question: a quadratic function f ( x ) attains a maximum of 3 at x = 1 . the value of the function at x = 0 is 1 . what is the value of f ( x ) at x = 10 ?
A.- 119.
B.- 159.
C.- 110.
D.- 180.
e ) - 105B.
explanation : let , the quadratic equation be ax 2 + bx + c . so , f ( x ) = ax 2 + bx + c at x = 0 , the value of function is 1 . x = 0 , f ( x ) = 1 ax 2 + bx + c = a * 0 + b * 0 + c = c c = 1 . at x = 1 , f ( x ) = 3 x = 1 , f ( x ) = 3 a * 1 + b * 1 + c = 3 since c = 1 , a + b = 2 . also , we know that f ( x ) is maximum when x = 1 . if f ( x ) is maximum , ( dx / dt ) ( f ( x ) ) = 0 differentiating f ( x ) , we have d / dt ( ax 2 + bx + c ) = 2 ax + b at x = 1 , 2 ax + b = 0 . 2 a + b = 0 . b = - 2 a . substituting we have a + b = 2 , or a + - 2 a = 2 . a = - 2 . so , b = 4 . so the equation is - 2 x 2 + 4 x + 1 . at x = 10 , the value is - 2 * 100 + 4 * 10 + 1 i . e - 159 . answer : b | null |
Question: in a certain company , a third of the workers do not have a retirement plan . 40 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
A.80.
B.95.
C.105.
D.120.
e ) 137E.
"set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,6 * 1 / 3 * x 120 = 14 / 30 x x = 257 257 - 120 = 137 answer e" | null |
Question: the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 48.0 billion from $ 72.0 billion , a year ago . by what percent did the revenue fall ?
A.20.8.
B.30.4.
C.31.8.
D.32.5.
e ) 33.3E.
"$ 72 - $ 48 = 24 $ ( 24 / 72 ) * 100 = 33.33 % answer : e" | null |
Question: a trader bought a car at 10 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
A.17 %.
B.62 %.
C.12 %.
D.19 %.
e ) 22 %B.
"original price = 100 cp = 90 s = 90 * ( 180 / 100 ) = 162 100 - 162 = 62 % answer : b" | null |
Question: sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 40 % nuts , what percent of the combined mixture is dried fruit ?
A.16.7 %.
B.23.33 %.
C.25 %.
D.33.3 %.
e ) 46.7 %E.
"40 % is 10 % - points above 30 % and 20 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 2 : 1 . 2 / 3 * 70 % = 140 % / 3 = 46.7 % the answer is e ." | null |
Question: a man buys a cycle for rs . 2800 and sells it at a loss of 25 % . what is the selling price of the cycle ?
A.s . 2090.
B.s . 2160.
C.s . 2100.
D.s . 2202.
e ) s . 2092C.
"s . p . = 75 % of rs . 2800 = rs . 75 x 2800 / 100 = rs . 1190 answer : option c" | null |
Question: if 42.12 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
A.5.
B.7.
C.8.
D.9.
e ) 10A.
"42.12 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.12 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.12 = km / 50 . . . . . . 12 / 100 = 3 m / 50 . . . . . . m = 2 k + m = 3 + 2 = 5 answer : a" | null |
Question: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 40 percent of b , what is the value of m / x ?
A.2 / 5.
B.3 / 4.
C.4 / 5.
D.5 / 4.
e ) 3 / 5E.
a / b = 4 / 5 m / x = ( 3 / 5 ) * 5 / ( 5 / 4 ) * 4 = 3 / 5 the answer is e . | null |
Question: a , b and c rents a pasture for rs . 730 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
A.270.
B.199.
C.676.
D.156.
e ) 227E.
"12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 730 = 227 answer : e" | null |
Question: the area of a triangle is with base 10 m and height 5 m ?
A.11.
B.25.
C.787.
D.122.
e ) 12B.
"1 / 2 * 10 * 5 = 25 m 2 answer : b" | null |
Question: a certain fraction is equivalent to 2 / 5 . if the numerator of the fraction is increased by 4 and the denominator is doubled , the new fraction is equivalent to 1 / 4 . what is the sum of the numerator and denominator of the original fraction ?
A.49.
B.35.
C.56.
D.26.
e ) 21C.
"x / y = 2 / 5 - > 1 ( x + 4 ) / 2 y = 1 / 4 - > 2 divide 1 by 2 : = > 2 x / ( x + 4 ) = 8 / 5 = > 5 x = 4 x + 16 = > x = 16 = > y = 5 / 2 * 16 = 40 so x + y = 56 the answer is c" | null |
Question: how many diagonals does a polygon with 13 sides have , if one of its vertices does not connect to any diagonal ?
A.65.
B.62.
C.58.
D.54.
e ) 60D.
"if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 13 - 1 then 12 * ( 12 - 3 ) / 2 = 54 correct option : d" | null |
Question: a car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 38 miles per hour , how many hours long is the trip ?
A.13.
B.14.
C.15.
D.16.
e ) 17C.
"let t be the total time of the trip . 30 * 5 + 42 ( t - 5 ) = 38 t 4 t = 210 - 150 t = 15 the answer is c ." | null |
Question: in a certain country 1 / 5 of 8 = 4 . assuming the same proportion , what would be the value of 1 / 4 of 16 ?
A.13.
B.12.
C.10.
D.16.
e ) 14C.
c 10 | null |
Question: in what ratio must a grocer mix two varieties of pulses costing rs . 15 and rs . 20 per kg respectively so as to get a mixture worth rs . 16.50 per kg ?
A.3 : 7.
B.5 : 7.
C.7 : 3.
D.7 : 5.
e ) noneC.
solution required ratio = 3.50 : 1.50 = 35 : 15 = 7 : 3 . answer c | null |
Question: a can do a piece of work in 4 days . b can do it in 10 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
A.22 days.
B.20 / 3 days.
C.67 days.
D.17 / 6 days.
e ) 18 daysB.
"c = 1 / 2 - 1 / 4 - 1 / 10 = 3 / 20 = > 20 / 3 days answer : b" | null |
Question: a and b invests rs . 1500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
A.9 : 5.
B.9 : 8.
C.9 : 2.
D.9 : 9.
e ) 9 : 16E.
"( 1.5 * 6 + 3 * 6 ) : ( 4 * 12 ) 27 : 48 = > 9 : 16 answer : e" | null |
Question: the length of a rectangular garden is 2 feet longer than 3 times its width . if the perimeter of the garden is 100 feet , find the length of the garden .
['A.42', 'B.38', 'C.28', 'D.57', 'e ) 49']B.
let l and w be the length and width of the garden . the statement ` ` the length of a rectangular garden is 2 feet longer than 3 times its width ' ' may be formulated by l = 2 + 3 w the formula for the perimeter is given by p = 2 l + 2 w substitute p and l in the above equation by 100 and 2 + 3 w respectively to obtain 100 = 2 ( 2 + 3 w ) + 2 w solve for w and l w = 12 and l = 2 + 3 w = 38 . check that the perimeter of the rectangular garden is 100 p = 2 l + 2 w = 76 + 24 = 100 correct answer b | null |
Question: calculate 24 x 99
A.2673.
B.2763.
C.2637.
D.2736.
e ) 2376E.
"= 24 - 1 = 23 = ( decrement each digit of the number obtained from 9 ) here we got 23 . now = 9 - 2 = 7 and 9 - 3 = 6 . so we have 76 just write these numbers together . that is we have 23 and 76 . hence answer is 2376 answer is e ." | null |
Question: a fill pipe can fill 1 / 4 of cistern in 16 minutes . in how many minutes , it can fill 3 / 4 of the cistern ?
A.24 min.
B.30 min.
C.48 min.
D.26 min.
e ) 16 minC.
"required time = 16 * 4 * 3 / 4 = 48 minutes answer is c" | null |
Question: a reduction of 40 % in the price of oil enables a house wife to obtain 8 kgs more for rs . 2400 , what is the reduced price for kg ?
A.rs . 120.
B.rs . 125.
C.rs . 130.
D.rs . 135.
e ) rs . 140A.
"explanation : 2400 * ( 40 / 100 ) = 960 - - - - 8 ? - - - - 1 = > rs . 120 answer : a" | null |
Question: a trail mix company keeps costs down by employing the peanuts : cashews : almonds ratio of 10 : 4 : 1 in each bag of up to 75 total nuts . what is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts ?
A.40 %.
B.48 %.
C.49 %.
D.50 %.
e ) 58 %B.
peanuts = 50 cashews = 20 almonds = 5 we want to remove as many peanuts as possible while still having peanuts represent more than half of the mixture . . . the number of cashews and almonds will stay the same though , so we have 20 + 5 = 25 of those non - peanuts in total . if we had 25 peanuts and 25 non - peanuts , then that would be 50 % exactly . we want more than 50 % though , so we need to add in 1 more peanut . this gives us . . . peanuts = 26 cashews = 20 almonds = 5 the question asked for the decrease in the number of peanuts as a percentage . we started with 50 peanuts and removed 24 = 24 / 50 = 48 % ; answer : b | null |
Question: there is a 30 % chance that tigers will not win at all during the whole season . there is a 30 % chance that portugeese will not play at all in the whole season . what is the greatest possible probability that the tigers will win and portugeese will play during the season ?
A.55 %.
B.60 %.
C.70 %.
D.72 %.
e ) 80 %C.
"there is a 30 % chance that tigers will not win at all during the whole season we can infer that there is 70 % chance tigers will win . similarly there is a 30 % chance that portugeese will not play at all in the whole season we can also infer that there is 70 % chance that portugeese will play . answer c" | null |
Question: we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 390 . how many math books did we buy ?
A.57.
B.60.
C.63.
D.66.
e ) 69B.
"m + h = 90 h = 90 - m 4 m + 5 h = 390 4 m + 5 * ( 90 - m ) = 390 m = 60 the answer is b ." | null |
Question: the sum of three consecutive even numbers is 60 . find the middle number of the three ?
A.14.
B.60.
C.18.
D.70.
e ) 45B.
"three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 60 6 p = 60 = > p = 10 . the middle number is : 10 p = 60 . answer : b" | null |
Question: a number when divided by 133 leaves 16 as a remainder . what will be the remainder if the number is divided by 50 ?
A.51.
B.56.
C.49.
D.17.
e ) 7C.
"133 + 16 = 149 dividing 149 evenly into whole numbers is 2 and leaves 49 remaining . the correct answer is c ." | null |
Question: the length of a rectangular floor is more than its breadth by 200 % . if rs . 240 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?
A.65.
B.44.
C.18.
D.15.49.
e ) 14D.
"let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 240 / 3 = 80 sq m l b = 80 i . e . , l * l / 3 = 240 l 2 = 240 = > l = 15.49 answer : d" | null |
Question: a train 100 m long crosses a platform 125 m long in 15 sec ; find the speed of the train ?
A.91.2 kmph.
B.61.9 kmph.
C.45.9 kmph.
D.61.2 kmph.
e ) 71.2 kmphD.
"d = 100 + 155 = 255 t = 15 s = 255 / 15 * 18 / 5 = 61.2 kmph answer : d" | null |
Question: john has 10 pairs of matched socks . if he loses 3 individual socks , what is the greatest number of pairs of matched socks he can have left ?
A.7.
B.8.
C.5.
D.4.
e ) 3B.
"because we have to maximize the pair of matched socks , we will remove 1 pairs ( 2 socks ) out of 10 pairs 1 sock from the 2 th pair . thus the no of matching socks pair remaining = 10 - 2 = 8 answer b" | null |
Question: a train 250 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
A.6 sec ..
B.7 sec ..
C.9 sec ..
D.15 sec ..
e ) noneD.
"solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 250 m at ( 50 / 3 ) m / sec = ( 250 x 3 / 50 ) sec = 15 sec . answer d" | null |
Question: a garrison of 400 men had a provision for 31 days . after 26 days 275 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
A.16 days.
B.45 days.
C.10 days.
D.17 days.
e ) 18 daysA.
"400 - - - 31 400 - - - 5 125 - - - ? 400 * 5 = 125 * x = > x = 16 days . answer : a" | null |
Question: if the cost price of 50 articles is equal to the selling price of 40 articles , then the gain or loss percent is ?
A.33 %.
B.29 %.
C.25 %.
D.55 %.
e ) 39 %C.
"c 25 % given that , cost price of 50 article is equal to selling price of 40 articles . let cost price of one article = rs . 1 selling price of 40 articles = rs . 50 but cost price of 40 articles = rs . 40 therefore , the trader made profit . \ percentage of profit = 10 / 40 * 100 = 25 %" | null |
Question: if two dice are thrown together , the probability of getting an even number on both dice is
A.1 / 4.
B.1 / 5.
C.1 / 6.
D.1 / 3.
e ) 1 / 2A.
"the number of exhaustive outcomes is 36 . let e be the event of getting an even number on both dies is 9 / 36 = 1 / 4 p ( e ) = 1 / 4 . a )" | null |
Question: an alloy of copper and zinc contains copper and zinc in the ratio 8 : 2 . another alloy of copper and zinc contains copper and zinc in the ratio 4 : 6 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
A.5 : 1.
B.4 : 1.
C.3 : 1.
D.6 : 1.
e ) 8 : 1C.
"let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 8 x / 10 , and fraction of zinc in alloy _ 1 = 2 x / 10 similarly , fraction of copper in alloy _ 2 = 4 y / 10 , and fraction of zinc in alloy _ 2 = 6 y / 10 . mixing them , we get copper = 8 x / 10 + 4 y / 10 ; zinc = 2 x / 10 + 6 y / 10 so , 8 x + 4 y = 2 x + 6 y - > 6 x = 2 y - > x / y = 6 / 2 = 3 / 1 so , they must be mixed in the ratio 3 : 1 answer : c" | null |
Question: the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is rs . 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p + q + r is :
A.16100.
B.15700.
C.17500.
D.16000.
e ) 16500E.
"explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) ( p + q + r ) ' s monthly income = rs . 16500 . answer : e" | null |
Question: if 1 / ( x + 1 ) + 1 / ( x - 1 ) = 1 / ( x - 1 ) , what is the value of x ?
A.2.
B.- 2.
C.1.
D.- 1.
e ) 5C.
if we solve the question , we get x = 1 . option : c | null |
Question: evaluate 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 = ?
A.3043.
B.5050.
C.5176.
D.9356.
e ) 4890B.
b 5050 you must have noticed that 50 pairs of n ^ 2 – ( n - 1 ) ^ 2 exist . n ^ 2 – ( n - 1 ) ^ 2 = n + ( n – 1 ) in such case , we may as well write 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 as 100 + 99 + 98 + . . . + 2 + 1 = ( 100 x 101 ) / 2 = 5050 | null |
Question: what percent of 14 is 14 percent of 1 ?
A.0.001.
B.0.01.
C.0.1.
D.101.
e ) 1E.
"14 % of 1 = ( 14 / 100 ) * 1 = 14 / 100 to determine what percentage of 14 this is : [ 14 ] [ / 100 * 14 ] * 100 = 1 % ans : e" | null |
Question: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years r in which the population would be doubled assuming there is no emigration or immigration is
A.20.
B.r = 25.
C.r = 30.
D.r = 35.
e ) 40D.
"suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ." | null |
Question: there are 15 balls in a jar . you take out 3 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 3 . how many blue balls were there in the beginning ?
A.12 ..
B.9 ..
C.8 ..
D.7 ..
e ) 6 .D.
"7 = 3 blue balls + 12 / 3 answer : d" | null |
Question: the average ( arithmetic mean ) of 8 numbers is 43.1 . if the sum of half of these numbers is 158.4 , what is the average of the other half ?
A.12.8.
B.24.2.
C.46.6.
D.72.1.
e ) 96.8C.
arithmetic mean = sum / total numbers sum = 43.1 * 8 = 344.8 sum of half of these numbers is 158.4 . so , 4 numbers sum is 158.4 . rest 4 numbers sum = 344.8 - 158.4 = 186.4 arithmetic mean of the 4 nos = 186.4 / 4 = 46.6 hence , c is the answer . | null |
Question: 12.5 * 6.2 * 8.8 = ?
A.352.
B.435.
C.224.
D.682.
e ) 742D.
"d 682 ? = 12.5 * 6.2 * 8.8 = 682" | null |
Question: if 5 and 8 are factors of 60 n , what is the minimum value of n ?
A.2.
B.3.
C.7.
D.14.
e ) 56A.
"60 n / 7 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 5 * 2 * 2 * 2 = 3 * n / 2 must be an integer for this to be true n must multiple of 2 , thus min of n = 2 hence a" | null |
Question: what is the probability of getting exactly 2 heads in a single throw of four fair coins ?
A.1 / 2.
B.3 / 4.
C.3 / 8.
D.3 / 16.
e ) 5 / 16C.
"one possible case is hhtt . p ( hhtt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 there are 4 c 2 = 6 possible cases . p ( 2 heads ) = 6 * 1 / 16 = 3 / 8 the answer is c ." | null |
Question: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 45 kms . what was the total distance traveled in 12 hours ?
A.252 kms.
B.152 kms.
C.672 kms.
D.752 kms.
e ) 152 kmsC.
explanation : total distance travelled in 12 hours = ( 45 + 47 + 49 + . . . . . upto 12 terms ) this is an a . p with first term , a = 45 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 45 + { 12 - 1 ) x 2 ] = 6 ( 112 ) = 672 kms . answer : c | null |
Question: n denotes the number obtained when n is rounded to the nearest tenth . for example 4.31 = 4.3 0.089 - 1.135 =
A.1.05.
B.1.04.
C.- 1.05.
D.- 1.0.
e ) - 0.1D.
here let the first quantity be a = > a rounded to nearest tenths = > 0.1 similarly let the second quantity be b = > b rounded to nearest tenths = > 1.1 = > a - b = 0.1 - 1.1 = - 1 hence a - b = - 1 answer : d | null |
Question: if x , y , and z are positive real numbers such that x + y - z = 50 , y - z + x = 60 , and z - x + y = 80 , then find the z value ?
A.10.
B.20.
C.5.
D.15.
e ) 25C.
"x + y - z = 50 , - - - - - - 1 ) y - z + x = 60 , - - - - - - 2 ) z - x + y = 80 - - - - - - 3 ) from ( 1 ) & ( 2 ) 2 z = 10 z = 5 correct option is c" | null |
Question: initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many w women are currently in the room ?
A.12.
B.14.
C.15.
D.24.
e ) 36D.
"the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d" | null |
Question: 12.5 * 3.2 * 7.8 = ?
A.312.
B.435.
C.224.
D.646.
e ) 742A.
"a 312 ? = 12.5 * 3.2 * 7.8 = 312" | null |
Question: a certain protective additive increases from 30 days to 45 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
A.25 %.
B.33 1 / 3 %.
C.50 %.
D.66 2 / 3 %.
e ) 75 %C.
general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 45 − 30 / 30 ∗ 100 = 50 answer : c . | null |
Question: an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1,220 , what was the total number of pairs of contact lenses that she sold ?
A.9.
B.13.
C.15.
D.17.
e ) 19A.
"( x + 5 ) * 150 + x * 85 = 1220 = > x = 2 total lens = 2 + ( 2 + 5 ) = 9 answer a" | null |
Question: a bus trip of 660 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
A.40.
B.45.
C.50.
D.55.
e ) 60D.
"the time is the distance / speed . the time difference is 1 hour . 660 / v - 660 / ( v + 5 ) = 1 660 ( v + 5 ) - 660 v = ( v ) ( v + 5 ) 3300 = ( v ) ( v + 5 ) 55 * 60 = ( v ) ( v + 5 ) v = 55 mph the answer is d ." | null |
Question: a man can row downstream at 35 kmph and upstream at 25 kmph . find the speed of the man in still water and the speed of stream respectively ?
A.35.
3.
B.25.
5.
C.35.
4.
D.5.
30.
e ) 30.
5E.
"let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 35 - - - ( 1 ) and x - y = 25 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 60 = > x = 30 , y = 5 . answer : e" | null |
Question: in an examination , 300 students appeared . out of these students ; 30 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
A.33.
B.37.
C.54.
D.99.
e ) 48E.
the number of students with first division = 30 % of 300 = 30 / 100 × 300 = 9000 / 100 = 90 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 90 + 162 ) = 48 answer : e | null |
Question: if two dice are thrown together , the probability of getting an even number on one die and an odd number on the other is ?
A.1 / 9.
B.1 / 2.
C.1 / 1.
D.1 / 5.
e ) 1 / 8B.
"the number of exhaustive outcomes is 36 . let e be the event of getting an even number on one die and an odd number on the other . let the event of getting either both even or both odd then = 18 / 36 = 1 / 2 p ( e ) = 1 - 1 / 2 = 1 / 2 . answer : b" | null |
Question: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 45 only . men â € ™ s wages are ?
A.6 rs.
B.7 rs.
C.8 rs.
D.4 rs.
e ) 3 rsE.
"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 45 rs . 5 m + 5 m + 5 m - - - - - 45 rs . 15 m - - - - - - 45 rs . = > 1 m = 3 rs . answer : e" | null |
Question: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 34 minutes , then the slower pipe alone will be able to fill the tank in
A.144 mins.
B.140 mins.
C.136 mins.
D.132 minw.
e ) none of theseC.
"explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 34 = > 4 / x = 1 / 34 x = 34 ∗ 4 = 136 mins option c" | null |
Question: two dice are rolled . what is the probability that the sum on the top face of both the dice will be greater than 9 ?
A.3 / 8.
B.2 / 3.
C.1 / 2.
D.1 / 3.
e ) 1 / 6E.
total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) hence , total number of outcomes possible two dice are rolled , n ( s ) = 6 × 6 = 36 e = getting a sum greater than 9 when the two dice are rolled = { ( 4 , 6 ) , { 5 , 5 } , { 5 , 6 } , { 6 , 4 } , { 6 , 5 } , ( 6 , 6 ) } hence , n ( e ) = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 36 = 1 / 6 | null |
Question: let a be the event that a randomly selected two digit number is divisible by 3 and let b be the event that a randomly selected two digit number is divisible by 10 . what is p ( a and b ) ?
A.1 / 30.
B.1 / 15.
C.1 / 5.
D.1 / 3.
e ) 1 / 2A.
"p ( a and b ) = 1 / 3 * 1 / 10 = 1 / 30 the answer is a ." | null |
Question: if x is 12 percent greater than 80 , then x =
A.89.6.
B.91.0.
C.88.0.
D.70.9.
e ) 71.2A.
"12 % of 80 = ( 80 * 0.12 ) = 9.6 12 % greater than 80 = 80 + 9.6 = 89.6 answer is clearly a ." | null |
Question: a and b complete a work in 6 days . a alone can do it in 8 days . if both together can do the work in how many days ?
A.3.75 days.
B.3.43 days.
C.2.99 days.
D.2.98 days.
e ) 2.44 daysB.
"1 / 6 + 1 / 8 = 7 / 24 24 / 7 = 3.43 days answer : b" | null |
Question: the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 8 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
A.25.
B.35.
C.75.
D.80.
e ) 90D.
"a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 8 = 76 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 â € “ 316 = 4 a = e + 4 = 76 + 4 = 80 d" | null |
Question: 130 kg of an alloy a is mixed with 160 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 4 , then the amount of tin in the new alloy is ?
A.140.6 kg.
B.145.3 kg.
C.146.5 kg.
D.110.8 kg.
e ) 114 kgC.
"quantity of tin in 130 kg of a = 130 * 3 / 5 = 78 kg quantity of tin in 160 kg of b = 160 * 3 / 7 = 68.5 kg quantity of tin in the new alloy = 78 + 68.5 = 146.5 kg answer is c" | null |
Question: if each side of a square is increased by 325 % in length , find the percentage change in its area ?
A.54 %.
B.957 %.
C.956.25 %.
D.958.25 %.
e ) 959.50 %C.
"let each side of the square be a , then area = a x a new side = 325 a / 100 = 13 a / 4 new area = ( 13 a x 13 a ) / ( 4 x 4 ) = ( 25 a ² / 16 ) increased area = = ( 169 a ² / 16 ) - a ² increase % = [ ( 153 a ² / 16 ) x ( 1 / a ² ) x 100 ] % = 956.25 % answer : c" | null |
Question: 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 $ 18.80 , how many discounted tickets did he buy ?
A.3.
B.4.
C.5.
D.6.
e ) 7A.
"let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 18.8 0.4 x = 2.8 = > x = 7 discounted tickets = 10 - x = 3 ans : a" | null |
Question: a can do a piece of work in 10 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 5 days and b leaves after 3 days from the beginning . how long will work lost ?
A.2.
B.4.
C.5.
D.6.
e ) 7D.
"5 / 10 + 3 / 15 + x / 20 = 1 x = 18 / 3 = 6 answer : d" | null |
Question: at the end of year x , automobile installment credit accounted for 35 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 40 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
A.120.
B.300.
C.401.36.
D.350.15.
e ) 342.86E.
"system of equations a = ( 35 / 100 ) c ( 1 / 3 ) a = 40 - - > a = 120 substitution 120 = ( 35 / 100 ) c c = ( 100 / 35 ) 120 answer - 120 / 35 * 100 the correct answer is e . - 342.86" | null |
Question: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 2 : 3 . the first number is :
A.A.27.
B.B.98.
C.C.34.
D.D.35.
e ) e ) 62A.
"( 3 x - 9 ) : ( 5 x - 9 ) = 2 : 3 x = 9 = > 3 x = 27 answer : a" | null |
Question: the length of the bridge , which a train 130 metres long and travelling at 54 km / hr can cross in 30 seconds , is :
A.200 m.
B.225 m.
C.320 m.
D.250 m.
e ) 240 mC.
"speed = [ 54 x 5 / 18 ] m / sec = [ 15 / 1 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 15 = > ( 130 + x ) = 450 = > x = 450 - 130 = 320 m answer : c" | null |
Question: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 40 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
A.18 %.
B.20 %.
C.21 %.
D.40 %.
e ) can not be determinedD.
answer : d . | null |
Question: what is 3 2 / 3 - 2 1 / 4 divided by 6 / 7 - 2 / 5 ?
A.17 / 36.
B.36 / 17.
C.17 / 64.
D.15 / 4.
e ) 14 / 4C.
"3 2 / 3 - 2 1 / 4 = 11 / 3 - 9 / 4 = ( 44 - 27 ) / 12 = 17 / 12 6 / 7 - 2 / 5 = ( 30 - 14 ) / 35 = 16 / 35 so 17 / 12 / 16 / 3 = 17 / 12 * 3 / 16 = 17 / 64 answer - c" | null |
Question: the sum of the ages of 5 children born at the intervals of 3 year each is 50 year . what is the age of the youngest child ?
A.4 year.
B.8 year.
C.10 year.
D.none of these.
e ) 9 yearA.
"solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 ⇔ 5 x = 20 ⇔ x = 4 . ∴ age of the youngest child = x = 4 years . answer a" | null |
Question: sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 2.5 per pound , and german chocolate cost $ 1.5 per pound . if the total the she spent on chocolate was $ 30 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
A.7.
B.18.
C.10.
D.12.
e ) 11B.
"if there were all the expensive ones 2.5 . . . . there would be 30 / 2.5 or 12 of them but since 1.5 $ ones are also there , answer has to be > 12 . . . . if all were 1.5 $ ones , there will be 30 / 1.5 or 20 . . . so only 18 is left ans b . ." | null |
Question: the total age of a and b is 16 years more than the total age of b and c . c is how many year younger than
A.14 years.
B.12 years.
C.56 years.
D.16 years.
e ) 55 yearsD.
"given that a + b = 16 + b + c = > a â € “ c = 16 + b â € “ b = 16 = > c is younger than a by 16 years answer : d" | null |
Question: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 30 ° is ?
['A.35 m 2', 'B.36 m 2', 'C.37 m 2', 'D.38 m 2', 'e ) 40 m 2']C.
30 / 360 * 22 / 7 * 12 * 12 = 37 m 2 answer : c | null |
Question: find large number from below question the difference of two numbers is 1360 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
A.1254.
B.1376.
C.1456.
D.1555.
e ) 1629E.
"let the smaller number be x . then larger number = ( x + 1360 ) . x + 1360 = 6 x + 15 5 x = 1345 x = 269 large number = 269 + 1360 = 1629 e" | null |
Question: solve the equation 2 – x = 2 b – 2 ax , where a and b are real parameters . find for which values of a the equation has for solution a natural number , if b = 7
A.0.
B.1.
C.2.
D.3.
e ) 4B.
solution : we write the given equation like this ( 2 a - 1 ) x = 2 ( b - 1 ) the following cases are possible : if 2 a - 1 ≠ 0 , i . e . a ≠ 1 / 2 , the equation has single solution x = 2 ( b - 1 ) / ( 2 a - 1 ) if a = 1 / 2 and b = 1 , the equation gets the kind 0 . x = 0 and every x is solution if a = 1 / 2 and b ≠ 1 , we get 0 . x = 2 ( b - 1 ) , where 2 ( b - 1 ) ≠ 0 in this case the equation has no solution . if b = 7 and a ≠ 1 / 2 the single solution is x = 2 ( 7 - 1 ) / ( 2 a - 1 ) = 12 / ( 2 a - 1 ) if a is whole number , then 2 a - 1 is also whole number and the solution x = 12 / ( 2 a - 1 ) is natural number when 2 a - 1 is positive divisor of 12 . to have a as whole number , the divisor of 12 mu be odd . but the only whole positive odd numbers divisible by 12 are 1 and 3 . therefore 2 a - 1 = 3 < = > a = 2 or 2 a - 1 = 1 < = > a = 1 a = 2 or 2 a - 1 = 1 < = > a = 1 answer b | null |
Question: in a caravan , in addition to 50 hens there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads , find the number of keepers .
A.25.
B.20.
C.15.
D.13.
e ) 14C.
let the number of keepers be x then , total number of heads = ( 50 + 45 + 8 + x ) = ( 103 + x ) . total number of feet = ( 45 + 8 ) x 4 + ( 50 + x ) x 2 = ( 312 + 2 x ) . ( 312 + 2 x ) - ( 103 + x ) = 224 = = > x = 15 . hence , number of keepers = 15 . answer c . | null |
Question: a motorcyclist goes from bombay to pune , a distance of 160 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
A.1 : 2.
B.2 : 5.
C.1 : 4.
D.1 : 1.
e ) 1 : 6B.
"t = 160 / 32 = 5 h t = 5 - 3 = 2 time ratio = 5 : 2 = 5 : 2 speed ratio = 2 : 5 answer : b" | null |
Question: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 40 % ?
A.95 %.
B.90 %.
C.85 %.
D.96 %.
e ) 25 %D.
"the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 40 % increase a surface = 6 * ( ( 1.4 a ) ^ 2 ) = 6 * 1.96 * a ^ 2 the increase in the surface area = ( 6 * 1.96 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.96 - 1 ) ) / ( 6 * a ^ 2 ) = 1.96 - 1 = 0.96 = 96 % answer : d" | null |
Question: how many shots of 1 cm radius can be prepared from a sphere of 5 cm radius ?
A.33.
B.88.
C.27.
D.125.
e ) 199D.
4 / 3 ï € * 5 * 5 * 5 = 4 / 3 ï € * 1 * 1 * 1 * x x = 125 answer : d | null |
Question: in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 10 % . what is population of after 2 year .
A.140.
B.141.
C.142.
D.143.
e ) 144B.
next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 10 % so total man = 150 * . 9 = 135 women will be = 175 - 135 = 40 so population after two years = [ 135 ^ 2 + 40 ^ 2 ] ^ . 5 = 140.80 = 141 so population after two year = 141 answer : b | null |
Question: a train 124 m long running at 68 kmph crosses a platform in 19 sec . what is the length of the platform ?
A.338.
B.234.
C.240.
D.881.
e ) 271B.
"d = 68 * 5 / 18 = 19 = 358 – 124 = 234 answer : b" | null |
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