1. If a, b, c, ........, x, y, z are 26 natural numbers , then the value of (x – a) (x – b) (x – c)........ (x – y) (x – z) is :
(a) 0
(b) 1
(c) 13
(d) 26
(e) ½
2. If 1
(a) 4m
(b) 2m
(c) 3m
(d) m
(e) m
3. If a and b are such numbers that a > 0 and b < 0, then which one of the following is always correct?
(a) a + b > 0
(b) a – b > 0
(c) a + b < 0
(d) a – b < 0
(e) a + b = 0
4. The sum of the numerator and denominators of a certain fraction is 8. If 2 is added to both the numerator and the denominator the value of the fraction is increased by 4/35 then the fraction is:
(a)
(b)
(c)
(d)
(e) None
5. In a number of three digits, the digits in the unit’s place and the ten’s place are equal and the sum of all the digits is 8. The digit of unit place is:
(a) 4
(b) 3
(c) 5
(d) 6
(e) None
6. If 1 × 2 × 3 × ......... x n is donated by n!, then (8! – 7! – 6!) is equal to :
(a) 6 × 7 × 8!
(b) 7 × 8 × 6!
(c) 6 × 8 × 6!
(d) 6 × 8 × 7!
(e) None
7. The sum of the squares of three consecutive natural numbers is 2030. Then what is the middle number?
(a) 27
(b) 26
(c) 25
(d) 28
(e) 24
8. 55% of a number is more than
(a) 240
(b) 69
(c) 96
(d) 144
(e) 345
9. If m and n are integers and √mn = 10, which of the following cannot be a value of m + n?
(a) 29
(b) 25
(c) 101
(d) 52
(e) 50
10. A two – digit number is four times the sum of the two digits. If the digits are reversed, the number so obtained is 18 more than the original number. What is the original number?
(a) 48
(b) 42
(c) 24
(d) 12
(e) 36
11. x and y are positive integers and x is less than y. If x2 + y2 equals two times 5 and xy equals two times 2. X/Y will equal.
(a) 1/2
(b) 1/√2
(c) 1
(d) 2
(e) 3/2
12. If x and y are different integers, both divisible by 5 , then which of the following is not necessarily true?
(a) (x – y) is divisible by 5
(b) x2 + y2 is divisible by 5
(c) x.y is divisible by 5
(d) x2 – y2 is divisible by 5
(e) (x + y) is divisible by 10
13. What will be the remainder when 5382 + 53 is divided by 54?
(a) 50
(b) 51
(c) 0
(d) 2
(e) 31
14. If the seven figure number 30x0103 is a multiple of 13, then x is:
(a) 7
(b) 1
(c) 8
(d) 6
(e) None
15. In a division sum, the divisor is 12 times the quotient and 5 times the remainder. If the remainder is 48, then the dividend is:
(a) 4808
(b) 4836
(c) 4824
(d) 3648
(e) 4848
16. The sum of all integers between 200 and 400 divisible by 9 is:
(a) 3366
(b) 6633
(c) 6336
(d) 3663
(e) None
17. The sum of two numbers is and their geometric mean is 20% lower than their arithmetic mean. Find the number.
(a) 13, 2
(b) 11, 4
(c) 10, 5
(d) 12, 3
(e) 9, 6
18. Which one of the following is the rational number lying between 6/7 and 7/8?
(a) 95/112
(b) 98/112
(c) 97/112
(d) 99/112
(e) 3/4
(a) √6 + √2
(b) √6 - √2
(c) √6 – 2
(d) 2 - √6
(e) None
20. {(√5 + √3)/(√5 - √3)}2 + {(√5 - √3)/(√5 + √3)}2 is equal to:
(a) 62
(b) 66
(c) 64
(d) 68
(e) 65
21. The greatest (√19 – √17), (√13 – √11), (√7 – √5) and (√5 – √3) is:
(a) (√19 – √17)
(b) (√13 – √11)
(c) (√7 – √5)
(d) (√5 – √3)
(e) None
22. Arrange the following in descending order:
∛4, √2, √(6&3) , ∜5
(a) √2 > √(6&3) > ∛4 > ∜5
(b) ∜5 > ∛4 > √(6&3) > √2
(c) ∜5 > ∛4 > √2 > √(6&3)
(d) √(6&3) > ∜5 > ∛4 √2
(e) None
23. If x = (√3+ 1)/(√3- 1) and y = (√3- 1)/(√3+ 1), then value of x2 + y2
(a) 13
(b) 14
(c) 15
(d) 10
(e) 8
24. (√1296)/? = ?/2.25
(a) 6
(b) 8
(c) 7
(d) 9
(e) 12
25. √(.00059049) =?
(a) .243
(b) .0243
(c) .00243
(d) .000243
(e) None
26. What is 25% of 25% equal to:
(a) 6.25
(b) .625
(c) 0.625
(d) .00625
(e) None
27. If 8% of x = 4% of y, then 20% of x is:
(a) 10 % of y
(b) 16 % of y
(c) 80 % of y
(d) 15 % of y
(e) None
28. 75% of a number when added to 75 is equal to the number. The number is:
(a) 150
(b) 200
(c) 225
(d) 300
(e) 320
29. In mathematics exam a student scored 30% marks in the first paper, out of a total of 180. How much should he score in second paper out of a total of 150. If he is to get an overall average of at least 50 %.
(a) 74 %.
(b) 76 %.
(c) 70 %.
(d) 80 %.
(e) 85 %.
30. Two number are less than a third number by 30% and 37% respectively. How much percent is second number less than the first?
(a) 4 %.
(b) 7 %.
(c) 3 %.
(d) 10 %.
(e) None.
31. A student who scores 20% marks in an examination fails by 30 marks. Another student who scores 32% marks get 42 marks more than those required to pass. The percentage of marks required to pass is:
(a) 28.
(b) 80.
(c) 25.
(d) 30.
(e) None.
32. In an election between two candidates, the candidates who gets 30% of the vote pulled is defeated by 15000 votes. The number of votes polled by the winning candidate is :
(a) 15000.
(b) 26250.
(c) 11250.
(d) 37500.
(e) 32200.
33. The capacity of two pots 120 litres and 56 litres respectively. The capacity of a container which can exactly measure the contents of the two pots, is –
(a) 7500 c.c.
(b) 7850 c.c.
(c) 8000 c.c.
(d) 9500 c.c.
(e) 9800 c.c.
34. The L.C.M. of two numbers in 12 times their H.C.F. The sum of H.C.F. and L.C.M. is 403. If one number is 93, then the other is –
(a) 128.
(b) 124.
(c) 134.
(d) 145.
(e) None.
35. The sum of two numbers is 45. Their difference is 1/9 of their sum. Their L.C.M. is –
(a) 100.
(b) 150.
(c) 200.
(d) 250.
(e) 300.
36. L.C.M. of 22, 54, 108, 135, 198 is –
(a) 330.
(b) 1980.
(c) 5940.
(d) 11880.
(e) None.
37. Four bells commence tolling together. The toll at intervals of 1, 11/4, 11/2 and 13/4 second respectively, after what interval will they toll together again –
(a) 2 min 40 sec.
(b) 1 min 40 sec. (c) 2 min 45 sec.
(d) 1 min 45 sec.
(e) 2 min 30 sec.
38. The L.C.M. of two numbers is 2310 and their H.C.F. is 30. If one of these numbers is 210, the second number is –
(a) 330.
(b) 1470.
(c) 2100.
(d) 16170.
(e) 17160.
39. What is the greatest possible length of a scale that can be used to measure exactly the lengths 3 m, 5 m 10 cm and 12m 90 cm?
(a) 10 cm.
(b) 20 cm.
(c) 25 cm.
(d) 30 cm.
(e) 35 cm.
40. What is the greatest number that will divide 38, 45 and 52 and leaves as remainders 2, 3 and 4 respectively?
(a) 4.
(b) 6.
(c) 8.
(d) 9.
(e) None.
41. What is the least number which, when divided by 52, leaves 33 as the remainder, and when divided by 78 leaves 59, and when divided by 117 leaves 98 as respective remainders?.
(a) 468.
(b) 449.
(c) 475.
(d) 494.
(e) None.
42. The average of 6 numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is –
(a) 25.
(b) 30.
(c) 35.
(d) 40.
(e) 45.
43. The average weight of 8 mans is increased by 1.5 kg when one of the men who weight 65 kg is replaced by a new man. The weight 65 kg is replaced by a new man. The weight of new man is –
(a) 70 kg.
(b) 74 kg.
(c) 76 kg.
(d) 77 kg.
(e) 82kg.
44. The average of x1, x2, x3, x4 is 16. Half the sum x2, x3, x4 is 23. What is the value of x1?
(a) 17.
(b) 18.
(c) 19.
(d) 20.
(e) 21.
45. A man bought 5 shirts at $ 450 each, 4 trousers at $ 750 each and 12 pairs of shoes at $ 750 each. What is the average expenditure per article?
(a) $ 678.50
(b) $ 900
(c) $ 800
(d) $ 1000
(e) None.
46. The average height of the student in a class of 10 is 105 cm. If 20 more students with an average height of 120 cm join the class, what will the new average height be?
(a) 105 cm.
(b) 110 cm.
(c) 112 cm.
(d) 115 cm.
(e) 117 cm.
47. The average weight of 8 persons is increased by 2.5 kg when one of them whose weight is 56 kg is replaced by a new man. The weight of new man is –
(a) 66 kg.
(b) 75 kg.
(c) 76 kg.
(d) 86 kg.
(e) None.
48. The difference between the present ages of Ryan and Bryan is 6 years. The ratio between their ages after 4 years will be 3:4. What can be the present age is Bryan?
(a) 15 years.
(b) 18 years.
(c) 20 years.
(d) 24 years.
(e) None.
49. The ratio of Clara’s age of her mother is 3:11. The difference between their ages is 24 years. The ratio between their ages after 3 years will be –
(a) 1:3
(b) 2:3
(c) 3:5
(d) 2:5
(e) 1:5
50. Fifteen years hence, a man will be just four times as old as he was 15 years age. His present age is –
(a) 10 years
(b) 15 years
(c) 20 years
(d) 25 years
(e) None
51. Tom was thrice as old as Ron 6 years back. Tom will be 5/3 times as old as Ron 6 years hence. How old is Ron today?
(a) 12 years
(b) 15 years
(c) 18 years
(d) 24 years
(e) 25 years
52. What number has to be added to each term of 3:5 to make the ratio 5:6?
(a) 6
(b) 7
(c) 12
(d) 13
(e) 17
53. Which of the following is the lowest ratio?
(a) 7:13
(b) 17:25
(c) 7:15
(d) 15:23
(e) 13:23
54. Rs. 680 is divided among A,B,C such that A gets 2/3 of what B gets and B gets ¼ of what C gets, then, their shares are respectively –
(a) Rs 75, Rs 325, Rs 280
(b) Rs 80, Rs 120, Rs 480
(c) Rs 80, Rs 120, Rs 480
(d) Rs 100, Rs 200, Rs 380
(e) Rs 100, Rs 120, Rs 280
55. The ratio of Monica’s and Victor’s present age is 9:10. After 4 years, the ratio of their ages becomes 11:12. What is Mona’s present age?
(a) 18 years
(b) 22 years
(c) 20 years
(d) Cannot be determined
(e) None of these
56. If y varies directly as (x + 3) and y = 8 when x =1. What is the value of y and when x = 2?
(a) 6
(b) 10
(c) 12
(d) 16
(e) 18
57. A mixture contains milk and water in the ratio 5:1. On adding 5 litres of water , the ratio of milk to water becomes 5:2. The quantity of milk in the original mixture is –
(a) 16 litres
(b) 22.75 litres
(c) 25 litres
(d) 32.5 litres
(e) 35 litres
58. Three numbers are in the ratio 3:4:5. The sum of the largest and the smallest equals the sum of the third and 52. The smallest number is –
(a) 20
(b) 27
(c) 39
(d) 52
(e) 63
59. If A exceeds B 40% and B is less than C by 20%. Then A:C = ?
a) 3:1
b) 3:2
c) 26:25
d) 28:25
e) 26:28
60. If 10% of m is the same as 20% of n, then m:n is equal to
a) 1:2
b) 2:1
c) 5:1
d) 10:1
e) None
61. If A:B = 2:3 and B:C = 4:5, then C:A is equal to –
a) 15:8
b) 12:10
c) 8:5
d) 8:15
e) None
62. Two vessels contains equal quantity of mixture of milk and water in the ratio 5:2 and 6:1 respectively. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture –
a) 10:7
b) 11:3
c) 10:3
d) 11:7
e) None
63. 729 ml of mixture contains milk and water in the ratio 7:2. How much more water is to be added to get a new mixture containing milk and water in the ratio 7:3?
a) 600 ml
b) 710 ml
c) 520 ml
d) 550 ml
e) 81 ml
64. How much water must be added to a bucket which contains 40 litres of milk at the cost price of $ 3.50 per litre so that the cost of milk reduced to $ 2 per litre?
a) 25 litres
b) 28 litres
c) 30 litres
d) 35 litres
e) None of these
65. Ron, David and Jack together started a business in partnership. The ratio of their capitals is 3:4:7. If their annual profit be $ 21000, what will be Jack share in this profit?
a) $ 12500
b) $ 10500
c) $ 15000
d) $ 10000
e) $ 12000
66. A, B and C start a business, each investing $ 20000. After a month A withdrew $ 5000, B $ 4000and C invested $ 6000 more. At the end of the year, a total profit of $ 69900 was recorded. What is the share of B?
a) $ 20500
b) $ 21200
c) $ 27300
d) $ 28200
e) None
67. A, B and C entered into a partnership. A invested $ 2560 and B invested $ 2000. At the end of the year, they gained $ 1105, out of which A got $ 320.C’s capital was –
a) $ 2840
b) $ 4028
c) $ 4280
d) $ 4820
e) $ 2420
68. 10 men can finish the construction of a wall in 8 days. How many men are added to finish the work in half a day?
a) 160
b) 100
c) 120
d) 150
e) 140
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