it is aptitude maths

1. Aptitude
Numbers

2. 1. Which one of the following is not a prime
number?
• 31
• 61
• 71
• 91

3. Explanation:
• 91 is divisible by 7. So, it is not a prime number.
Ans: 91

4. 2. (112 x ) = ?
• 67000
• 70000
• 76500
• 77200

5. Explanation:
• (112 x) = 112 x = 112 x 104 = 1120000 = 70000
• Ans: 70000

6. 3. It is being given that ( + 1) is completely divisible by a whole number.
Which of the following numbers is completely divisible by this number?
• ( + 1)
• (- 1)
• (7 x)
• ( + 1)

7. Explanation:
• Let = x. Then, (+ 1) = (x + 1).
• Let (x + 1) be completely divisible by the natural number N. Then,
( + 1) = [()3
+ 1] = (x3
+ 1) = (x + 1)(x2
- x + 1), which is completely divisible
by N,
since (x + 1) is divisible by N.
Ans: (+ 1)

8. 4. What least number must be added to 1056,
so that the sum is completely divisible by 23
• 2
• 3
• 18
• 21
• None of these

9. Explanation:
• 23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21) = 2.
Ans: 2

10. 5. 1397 x 1397 = ?
• 1951609
• 1981709
• 18362619
• 2031719
• None of these

11. Explanation:
1397 x 1397 =(
= (+ - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.

12. 6. (935421 x 625) = ?
• 575648125
• 584638125
• 584649125
• 585628125

13. Explanation:
• 935421 x 625 = 935421 x 54 = 935421 x
• 935421 x /= 9354210000 /16
= 584638125
Ans: 584638125

14. 7. The largest 4 digit number exactly divisible by
88 is:
• 9944
• 9768
• 9988
• 8888
• None of these

15. Explanation:
• Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55) = 9944.
Ans: 9944

16. 8. What is the unit digit in {x x}?
• 0
• 2
• 3
• 5

17. Explanation:
• Unit digit in = Unit digit in = Unit digit in [(42) 896 x 4]
= Unit digit in (6 x 4) = 4
Unit digit in (625)317 = Unit digit in (5)317 = 5
Unit digit in (341)491 = Unit digit in (1)491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
Ans: 0

18. 9. The sum of first five prime numbers is:
• 11
• 18
• 26
• 28

19. Explanation
• Definition: A prime number (or a prime) is a natural number that has
exactly two distinct natural number divisors: 1 and itself.
• Ans: 28

20. 10. The difference of two numbers is 1365. On dividing the
larger number by the smaller, we get 6 as quotient and the 15
as remainder. What is the smaller number ?
• 240
• 270
• 295
• 360

21. Explanation
• Let the smaller number be x.
Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270
Smaller number = 270
Ans: 270

22. 11. x ÷ 432 = ?
• 5184
• 5060
• 5148
• 5084
• None of these

23. Explanation:
• Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
• Ans: 5184

24. 12. If the number 517*324 is completely divisible by 3,
then the smallest whole number in the place of * will
be:
• 0
• 1
• 2
• None of these

25. Explanation:
• Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be
divisible by 3. x = 2.
• Ans: 2

26. 13. Which one of the following numbers is
exactly divisible by 11?
• 235641
• 245642
• 315624
• 415624

27. Explanation:
• (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
• (2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
• (4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
• (4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11
• Ans: 415624

28. 14. The sum of first 45 natural numbers is:
• 1035
• 1280
• 2070
• 2140

29. Explanation:
• Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.
• Sn = n/2 [2a + (n - 1)d] = 45/2 x [2 x 1 + (45 - 1) x 1] = 45/ 2 x 46 = (45
x 23)
= 45 x (20 + 3)
= 45 x 20 + 45 x 3
=900 + 135 = 1035.
Ans: 1035

30. 15. (753 x 753 + 247 x 247- 753 x 247)/(753 x
753 x 753 + 247 x 247 x 247) =

31. Explanation:
• Given Exp. = (a 2 + b 2 - ab) = 1 = 1 = 1 (a 3 + b 3) (a + b) (753 + 247)
1000

32. 16. If the number 481 * 673 is completely divisible by 9,
then the smallest whole number in place of * will be:
• 2
• 5
• 6
• 7
• None of these

33. Explanation:
• Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be
divisible by 9. x = 7.
• Ans: 7

34. 17. On dividing a number by 56, we get 29 as remainder. On
dividing the same number by 8, what will be the remainder ?
• 4
• 5
• 6
• 7

35. Explanation:
Formula: (Divisor*Quotient) + Remainder = Dividend.
Soln: (56*Q)+29 = D -------(1)
D%8 = R -------------(2)
From equation(2), ((56*Q)+29)%8 = R.
=> Assume Q = 1.
Þ(56+29)%8 = R.
Þ85%8 = R
Þ 5 = R
ÞAns: 5

36. 18. If n is a natural number, then (6n2 + 6n) is
always divisible by
• 6 only
• 6 and 12 both
• 12 only
• by 18 only

37. Explanation:
• (6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both,
since n(n + 1) is always even.
• Ans: 6 and 12 both

38. 19. 107 x 107 + 93 x 93 = ?
• 19578
• 19418
• 20098
• 21908
• None of these

39. Explanation:
• 107 x 107 + 93 x 93 = (107)2 + (93)2
= (100 + 7)2 + (100 - 7)2
= 2 x [(100)2 + 72]
[Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)]
= 20098
Ans: 20098

40. 20. What will be remainder when (6767 + 67)
is divided by 68 ?
• 1
• 63
• 66
• 67

41. Explanation:
• (x n + 1) will be divisible by (x + 1) only when n is odd.
(6767 + 1) will be divisible by (67 + 1)
(6767 + 1) + 66, when divided by 68 will give 66 as remainder.
Ans: 66