Numbers problems
- 1. 2 + 22 + 23 + ... + 29 =?
Options- A. 2044
- B. 1022
- C. 1056
- D. None of these Discuss
Correct Answer: 1022
Explanation:
| This is a G.P. in which a = 2, r = | 22 | = 2 and n = 9. |
| 2 |
| ∴Sn = | a(rn - 1) | = | 2 x (29 - 1) | = 2 x (512 - 1) = 2 x 511 = 1022. |
| (r - 1) | (2 - 1) |
- 2. 217 x 217 + 183 x 183 =?
Options- A. 79698
- B. 80578
- C. 80698
- D. 81268 Discuss
Correct Answer: 80578
Explanation:
| (217)2 + (183)2 | = (200 + 17)2 + (200 - 17)2 |
| = 2 x [(200)2 + (17)2] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)] | |
| = 2[40000 + 289] | |
| = 2 x 40289 | |
| = 80578. |
- 3. What will be remainder when (6767 + 67) is divided by 68?
Options- A. 1
- B. 63
- C. 66
- D. 67 Discuss
Correct Answer: 66
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.
- 4.
9 + 3 + 7 + 2 - ❨ 9 + 1 ❩ =? 4 17 15
Options- A. 7+719⁄1020
- B. 9+817⁄1020
- C. 9+719⁄1020
- D. 7+817⁄1020
- E. None of these Discuss
Correct Answer: 7+817⁄1020
Explanation:
| Given sum |
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- 5. Which one of the following numbers is exactly divisible by 11?
Options- A. 235641
- B. 245642
- C. 315624
- D. 415624 Discuss
Correct Answer: 415624
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.
- 6. 3897 x 999 =?
Options- A. 3883203
- B. 3893103
- C. 3639403
- D. 3791203
- E. None of these Discuss
Correct Answer: 3893103
Explanation:
| 3897 x 999 | = 3897 x (1000 - 1) |
| = 3897 x 1000 - 3897 x 1 | |
| = 3897000 - 3897 | |
| = 3893103. |
- 7. (800 / 64) x (1296 / 36) =?
Options- A. 420
- B. 460
- C. 500
- D. 540
- E. None of these Discuss
Correct Answer: None of these
Explanation:
| Given Exp. = | 800 | x | 1296 | = 450 |
| 64 | 36 |
- 8. 2056 x 987 =?
Options- A. 1936372
- B. 2029272
- C. 1896172
- D. 1926172
- E. None of these Discuss
Correct Answer: 2029272
Explanation:
| 2056 x 987 | = 2056 x (1000 - 13) |
| = 2056 x 1000 - 2056 x 13 | |
| = 2056000 - 26728 | |
| = 2029272. |
- 9. If a and b are odd numbers, then which of the following is even?
Options- A. a + b
- B. a + b + 1
- C. ab
- D. ab + 2
- E. None of these Discuss
Correct Answer: a + b
Explanation:
The sum of two odd number is even. So, a + b is even.
- 10. How many natural numbers are there between 23 and 100 which are exactly divisible by 6?
Options- A. 8
- B. 11
- C. 12
- D. 13
- E. None of these Discuss
Correct Answer: 13
Explanation:
Required numbers are 24, 30, 36, 42, ..., 96
This is an A.P. in which a = 24, d = 6 and l = 96
Let the number of terms in it be n.
Then tn = 96 ⟹ a + (n - 1)d = 96
⟹ 24 + (n - 1) x 6 = 96
⟹ (n - 1) x 6 = 72
⟹ (n - 1) = 12
⟹ n = 13
Required number of numbers = 13.
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