Numbers problems
- 1. How many terms are there in the G.P. 3, 6, 12, 24, ... , 384?
Options- A. 8
- B. 9
- C. 10
- D. 11
- E. 7 Discuss
Correct Answer: 8
Explanation:
| Here a = 3 and r = | 6 | = 2. Let the number of terms be n. |
| 3 |
Then, tn = 384 ⟹ arn-1 = 384
⟹ 3 x 2n - 1 = 384
⟹ 2n-1 = 128 = 27
⟹ n - 1 = 7
⟹ n = 8
∴ Number of terms = 8.
- 2.
(963 + 476)2 + (963 - 476)2 =? (963 x 963 + 476 x 476)
Options- A. 1449
- B. 497
- C. 2
- D. 4
- E. None of these Discuss
Correct Answer: 2
Explanation:
| Given Exp. = | (a + b)2 + (a - b)2 | = | 2(a2 + b2) | = 2 |
| (a2 + b2) | (a2 + b2) |
- 3. Which of the following number is divisible by 24?
Options- A. 35718
- B. 63810
- C. 537804
- D. 3125736 Discuss
Correct Answer: 3125736
Explanation:
24 = 3 x8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Consider option (D),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
∴ 3125736 is divisible by (3 x 8), i.e., 24.
- 4. If the number 5 * 2 is divisible by 6, then * =?
Options- A. 2
- B. 3
- C. 6
- D. 7 Discuss
Correct Answer: 2
Explanation:
6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x
Then, (5 + x + 2) must be divisible by 3. So, x = 2.
- 5. On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5?
Options- A. 0
- B. 1
- C. 2
- D. 4 Discuss
Correct Answer: 4
Explanation:
Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
∴ x = 5k + 3
⟹ x2 = (5k + 3)2
= (25k2 + 30k + 9)
= 5(5k2 + 6k + 1) + 4
∴On dividing x2 by 5, we get 4 as remainder.
- 6. 35 + 15 x 1.5 =?
Options- A. 85
- B. 51.5
- C. 57.5
- D. 5.25
- E. None of these Discuss
Correct Answer: 57.5
Explanation:
| Given Exp. = 35 + 15 x | 3 | = 35 + | 45 | = 35 + 22.5 = 57.5 |
| 2 | 2 |
- 7. (12 + 22 + 32 + ... + 102) =?
Options- A. 330
- B. 345
- C. 365
- D. 385 Discuss
Correct Answer: 385
Explanation:
| We know that (12 + 22 + 32 + ... + n2) = | 1 | n(n + 1)(2n + 1) |
| 6 |
| Putting n = 10, required sum = | ❨ | 1 | x 10 x 11 x 21 | ❩ | = 385 |
| 6 |
- 8. 8597 -? = 7429 - 4358
Options- A. 5426
- B. 5706
- C. 5526
- D. 5476
- E. None of these Discuss
Correct Answer: 5526
Explanation:
7429 Let 8597 - x = 3071 -4358 Then, x = 8597 - 3071 ---- = 5526 3071 ----
- 9. A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:
Options- A. 0
- B. 1
- C. 2
- D. 3 Discuss
Correct Answer: 3
Explanation:
Let x = 6 q + 3.
Then, x2 = (6q + 3)2
= 36q2 + 36q + 9
= 6(6q2 + 6q + 1) + 3
Thus, when x2 is divided by 6, then remainder = 3.
- 10. 287 x 287 + 269 x 269 - 2 x 287 x 269 =?
Options- A. 534
- B. 446
- C. 354
- D. 324
- E. None of these Discuss
Correct Answer: 324
Explanation:
| Given Exp. | = a2 + b2 - 2ab, where a = 287 and b = 269 |
| = (a - b)2 = (287 - 269)2 | |
| = (182) | |
| = 324 |
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