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- Question
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11?
Options- A. 4x + 6y
- B. x + y + 4
- C. 9x + 4y
- D. 4x - 9y
- Correct Answer
- 4x - 9y
Explanation
By hit and trial, we put x = 5 and y = 1 so that (3 x + 7 y ) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.∴ (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.
- 1. On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:
Options- A. 10
- B. 11
- C. 12
- D. 13 Discuss
- 2. 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
- 3. 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
- 4. 8597 -? = 7429 - 4358
Options- A. 5426
- B. 5706
- C. 5526
- D. 5476
- E. None of these Discuss
- 5. (12 + 22 + 32 + ... + 102) =?
Options- A. 330
- B. 345
- C. 365
- D. 385 Discuss
- 6. The smallest prime number is:
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 7. 9548 + 7314 = 8362 + (?)
Options- A. 8230
- B. 8410
- C. 8500
- D. 8600
- E. None of these Discuss
- 8. Which of the following numbers will completely divide (461 + 462 + 463 + 464)?
Options- A. 3
- B. 10
- C. 11
- D. 13 Discuss
- 9. The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800?
Options- A. 16
- B. 24
- C. 20
- D. 18
- E. 22 Discuss
- 10. 666 / 6 / 3 =?
Options- A. 37
- B. 333
- C. 111
- D. 84
- E. None of these Discuss
Numbers problems
Search Results
Correct Answer: 10
Explanation:
Clearly, (2272 - 875) = 1397, is exactly divisible by N.
Now, 1397 = 11 x 127
∴ The required 3-digit number is 127, the sum of whose digits is 10.
Correct Answer: 324
Explanation:
| Given Exp. | = a2 + b2 - 2ab, where a = 287 and b = 269 |
| = (a - b)2 = (287 - 269)2 | |
| = (182) | |
| = 324 |
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.
Correct Answer: 5526
Explanation:
7429 Let 8597 - x = 3071 -4358 Then, x = 8597 - 3071 ---- = 5526 3071 ----
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 |
Correct Answer: 2
Explanation:
The smallest prime number is 2.
Correct Answer: 8500
Explanation:
9548 16862 = 8362 + x + 7314 x = 16862 - 8362 ----- = 8500 16862 -----
Correct Answer: 10
Explanation:
(4 61 + 4 62 + 4 63 + 4 64 ) = 4 61 x (1 + 4 + 4 2 + 4 3 ) = 4 61 x 85
= 460 x (4 x 85)
= (460 x 340), which is divisible by 10.
Correct Answer: 24
Explanation:
This is an A.P. in which a = 6, d = 6 and S n = 1800
| Then, | n | [2a + (n - 1)d] = 1800 |
| 2 |
| ⟹ | n | [2 x 6 + (n - 1) x 6] = 1800 |
| 2 |
⟹ 3n (n + 1) = 1800
⟹ n(n + 1) = 600
⟹ n2 + n - 600 = 0
⟹ n2 + 25n - 24n - 600 = 0
⟹ n(n + 25) - 24(n + 25) = 0
⟹ (n + 25)(n - 24) = 0
⟹ n = 24
Number of terms = 24.
Correct Answer: 37
Explanation:
| Given Exp. = 666 x | 1 | x | 1 | = 37 |
| 6 | 3 |
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