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- Question
2 + 22 + 23 + ... + 29 =?
Options- A. 2044
- B. 1022
- C. 1056
- D. None of these
- Correct Answer
- 1022
ExplanationThis 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) - 1. 1904 x 1904 =?
Options- A. 3654316
- B. 3632646
- C. 3625216
- D. 3623436
- E. None of these Discuss
- 2. If the number 42573 * is exactly divisible by 72, then the minimum value of * is:
Options- A. 4
- B. 5
- C. 6
- D. 7
- E. 8 Discuss
- 3. 397 x 397 + 104 x 104 + 2 x 397 x 104 =?
Options- A. 250001
- B. 251001
- C. 260101
- D. 261001 Discuss
- 4. If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:
Options- A. 2
- B. 5
- C. 6
- D. 7
- E. None of these Discuss
- 5. If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y =?
Options- A. 2 or 6
- B. 4
- C. 4 or 8
- D. 8
- E. None of these Discuss
- 6. 217 x 217 + 183 x 183 =?
Options- A. 79698
- B. 80578
- C. 80698
- D. 81268 Discuss
- 7. What will be remainder when (6767 + 67) is divided by 68?
Options- A. 1
- B. 63
- C. 66
- D. 67 Discuss
- 8.
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
- 9. Which one of the following numbers is exactly divisible by 11?
Options- A. 235641
- B. 245642
- C. 315624
- D. 415624 Discuss
- 10. 3897 x 999 =?
Options- A. 3883203
- B. 3893103
- C. 3639403
- D. 3791203
- E. None of these Discuss
Numbers problems
Search Results
Correct Answer: 3625216
Explanation:
| 1904 x 1904 | = (1904)2 |
| = (1900 + 4)2 | |
| = (1900)2 + (4)2 + (2 x 1900 x 4) | |
| = 3610000 + 16 + 15200. | |
| = 3625216. |
Correct Answer: 6
Explanation:
72 = 9 x8, where 9 and 8 are co-prime.
The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.
Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.
∴Required value of * is 6.
Correct Answer: 251001
Explanation:
| Given Exp. | = (397)2 + (104)2 + 2 x 397 x 104 |
| = (397 + 104)2 | |
| = (501)2 = (500 + 1)2 | |
| = (5002) + (1)2 + (2 x 500 x 1) | |
| = 250000 + 1 + 1000 | |
| = 251001 |
Correct Answer: 7
Explanation:
Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
∴ x = 7.
Correct Answer: 2 or 6
Explanation:
80 = 2 x 5 x 8
Since 653xy is divisible by 2 and 5 both, so y = 0.
Now, 653x is divisible by 8, so 13x should be divisible by 8.
This happens when x = 6.
∴x + y = (6 + 0) = 6.
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. |
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.
Correct Answer: 7+817⁄1020
Explanation:
| Given sum |
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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.
Correct Answer: 3893103
Explanation:
| 3897 x 999 | = 3897 x (1000 - 1) |
| = 3897 x 1000 - 3897 x 1 | |
| = 3897000 - 3897 | |
| = 3893103. |
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