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- Question
397 x 397 + 104 x 104 + 2 x 397 x 104 =?
Options- A. 250001
- B. 251001
- C. 260101
- D. 261001
- Correct Answer
- 251001
ExplanationGiven 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 - 1. 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
- 2. 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
- 3. What value should come in place of the question mark(?) in the following question? (?) - 19657 - 33994 = 9999
Options- A. 63650
- B. 53760
- C. 59640
- D. 61560
- E. None of these Discuss
- 4. Which of the following numbers is divisible by each one of 3, 7, 9 and 11?
Options- A. 639
- B. 2079
- C. 3791
- D. 37911
- E. None of these Discuss
- 5. (12)3 x 64 ÷ 432 =?
Options- A. 5184
- B. 5060
- C. 5148
- D. 5084
- E. None of these Discuss
- 6. 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
- 7. 1904 x 1904 =?
Options- A. 3654316
- B. 3632646
- C. 3625216
- D. 3623436
- E. None of these Discuss
- 8. 2 + 22 + 23 + ... + 29 =?
Options- A. 2044
- B. 1022
- C. 1056
- D. None of these Discuss
- 9. 217 x 217 + 183 x 183 =?
Options- A. 79698
- B. 80578
- C. 80698
- D. 81268 Discuss
- 10. What will be remainder when (6767 + 67) is divided by 68?
Options- A. 1
- B. 63
- C. 66
- D. 67 Discuss
Numbers problems
Search Results
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: 63650
Explanation:
19657 Let x - 53651 = 9999 33994 Then, x = 9999 + 53651 = 63650 ----- 53651 -----
Correct Answer: 2079
Explanation:
639 is not divisible by 7
2079 is divisible by each of 3, 7, 9, 11.
Correct Answer: 5184
Explanation:
| Given Exp. = | (12)3 x 64 | = | (12)3 x 64 | = (12)2 x 62 = (72)2 = 5184 |
| 432 | 12 x 62 |
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: 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: 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) |
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.
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