Numbers problems
- 1. Which one of the following is not a prime number?
Options- A. 31
- B. 61
- C. 71
- D. 91 Discuss
Correct Answer: 91
Explanation:
91 is divisible by 7. So, it is not a prime number.
- 2. If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be:
Options- A. 1
- B. 2
- C. 3
- D. 4
- E. None of these Also asked in: Bank Exams, CAT
Correct Answer: 3
Explanation:
Then number 6 x 2 must be divisible by 8.
∴ x = 3, as 632 is divisible 8.
- 3. (12)3 x 64 ÷ 432 =?
Options- A. 5184
- B. 5060
- C. 5148
- D. 5084
- E. None of these Discuss
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 |
- 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
Correct Answer: 2079
Explanation:
639 is not divisible by 7
2079 is divisible by each of 3, 7, 9, 11.
- 5. 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
Correct Answer: 63650
Explanation:
19657 Let x - 53651 = 9999 33994 Then, x = 9999 + 53651 = 63650 ----- 53651 -----
- 6. 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
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.
- 7. 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
Correct Answer: 7
Explanation:
Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
∴ x = 7.
- 8. 397 x 397 + 104 x 104 + 2 x 397 x 104 =?
Options- A. 250001
- B. 251001
- C. 260101
- D. 261001 Discuss
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 |
- 9. 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 Also asked in: Bank Exams
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.
- 10. 1904 x 1904 =?
Options- A. 3654316
- B. 3632646
- C. 3625216
- D. 3623436
- E. None of these Discuss
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. |
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