Numbers problems
- 1. What least number must be subtracted from 13601, so that the remainder is divisible by 87?
Options- A. 23
- B. 31
- C. 29
- D. 37
- E. 49 Discuss
Correct Answer: 29
Explanation:
87) 13601 (156
87
----
490
435
----
551
522
---
29
---
Therefore, the required number = 29.
- 2. If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
Options- A. 2
- B. 5
- C. 6
- D. 8
- E. None of these Discuss
Correct Answer: None of these
Explanation:
Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
∴ P = 1.
- 3. Which natural number is nearest to 8485, which is completely divisible by 75?
Options- A. 8475
- B. 8500
- C. 8550
- D. 8525
- E. None of these Discuss
Correct Answer: 8475
Explanation:
On dividing, we get
75) 8485 (113
75
---
98
75
----
235
225
---
10
---
Required number = (8485 - 10) // Because 10 < (75 - 10)
= 8475.
- 4.
❨ 1 - 1 ❩ + ❨ 1 - 2 ❩ + ❨ 1 - 3 ❩ + ... up to n terms =? n n n
Options- A. 1⁄2 n
- B. 1⁄2 (n - 1)
- C. 1⁄2 n(n - 1)
- D. None of these Discuss
Correct Answer: 1⁄2 n(n - 1)
Explanation:
| Given sum |
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- 5. 3 + 33 + 333 + 3.33 =?
Options- A. 362.3
- B. 372.33
- C. 702.33
- D. 702
- E. None of these Discuss
Correct Answer: 372.33
Explanation:
3 + 33 + 333 + 3.33 ------ 372.33 ------
- 6. A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:
Options- A. 553681
- B. 555181
- C. 555681
- D. 556581 Discuss
Correct Answer: 555681
Explanation:
987 = 3 x 7 x 47
So, the required number must be divisible by each one of 3, 7, 47
553681 → (Sum of digits = 28, not divisible by 3)
555181 → (Sum of digits = 25, not divisible by 3)
555681 is divisible by 3, 7, 47.
- 7. If 60% of 3/5 of a number is 36, then the number is:
Options- A. 80
- B. 100
- C. 75
- D. 90 Discuss
Correct Answer: 100
Explanation:
Let the number be x . Then
| 60% of | 3 | of x = 36 |
| 5 |
| ⟹ | 60 | x | 3 | x x = 36 |
| 100 | 5 |
| ⟹ x = | ❨ | 36 x | 25 | ❩ | = 100 |
| 9 |
∴ Required number = 100
- 8.
768 x 768 x 768 + 232 x 232 x 232 =? 768 x 768 - 768 x 232 + 232 x 232
Options- A. 1000
- B. 536
- C. 500
- D. 268
- E. None of these Discuss
Correct Answer: 1000
Explanation:
| Given Exp. = | (a3 + b3) | = (a + b) = (768 + 232) = 1000 |
| (a2 - ab + b2) |
- 9. 476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:
Options- A. 7 and 4
- B. 7 and 5
- C. 8 and 5
- D. None of these Discuss
Correct Answer: 8 and 5
Explanation:
Let the given number be 476 xy 0.
Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.
And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.
x - y - 3 = 0 ⟹ y = x - 3
(17 + x + y) = (17 + x + x - 3) = (2x + 14)
⟹ x= 2 or x = 8.
∴ x = 8 and y = 5.
- 10. (4300731) -? = 2535618
Options- A. 1865113
- B. 1775123
- C. 1765113
- D. 1675123
- E. None of these Discuss
Correct Answer: 1765113
Explanation:
Let 4300731 - x = 2535618
Then x, = 4300731 - 2535618 = 1765113
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