Numbers problems
- 1. (51+ 52 + 53 + ... + 100) =?
Options- A. 2525
- B. 2975
- C. 3225
- D. 3775 Discuss
Correct Answer: 3775
Explanation:
This is an A.P. in which a = 51, l = 100 and n = 50.
| ∴Sum = | n | (a + l) | = | 50 | x (51 + 100) = (25 x 151) = 3775. |
| 2 | 2 |
- 2. What is the unit digit in(795 - 358)?
Options- A. 0
- B. 4
- C. 6
- D. 7 Discuss
Correct Answer: 4
Explanation:
Unit digit in 7 95 = Unit digit in [(7 4 ) 23 x 7 3 ]
= Unit digit in [(Unit digit in(2401)) 23 x (343)]
= Unit digit in (1 23 x 343)
= Unit digit in (343)
= 3
Unit digit in 358 = Unit digit in [(34)14 x 32]
= Unit digit in [Unit digit in (81)14 x 32]
= Unit digit in [(1)14 x 32]
= Unit digit in (1 x 9)
= Unit digit in (9)
= 9
Unit digit in (795 - 358) = Unit digit in (343 - 9) = Unit digit in (334) = 4.
So, Option B is the answer.
- 3. The smallest 5 digit number exactly divisible by 41 is:
Options- A. 1004
- B. 10004
- C. 10045
- D. 10025
- E. None of these Discuss
Correct Answer: 10004
Explanation:
The smallest 5-digit number = 10000.
41) 10000 (243
82
---
180
164
----
160
123
---
37
---
Required number = 10000 + (41 - 37)
= 10004.
- 4. 4500 x? = 3375
Options- A. 2⁄5
- B. 3⁄4
- C. 1⁄4
- D. 3⁄5
- E. None of these Discuss
Correct Answer: 3⁄4
Explanation:
| 4500 x x = 3375 ⟹ x = | = | 3 | |
| 4 |
- 5. What value should come in place of the question mark(?) in the following question? (?) + 3699 + 1985 - 2047 = 31111
Options- A. 34748
- B. 27474
- C. 30154
- D. 27574
- E. None of these Discuss
Correct Answer: 27474
Explanation:
x + 3699 + 1985 - 2047 = 31111
⟹ x + 3699 + 1985 = 31111 + 2047
⟹ x + 5684 = 33158
⟹ x = 33158 - 5684 = 27474.
- 6. 72519 x 9999 =?
Options- A. 725117481
- B. 674217481
- C. 685126481
- D. 696217481
- E. None of these Discuss
Correct Answer: 725117481
Explanation:
| 72519 x 9999 | = 72519 x (10000 - 1) |
| = 72519 x 10000 - 72519 x 1 | |
| = 725190000 - 72519 | |
| = 725117481. |
- 7. The difference of the squares of two consecutive odd integers is divisible by which of the following integers?
Options- A. 3
- B. 6
- C. 7
- D. 8 Discuss
Correct Answer: 8
Explanation:
Let the two consecutive odd integers be (2 n + 1) and (2 n + 3). Then,
(2n + 3)2 - (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)
= (4n + 4) x 2
= 8(n + 1), which is divisible by 8.
- 8. In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
Options- A. 24
- B. 144
- C. 292
- D. 584 Discuss
Correct Answer: 584
Explanation:
5 | x z = 13 x 1 + 12 = 25
--------------
9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
--------------
13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
--------------
| 1 -12
585) 1169 (1
585
---
584
---
Therefore, on dividing the number by 585, remainder = 584.
- 9. The sum of all two digit numbers divisible by 5 is:
Options- A. 1035
- B. 1245
- C. 1230
- D. 945
- E. None of these Discuss
Correct Answer: 945
Explanation:
Required numbers are 10, 15, 20, 25, ..., 95
This is an A.P. in which a = 10, d = 5 and l = 95.
tn = 95 ⟹ a + (n - 1)d = 95
⟹ 10 + (n - 1) x 5 = 95
⟹ (n - 1) x 5 = 85
⟹ (n - 1) = 17
⟹ n = 18
| ∴Requuired Sum = | n | (a + l) | = | 18 | x (10 + 95) = (9 x 105) = 945. |
| 2 | 2 |
- 10. (35423 + 7164 + 41720) - (317 x 89) =?
Options- A. 28213
- B. 84307
- C. 50694
- D. 56094
- E. None of these Discuss
Correct Answer: 56094
Explanation:
35423 317 x 89 = 317 x (90 -1 ) + 7164 = (317 x 90 - 317) + 41720 = (28530 - 317) ----- = 28213 84307 - 28213 ----- 56094 -----
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