Numbers problems
- 1. On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:
Options- A. 10
- B. 11
- C. 12
- D. 13 Discuss
Correct Answer: 10
Explanation:
Clearly, (2272 - 875) = 1397, is exactly divisible by N.
Now, 1397 = 11 x 127
∴ The required 3-digit number is 127, the sum of whose digits is 10.
- 2. If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11?
Options- A. 4x + 6y
- B. x + y + 4
- C. 9x + 4y
- D. 4x - 9y Discuss
Correct Answer: 4x - 9y
Explanation:
By hit and trial, we put x = 5 and y = 1 so that (3 x + 7 y ) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
∴ (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.
- 3. The smallest prime number is:
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Correct Answer: 2
Explanation:
The smallest prime number is 2.
- 4. 9548 + 7314 = 8362 + (?)
Options- A. 8230
- B. 8410
- C. 8500
- D. 8600
- E. None of these Discuss
Correct Answer: 8500
Explanation:
9548 16862 = 8362 + x + 7314 x = 16862 - 8362 ----- = 8500 16862 -----
- 5. Which of the following numbers will completely divide (461 + 462 + 463 + 464)?
Options- A. 3
- B. 10
- C. 11
- D. 13 Discuss
Correct Answer: 10
Explanation:
(4 61 + 4 62 + 4 63 + 4 64 ) = 4 61 x (1 + 4 + 4 2 + 4 3 ) = 4 61 x 85
= 460 x (4 x 85)
= (460 x 340), which is divisible by 10.
- 6. The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800?
Options- A. 16
- B. 24
- C. 20
- D. 18
- E. 22 Discuss
Correct Answer: 24
Explanation:
This is an A.P. in which a = 6, d = 6 and S n = 1800
| Then, | n | [2a + (n - 1)d] = 1800 |
| 2 |
| ⟹ | n | [2 x 6 + (n - 1) x 6] = 1800 |
| 2 |
⟹ 3n (n + 1) = 1800
⟹ n(n + 1) = 600
⟹ n2 + n - 600 = 0
⟹ n2 + 25n - 24n - 600 = 0
⟹ n(n + 25) - 24(n + 25) = 0
⟹ (n + 25)(n - 24) = 0
⟹ n = 24
Number of terms = 24.
- 7. 666 / 6 / 3 =?
Options- A. 37
- B. 333
- C. 111
- D. 84
- E. None of these Discuss
Correct Answer: 37
Explanation:
| Given Exp. = 666 x | 1 | x | 1 | = 37 |
| 6 | 3 |
- 8. Which one of the following numbers is completely divisible by 99?
Options- A. 3572404
- B. 135792
- C. 913464
- D. 114345
- E. None of these Discuss
Correct Answer: 114345
Explanation:
99 = 11 x 9, where 11 and 9 are co-prime.
By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99.
- 9. (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 |
- 10. The difference between the place value and the face value of 7 in the numeral 967452 is
Options- A. 6393
- B. 5831
- C. 6993
- D. 6339 Discuss
Correct Answer: 6993
Explanation:
(Place value of 7)-(face value of 7)
=7000-7=6993.
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