Numbers problems
- 1. The difference of the squares of two consecutive even integers is divisible by which of the following integers?
Options- A. 3
- B. 4
- C. 6
- D. 7 Discuss
Correct Answer: 4
Explanation:
Let the two consecutive even integers be 2 n and (2 n + 2). Then,
(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.
- 2. When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number?
Options- A. 339
- B. 349
- C. 369
- D. Data inadequate Discuss
Correct Answer: 349
Explanation:
x = 13 p + 11 and x = 17 q + 9
∴ 13p + 11 = 17q + 9
⟹ 17q - 13p = 2
| ⟹ q = | 2 + 13p |
| 17 |
| The least value of p for which q = | 2 + 13p | is a whole number is p = 26 |
| 17 |
∴ x = (13 x 26 + 11)
= (338 + 11)
= 349
- 3. The largest 5 digit number exactly divisible by 91 is:
Options- A. 99921
- B. 99918
- C. 99981
- D. 99971
- E. None of these Discuss
Correct Answer: 99918
Explanation:
Largest 5-digit number = 99999
91) 99999 (1098
91
---
899
819
----
809
728
---
81
---
Required number = (99999 - 81)
= 99918.
- 4. The sum of even numbers between 1 and 31 is:
Options- A. 6
- B. 28
- C. 240
- D. 512 Discuss
Correct Answer: 240
Explanation:
Let S n = (2 + 4 + 6 + ... + 30). This is an A.P. in which a = 2, d = 2 and l = 30
Let the number of terms be n. Then,
a + (n - 1)d = 30
⟹ 2 + (n - 1) x 2 = 30
⟹ n = 15.
| ∴Sn = | n | (a + l) | = | 15 | x (2 + 30) = (15 x 16) = 240. |
| 2 | 2 |
- 5. On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:
Options- A. 47619
- B. 47719
- C. 48619
- D. 47649 Discuss
Correct Answer: 47619
Explanation:
By hit and trial, we find that
47619 x 7 = 333333.
- 6. A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:
Options- A. 1
- B. 2
- C. 8
- D. 11 Discuss
Correct Answer: 1
Explanation:
Let x = 296 q + 75
= (37 x 8q + 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1.
- 7. A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be
Options- A. 1, 2
- B. 2, 3
- C. 3, 2
- D. 4, 1 Discuss
Correct Answer: 2, 3
Explanation:
4 | x y = (5 x 1 + 4) = 9 -------- 5 | y -1 x = (4 x y + 1) = (4 x 9 + 1) = 37 -------- | 1 -4 Now, 37 when divided successively by 5 and 4, we get 5 | 37 --------- 4 | 7 - 2 --------- | 1 - 3 Respective remainders are 2 and 3.
- 8. (935421 x 625) =?
Options- A. 575648125
- B. 584638125
- C. 584649125
- D. 585628125 Discuss
Correct Answer: 584638125
Explanation:
| 935421 x 625 = 935421 x 54 = 935421 x | ❨ | 10 | ❩ | 4 |
| 2 |
| = | 935421 x 104 | = | 9354210000 |
| 24 | 16 |
= 584638125
- 9.
753 x 753 + 247 x 247 - 753 x 247 =? 753 x 753 x 753 + 247 x 247 x 247
Options- A. 1⁄1000
- B. 1⁄506
- C. 253⁄500
- D. None of these Discuss
Correct Answer: 1⁄1000
Explanation:
| Given Exp. = | (a2 + b2 - ab) | = | 1 | = | 1 | = | 1 |
| (a3 + b3) | (a + b) | (753 + 247) | 1000 |
- 10. A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:
Options- A. 214
- B. 476
- C. 954
- D. 1908 Discuss
Correct Answer: 214
Explanation:
4 | x z = 6 x 1 + 4 = 10 ----------- 5 | y -2 y = 5 x z + 3 = 5 x 10 + 3 = 53 ----------- 6 | z - 3 x = 4 x y + 2 = 4 x 53 + 2 = 214 ----------- | 1 - 4 Hence, required number = 214.
More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.