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- Question
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
- 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.
- 1. How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336
Options- A. 4
- B. 5
- C. 6
- D. 7 Discuss
- 2. (51 + 52 + 53 + ... + 100) =?
Options- A. 2525
- B. 2975
- C. 3225
- D. 3775 Discuss
- 3. How many prime numbers are less than 50?
Options- A. 16
- B. 15
- C. 14
- D. 18 Discuss
- 4. The sum all even natural numbers between 1 and 31 is:
Options- A. 16
- B. 128
- C. 240
- D. 512 Discuss
- 5. The sum of first five prime numbers is:
Options- A. 11
- B. 18
- C. 26
- D. 28 Discuss
- 6. 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
- 7. The largest 5 digit number exactly divisible by 91 is:
Options- A. 99921
- B. 99918
- C. 99981
- D. 99971
- E. None of these Discuss
- 8. The sum of even numbers between 1 and 31 is:
Options- A. 6
- B. 28
- C. 240
- D. 512 Discuss
- 9. 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
- 10. 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
Numbers problems
Search Results
Correct Answer: 4
Explanation:
132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 → 11,3,4 (/)
396 → 11,3,4 (/)
462 → 11,3 (X)
792 → 11,3,4 (/)
968 → 11,4 (X)
2178 → 11,3 (X)
5184 → 3,4 (X)
6336 → 11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
Correct Answer: 3775
Explanation:
S n = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)
| = | 100 | x (1 + 100) - | 50 | x (1 + 50) |
| 2 | 2 |
= (50 x 101) - (25 x 51)
= (5050 - 1275)
= 3775.
Correct Answer: 15
Explanation:
Prime numbers less than 50 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Their number is 15
Correct Answer: 240
Explanation:
Required sum = (2 + 4 + 6 + ... + 30)
This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30.
Let the number of terms be n. Then,
tn = 30 ⟹ a + (n - 1)d = 30
⟹ 2 + (n - 1) x 2 = 30
⟹ n - 1 = 14
⟹ n = 15
| ∴Sn = | n | (a + l) | = | 15 | x (2 + 30) = 240. |
| 2 | 2 |
Correct Answer: 28
Explanation:
Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
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
Correct Answer: 99918
Explanation:
Largest 5-digit number = 99999
91) 99999 (1098
91
---
899
819
----
809
728
---
81
---
Required number = (99999 - 81)
= 99918.
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 |
Correct Answer: 47619
Explanation:
By hit and trial, we find that
47619 x 7 = 333333.
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.
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