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- Question
On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will the remainder?
Options- A. 0
- B. 1
- C. 2
- D. 3
- Correct Answer
- 1
ExplanationNumber = 269 x 68 + 0 = 18292 67) 18292 (273 134 ---- 489 469 ---- 202 201 --- 1 --- Therefore, Required remainder = 1 - 1. 107 x 107 + 93 x 93 =?
Options- A. 19578
- B. 19418
- C. 20098
- D. 21908
- E. None of these Discuss
- 2. Which natural number is nearest to 9217, which is completely divisible by 88?
Options- A. 9152
- B. 9240
- C. 9064
- D. 9184
- E. None of these Discuss
- 3. The unit digit in the product (784 x 618 x 917 x 463) is:
Options- A. 2
- B. 3
- C. 4
- D. 5 Discuss
- 4. Which of the following numbers will completely divide (4915 - 1)?
Options- A. 8
- B. 14
- C. 46
- D. 50 Discuss
- 5. If n is a natural number, then (6n2 + 6n) is always divisible by:
Options- A. 6 only
- B. 6 and 12 both
- C. 12 only
- D. by 18 only Discuss
- 6. What least number must be added to 1056, so that the sum is completely divisible by 23?
Options- A. 2
- B. 3
- C. 18
- D. 21
- E. None of these Discuss
- 7. Which one of the following can't be the square of natural number?
Options- A. 30976
- B. 75625
- C. 28561
- D. 143642
- E. None of these Discuss
- 8. Which one of the following is a prime number?
Options- A. 119
- B. 187
- C. 247
- D. 551
- E. None of these Discuss
- 9. The sum of first five prime numbers is:
Options- A. 11
- B. 18
- C. 26
- D. 28 Discuss
- 10. The sum all even natural numbers between 1 and 31 is:
Options- A. 16
- B. 128
- C. 240
- D. 512 Discuss
Numbers problems
Search Results
Correct Answer: 20098
Explanation:
| 107 x 107 + 93 x 93 | = (107)2 + (93)2 |
| = (100 + 7)2 + (100 - 7)2 | |
| = 2 x [(100)2 + 72] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2) ] | |
| = 20098 |
Correct Answer: 9240
Explanation:
On dividing we get,
88) 9217 (104
88
----
417
352
----
65
----
Therefore, Required number = 9217 + (88 - 65) // Because (88 - 65) < 65.
= 9217 + 23
= 9240.
Correct Answer: 2
Explanation:
Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2
Correct Answer: 8
Explanation:
( x n - 1) will be divisibly by ( x + 1) only when n is even.
(4915 - 1) = {(72)15 - 1} = (730 - 1), which is divisible by (7 +1), i.e., 8.
Correct Answer: 6 and 12 both
Explanation:
(6 n 2 + 6 n ) = 6 n ( n + 1), which is always divisible by 6 and 12 both, since n ( n + 1) is always even.
Correct Answer: 2
Explanation:
23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2.
Correct Answer: 143642
Explanation:
The square of a natural number nerver ends in 2.
∴ 143642 is not the square of natural number.
Correct Answer: None of these
Explanation:
√551 > 22
All prime numbers less than 24 are : 2, 3, 5, 7, 11, 13, 17, 19, 23.
119 is divisible by 7; 187 is divisible by 11; 247 is divisible by 13 and 551 is divisible by 19.
So, none of the given numbers is prime.
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: 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 |
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