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- Question
Which of the following numbers will completely divide (325 + 326 + 327 + 328)?
Options- A. 11
- B. 16
- C. 25
- D. 30
- Correct Answer
- 30
Explanation
(3 25 + 3 26 + 3 27 + 3 28 ) = 3 25 x (1 + 3 + 3 2 + 3 3 ) = 3 25 x 40= 324 x 3 x 4 x 10
= (324 x 4 x 30), which is divisible by30.
- 1. What will be remainder when 17200 is divided by 18?
Options- A. 17
- B. 16
- C. 1
- D. 2 Discuss
- 2. (112 + 122 + 132 + ... + 202) =?
Options- A. 385
- B. 2485
- C. 2870
- D. 3255 Discuss
- 3. The difference between the local value and the face value of 7 in the numeral 32675149 is
Options- A. 75142
- B. 64851
- C. 5149
- D. 69993
- E. None of these Discuss
- 4. What smallest number should be added to 4456 so that the sum is completely divisible by 6?
Options- A. 4
- B. 3
- C. 2
- D. 1
- E. None of these Discuss
- 5. If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:
Options- A. 3
- B. 2
- C. 1
- D. 5
- E. None of these Discuss
- 6.
(489 + 375)2 - (489 - 375)2 =? (489 x 375)
Options- A. 144
- B. 864
- C. 2
- D. 4
- E. None of these Discuss
- 7. On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder?
Options- A. 4
- B. 5
- C. 6
- D. 7 Discuss
- 8. Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347)?
Options- A. (47 - 43)
- B. (47 + 43)
- C. (4743 + 4343)
- D. None of these Discuss
- 9. If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
Options- A. 0
- B. 1
- C. 2
- D. None of these Discuss
- 10. Which of the following is a prime number?
Options- A. 33
- B. 81
- C. 93
- D. 97 Discuss
Numbers problems
Search Results
Correct Answer: 1
Explanation:
When n is even. ( x n - a n ) is completely divisibly by ( x + a )
(17200 - 1200) is completely divisible by (17 + 1), i.e., 18.
⟹ (17200 - 1) is completely divisible by 18.
⟹ On dividing 17200 by 18, we get 1 as remainder.
Correct Answer: 2485
Explanation:
(11 2 + 12 2 + 13 2 + ... + 20 2 ) = (1 2 + 2 2 + 3 2 + ... + 20 2 ) - (1 2 + 2 2 + 3 2 + ... + 10 2 )
| [ | Ref: (12 + 22 + 32 + ... + n2) = | 1 | n(n + 1)(2n + 1) | ] | |
| 6 |
| = | ❨ | 20 x 21 x 41 | - | 10 x 11 x 21 | ❩ |
| 6 | 6 |
= (2870 - 385)
= 2485.
Correct Answer: 69993
Explanation:
(Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
Correct Answer: 2
Explanation:
6) 4456 (742
42
---
25
24 Therefore, Required number = (6 - 4) = 2.
---
16
12
---
4
Correct Answer: 3
Explanation:
Given number = 97215 x 6
(6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11.
∴ x = 3
Correct Answer: 4
Explanation:
| Given Exp. = | (a + b)2 - (a - b)2 | = | 4ab | = 4 |
| ab | ab |
Correct Answer: 5
Explanation:
Formula: (Divisor*Quotient) + Remainder = Dividend.
Soln:
(56*Q)+29 = D -------(1)
D%8 = R -------------(2)
From equation(2),
((56*Q)+29)%8 = R.
=> Assume Q = 1.
=> (56+29)%8 = R.
=> 85%8 = R
=> 5 = R.
Correct Answer: (47 + 43)
Explanation:
When n is odd, ( x n + a n ) is always divisible by ( x + a ).
∴Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43).
Correct Answer: 2
Explanation:
Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x ), which must be divisible by 3.
∴ x = 2.
Correct Answer: 97
Explanation:
Clearly, 97 is a prime number.
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