Numbers problems
- 1. What will be remainder when 17200 is divided by 18?
Options- A. 17
- B. 16
- C. 1
- D. 2 Discuss
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.
- 2. Which of the following numbers will completely divide (325 + 326 + 327 + 328)?
Options- A. 11
- B. 16
- C. 25
- D. 30 Discuss
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.
- 3.
(489 + 375)2 - (489 - 375)2 =? (489 x 375)
Options- A. 144
- B. 864
- C. 2
- D. 4
- E. None of these Discuss
Correct Answer: 4
Explanation:
| Given Exp. = | (a + b)2 - (a - b)2 | = | 4ab | = 4 |
| ab | ab |
- 4. 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 Also asked in: Bank Exams
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.
- 5. 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
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).
- 6. 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
Correct Answer: 2
Explanation:
Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x ), which must be divisible by 3.
∴ x = 2.
- 7. Which of the following is a prime number?
Options- A. 33
- B. 81
- C. 93
- D. 97 Discuss
Correct Answer: 97
Explanation:
Clearly, 97 is a prime number.
- 8. The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
Options- A. 3⁄5
- B. 3⁄10
- C. 4⁄5
- D. 4⁄3 Discuss
Correct Answer: 4⁄5
Explanation:
| Let the required fraction be x. Then | 1 | - x = | 9 |
| x | 20 |
| ∴ | 1 - x2 | = | 9 |
| x | 20 |
⟹ 20 - 20x2 = 9x
⟹ 20x2 + 9x - 20 = 0
⟹ 20x2 + 25x - 16x - 20 = 0
⟹ 5x(4x + 5) - 4(4x + 5) = 0
⟹ (4x + 5)(5x - 4) = 0
| x = | 4 |
| 5 |
- 9. -84 x 29 + 365 =?
Options- A. 2436
- B. 2801
- C. -2801
- D. -2071
- E. None of these Discuss
Correct Answer: -2071
Explanation:
| Given Exp. | = -84 x (30 - 1) + 365 |
| = -(84 x 30) + 84 + 365 | |
| = -2520 + 449 | |
| = -2071 |
- 10. It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Options- A. (216 + 1)
- B. (216 - 1)
- C. (7 x 223)
- D. (296 + 1) Discuss
Correct Answer: (296 + 1)
Explanation:
Let 2 32 = x . Then, (2 32 + 1) = ( x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
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