ExamAdept

A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:

A:

1

B:

2

C:

8

D:

11

Answer: A

Let x = 296q + 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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-84 x 29 + 365 = ?

A:

2436

B:

2801

C:

-2801

D:

-2071

Answer: D

Given Exp.	= -84 x (30 - 1) + 365
	= -(84 x 30) + 84 + 365
	= -2520 + 449
	= -2071

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Which one of the following is the common factor of (47⁴³ + 43⁴³) and (47⁴⁷ + 43⁴⁷) ?

A:

(47 - 43)

B:

(47 + 43)

C:

(47⁴³ + 43⁴³)

D:

None of these

Answer: B

When n is odd, (xⁿ + aⁿ) is always divisible by (x + a).

Each one of (47⁴³ + 43⁴³) and (47⁴⁷ + 43⁴⁷) is divisible by (47 + 43).

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If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:

A:

2

B:

5

C:

6

D:

8

Answer: E

Clearly, 4864 is divisible by 4.

So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.

P = 1.

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On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?

A:

0

B:

3

C:

5

D:

11

Answer: C

Let x be the number and y be the quotient. Then,

x = 357 x y + 39

= (17 x 21 x y) + (17 x 2) + 5

= 17 x (21y + 2) + 5)

Required remainder = 5.

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Questions for: Numbers