ExamAdept

Which of the following numbers will completely divide (49¹⁵ - 1) ?

A:

8

B:

14

C:

46

D:

50

Answer: A

(xⁿ - 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.

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If the number 5 * 2 is divisible by 6, then * = ?

A:

2

B:

3

C:

6

D:

7

Answer: A

6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.

Then, (5 + x + 2) must be divisible by 3. So, x = 2.

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(11² + 12² + 13² + ... + 20²) = ?

A:

385

B:

2485

C:

2870

D:

3255

Answer: B

(11² + 12² + 13² + ... + 20²) = (1² + 2² + 3² + ... + 20²) - (1² + 2² + 3² + ... + 10²)

	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.

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If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:

A:

3

B:

2

C:

1

D:

5

Answer: A

Given number = 97215x6

(6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11.

x = 3

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476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:

A:

7 and 4

B:

7 and 5

C:

8 and 5

D:

None of these

Answer: C

Let the given number be 476 xy 0.

Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.

And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.

x - y - 3 = 0 y = x - 3

(17 + x + y) = (17 + x + x - 3) = (2x + 14)

x= 2 or x = 8.

x = 8 and y = 5.

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Questions for: Numbers