ExamAdept

What is the unit digit in(7⁹⁵ - 3⁵⁸)?

A:

0

B:

4

C:

6

D:

7

Answer: B

Unit digit in 7⁹⁵ = Unit digit in [(7⁴)²³ x 7³]
= Unit digit in [(Unit digit in(2401))²³ x (343)]
= Unit digit in (1²³ x 343)
= Unit digit in (343)
= 3

Unit digit in 3⁵⁸ = Unit digit in [(3⁴)¹⁴ x 3²]
= Unit digit in [Unit digit in (81)¹⁴ x 3²]
= Unit digit in [(1)¹⁴ x 3²]
= Unit digit in (1 x 9)
= Unit digit in (9)
= 9

Unit digit in (7⁹⁵ - 3⁵⁸) = Unit digit in (343 - 9) = Unit digit in (334) = 4.

So, Option B is the answer.

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1904 x 1904 = ?

A:

3654316

B:

3632646

C:

3625216

D:

3623436

Answer: C

1904 x 1904	= (1904)²
	= (1900 + 4)²
	= (1900)² + (4)² + (2 x 1900 x 4)
	= 3610000 + 16 + 15200.
	= 3625216.

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(51+ 52 + 53 + ... + 100) = ?

A:

2525

B:

2975

C:

3225

D:

3775

Answer: D

This is an A.P. in which a = 51, l = 100 and n = 50.

Sum =	n	(a + l)	=	50	x (51 + 100) = (25 x 151) = 3775.
	2			2

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The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ?

A:

16

B:

24

C:

20

D:

18

Answer: B

This is an A.P. in which a = 6, d = 6 and S_n = 1800

Then,	n	[2a + (n - 1)d] = 1800
	2

	n	[2 x 6 + (n - 1) x 6] = 1800
	2

3n (n + 1) = 1800

n(n + 1) = 600

n² + n - 600 = 0

n² + 25n - 24n - 600 = 0

n(n + 25) - 24(n + 25) = 0

(n + 25)(n - 24) = 0

n = 24

Number of terms = 24.

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Which one of the following numbers is completely divisible by 99?

A:

3572404

B:

135792

C:

913464

D:

114345

Answer: D

99 = 11 x 9, where 11 and 9 are co-prime.

By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99.

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Questions for: Numbers