ExamAdept

The sum of even numbers between 1 and 31 is:

A:

6

B:

28

C:

240

D:

512

Answer: C

Let S_n = (2 + 4 + 6 + ... + 30). This is an A.P. in which a = 2, d = 2 and l = 30

Let the number of terms be n. Then,

a + (n - 1)d = 30

2 + (n - 1) x 2 = 30

n = 15.

S_n =	n	(a + l)	=	15	x (2 + 30) = (15 x 16) = 240.
	2			2

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2 + 2² + 2³ + ... + 2⁹ = ?

A:

2044

B:

1022

C:

1056

D:

None of these

Answer: B

This is a G.P. in which a = 2, r =	2²	= 2 and n = 9.
	2

S_n =	a(rⁿ - 1)	=	2 x (2⁹ - 1)	= 2 x (512 - 1) = 2 x 511 = 1022.
	(r - 1)		(2 - 1)

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In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?

A:

0

B:

12

C:

13

D:

20

Answer: D

Number = (12 x 35)

Correct Quotient = 420 ÷ 21 = 20

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9548 + 7314 = 8362 + (?)

A:

8230

B:

8410

C:

8500

D:

8600

Answer: C

  9548          16862 = 8362 + x 
+ 7314          x  = 16862 - 8362 
 -----             = 8500 
 16862
 -----

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If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?

A:

4x + 6y

B:

x + y + 4

C:

9x + 4y

D:

4x - 9y

Answer: D

By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.

(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;

(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;

(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;

(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.

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Questions for: Numbers