When a number is divided by 13 the remainder is 11?

Answer: Option B

Explanation:

x = 13p + 11 and x = 17q + 9

q =	2 + 13p
17

   = (338 + 11)

   = 349

Answer: Option D

Explanation:

Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)

    = (50 x 101) - (25 x 51)

    = (5050 - 1275)

    = 3775.

Answer: Option B

Explanation:

Let the two consecutive even integers be 2n and (2n + 2). Then,

(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)

     = 2(4n + 2)

     = 4(2n + 1), which is divisible by 4.

Answer: Option E

Explanation:

551 > 22

All prime numbers less than 24 are : 2, 3, 5, 7, 11, 13, 17, 19, 23.

119 is divisible by 7; 187 is divisible by 11; 247 is divisible by 13 and 551 is divisible by 19.

So, none of the given numbers is prime.

Answer: Option C

Explanation:

437 > 22

All prime numbers less than 22 are : 2, 3, 5, 7, 11, 13, 17, 19.

161 is divisible by 7, and 221 is divisible by 13.

373 is not divisible by any of the above prime numbers.

Answer: Option C

Explanation:

Let Sn = (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

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

Answer: Option C

Explanation:

Unit digit in 34 = 1

Unit digit in 659 = 6

Unit digit in 74

Unit digit in 771 = Unit digit in [(74)17 x 73] = (1 x 3) = 3

Answer: Option D

Explanation:

Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.

   = (25k2 + 30k + 9)

   = 5(5k2 + 6k + 1) + 4

Answer: Option B

Explanation:

3-digit number divisible by 6 are: 102, 108, 114,... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then tn = 996.

Answer: Option C

Explanation:

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)

Answer: Option E

Explanation:

Clearly, 4864 is divisible by 4.

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

Answer: Option C

Explanation:

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   

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

Answer: Option A

Explanation:

Given number = 97215x6

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

Answer: Option D

Explanation:

Required sum = (2 + 3 + 5 + 7 + 11) = 28.

Note: 1 is not a prime number.

Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

Answer: Option D

Explanation:

24 = 3 x8, where 3 and 8 co-prime.

Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.

Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.

Consider option (D),

Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.

Also, 736 is divisible by 8.