Number System - Online Test

Answer : Option C
Explaination / Solution:

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.

  x = 2.

Answer : Option A
Explaination / Solution:

The smallest 3-digit number is 100, which is divisible by 2.

 100 is not a prime number.

√101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.

101 is a prime number.

Hence 101 is the smallest 3-digit prime number.

Answer : Option D
Explaination / Solution:

(4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.

(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.

Answer : Option A
Explaination / Solution:

Answer : Option A
Explaination / Solution:

Let S_n =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.

Sn =	n	[2a + (n - 1)d]	=	45	x [2 x 1 + (45 - 1) x 1]	=		45	x 46		= (45 x 23)
	2			2				2

= 45 x (20 + 3)

= 45 x 20 + 45 x 3

= 900 + 135

= 1035.

Shorcut Method:

Sn =	n(n + 1)	=	45(45 + 1)	= 1035.
	2		2

Answer : Option D
Explaination / Solution:

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.

 3125736 is divisible by (3 x 8), i.e., 24.

Answer : Option A
Explaination / Solution:

Answer : Option B
Explaination / Solution:

x + 3699 + 1985 - 2047 = 31111

   x + 3699 + 1985 = 31111 + 2047

   x + 5684 = 33158

   x = 33158 - 5684 = 27474.

Answer : Option D
Explaination / Solution:

Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.

   x = 7.

Answer : Option D
Explaination / Solution:

(Local value of 7) - (Face value of 7) = (70000 - 7) = 69993