Below are 3 number system questions to practice for CTS papers.

Question 1

Find the remainder when 6²³ is divided by 5 ?

a. 2 b. 4 c. 1 d. 3

Answer : c.1

Solution :

6² = 36 which has 6 in unit digit again.
6³ = 216 which has 6 in unit digit again.
Similarly for any higher powers, the unit digit will be 6 always.
Hence, 6²³ will have 6 in unit's digit as well.
Any number with 6 in unit's digit will understandably give a remainder 1 when divided by 5. Hence 1 is the answer.

Question 2

The difference between 3/5 of 2/3 of a number and 2/5 of 1/4 of the same number is 288. What is the number?

a)960 b) 850 c)895 d)955

Answer : a) 960

Solution :

Let the number be N
According to the question, (3/5 x 2/3 x N) - ( 2/5 x 1/4 x N ) = 288
2/5 N - 1/10 N = 288
4 N – N = 2880
N = 2880/3 = 960

Question 3

What is the number that should come in the place of question mark?
1050 420 168 67.2 ?

a) 29.88 b)10.752 c)4.3008 d)26.88

Answer : d) 26.88

Solution :

In the given sequence, you can easily find that every term is obtained from its predecessor by dividing it by 2.5 as given below.
1050 divided by 2.5 = 420
420 divided by 2.5 = 168
168 divided by 2.5 = 67.2
67.2 divided by 2.5 = 26.88
Hence the answer is 26.88