Dear Reader, Below are three sample number system questions to practice for CTS.

Question 1

25^2.7 x 5^4.2÷ 5^6.4 = 25^(?)

a) 1.7 b) 3.2 c) 1.6 d) 3.6

Answer : c)1.6

Solution :

(5²)^2.7 x 5^4.2÷ 5 ^6.4 =(5²) ^?

(5^5.4 x 5^4.2)/ 5^6.4 = (5²)^?

5^3.2 = (5²)^?
2? = 3.2
? = 3.2 / 2 = 1.6

Question 2

When a number is divided by 138 the remainder is 26. What will be the remainder if the same number is divided by 23?

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

Answer : b)3

Solution :

138 is a multiple of 23. (23 x 6 = 138).
So when the number is divided by 23 the remainder will be 26-23 = 3.

Question 3

Mr. Mukhambo has two numbers and say that their difference, their sum and their product are to one another as 1:7:24. Mukhambo wants to find out whether you can get him the product of those two numbers:

a) 24 b) 6 c) 48 d) 12

Answer : c)48

Solution :

Difference between the two numbers ratio wise is 1
Sum of the two numbers ratio wise is 7
Products of the two numbers ratio wise is 24.
i.e 1:7:24
Choice b) and d) cannot be the answer because product has to be ratio wise 24.
It is case a) or c)
For product to be 24 it has to be 4 and 6. But their sum is 10 and difference is 6
So 2:10:24 simplifying also it comes 1:5:12. This cannot be the answer.
For product to be 48 – numbers can be 6 and 8.
Sum – 14
Product – 48 So difference:sum:product = 2:14:48 = 1: 7: 24