A number consists of two digits whose sum is 10 If the digits of the number are reversed then the nu...........

Quantitative Aptitude (CDS) Number System

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A number consists of two digits whose sum is 10. If the digits of the number are reversed, then the

number decreased by 36. Which of the following is/are correct?

I. The number is divisible by a composite number.

II. The number is a multiple of a prime number.

Select the correct answer using the codes given below

Only I

Only II

Both I and II

Neither I nor II

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Explanation:

Let the two- digit number be 10x+y
According to the question
x + y = 10 … … . . (i)
10y + x + 36 = 10x + y
⇒ −9y + 9x = 36
⇒ x + y = 10
⇒ x − y = 4 … … … (ii)
On adding (i) and (ii) we get
⇒ 2x = 14 ⇒ x = 7
On putting the value of x in equation (i) we get
7 + y = 10 ⇒ y = 3
The required number is 73 which is neither divisible by a composite number nor a multiple of a prime number.