Discussion of Question with ID = 026 under Problems-on-Numbers

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Question

When a two digit number is reversed and added to itself we get 44. The product of the digits of that number is 3. What is the number?

A

13.

B

14.

C

12.

D

15.

Soln.
Ans: a

Let the number be ab. When it is reversed and added to itself we get (10a + b) + (10b + a) = 11 × (a + b). We are given 44 = 11 × (a + b) ⇒ $a + b = 44 / 11 = 4$, so the digits are $a$ and $4 - a$. We are given their product as a × (4 - a) = 3, which is a quadratic expression that can be simplified to $(a - 1) × (3 - a) = 0$. So the number could be 13 or 31.


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