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### Question

When a two digit number is reversed and added to itself we get 55. The product of the digits of that number is 6. What is the number?

**A**

32.

**B**

33.

**C**

31.

**D**

34.

**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 55 = 11 × (a + b) ⇒ $a + b = 55 / 11 = 5$, so the digits are $a$ and $5 - a$. We are given their product as a × (5 - a) = 6, which is a quadratic expression that can be simplified to $(a - 3) × (2 - a) = 0$. So the number could be 32 or 23.