# Discussion of Question with ID = 046 under Problems-on-Numbers

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### Question

When a two digit number is reversed and added to itself we get 154. The product of the digits of that number is 49. What is the number?

A

77.

B

78.

C

76.

D

79.

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 154 = 11 × (a + b) ⇒ \$a + b = 154 / 11 = 14\$, so the digits are \$a\$ and \$14 - a\$. We are given their product as a × (14 - a) = 49, which is a quadratic expression that can be simplified to \$(a - 7) × (7 - a) = 0\$. So the number could be 77 or 77.