Question

Determine how many two-digit numbers satisfy the following property:

When the number is added to the number obtained by reversing its digits, the sum is $132.$

$5$

$7$

$9$

$11$

$12$

Answer: B

Concepts:digits place value

Difficulty rating: 1100

Video solution:

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Written solution:

Let $a$ be the tens digit and $b$ the units digit. Adding the number and its reversal gives $\begin{aligned} (10a+b)+(10b+a)&=132\\ 11(a+b)&=132, \end{aligned}$ so $a+b=12$ . The valid digit pairs are $(3,9),(4,8),(5,7),(6,6),$ $(7,5),(8,4),(9,3),$ giving $7$ numbers.

Thus, B is the correct answer.

2016 AMC 8 Problem 11

Answer: B

Difficulty rating: 1100

Video solution:

Written solution:

Problem 11 in Other Years