AMC8 2016

AMC8 2016 · Q11

AMC8 2016 · Q11. It mainly tests Fractions, Digit properties (sum of digits, divisibility tests).

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.

确定有多少个两位数满足以下性质：将该数与其数字反转后得到的数相加，和为132。

(A) 5 5

(B) 7 7

(D) 11 11

(E) 12 12

Answer

Correct choice: (B)

正确答案：（B）

Solution

Let $ab$ be the two-digit number. Then $132=(10a+b)+(10b+a)=11(a+b)$. Thus $a+b=12$. The possible numbers are: $39, 93, 48, 84, 57, 75,$ and $66$. There are seven two-digit numbers that meet this criterion.

设两位数为 $ab$。则 $132=(10a+b)+(10b+a)=11(a+b)$，因此 $a+b=12$。可能的数有：$39, 93, 48, 84, 57, 75, 66$。共有七个符合条件的两位数。

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