Question

When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. By which of the following might her incorrect sum have differed from the correct one?

$45$

$46$

$47$

$48$

$49$

Video solution:

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Written solution:

If the last two digits of the score are $10a+b$ , then reversing those digits gives $10b+a$ . The difference is $(10a+b)-(10b+a)=9(a-b),$ so the incorrect sum must differ from the correct sum by a multiple of $9$ .

Among the answer choices, only $45$ is divisible by $9$ .

Thus, A is the correct answer.

2013 AMC 8 Problem 13

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Written solution:

Problem 13 in Other Years