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Problem 182

Number theory Difficulty 1.4 Multiple choice CEMC Pascal · Canada · 2014

In the subtraction shown, $X$ and $Y$ are digits. What is the value of $X+Y$ ?

Pick one

Official solution

We rearrange the given subtraction to create the addition statement $45+8Y=1X2$ .

Next, we consider the units digits.

From the statement, the sum $5+Y$ has a units digit of 2. This means that $Y=7$ . This is the only possibility. Therefore, we have $45+87 = 1X2$ .

But $45+87=132$ , so $X=3$ .

Therefore, $X+Y=3+7=10$ .

(We can check that $132 - 87 = 45$ , as required.)

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.