Library / /225 of 482

, 2014

Number theory Difficulty 1.4 Junior Find the answer Canada

In the subtraction shown, $X$ and $Y$ are digits. What is the value of $X+Y$ ?
IMG0

Figure for this problem

Pick one

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.)

Figure for this problem

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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