Maths Olympiad Prep

Track / Stage 1 / 186 of 240 #186 of 2444

Problem 186

Number theory Difficulty 1.5 Multiple choice CEMC Gauss (Grade 7) · Canada · 2012

The digits 2, 4, 6 and 8 are each used once to create two 2-digit numbers. What is the largest possible difference between the two 2-digit numbers?

Pick one

Next problem →

Official solution

To make the difference as large as possible, we make one number as large as possible and the other number as small as possible.

The tens digit of a number contributes more to its value than its units digit.

Thus, we construct the largest possible number by choosing 8 (the largest digit) to be its tens digit, and by choosing 6 (the second largest digit) to be the ones digit.

Similarly, we construct the smallest possible number by choosing 2 (the smallest digit) to be its tens digit, and 4 (the second smallest digit) to be its ones digit.
The largest possible difference is 86−24=6286-24=62.

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