GMAT Question of the Day – Data Sufficiency – Number Properties/Digits

If n is a two digit positive integer, what is the units digit of n?

1) The units digit of \( n^2-n \) is 0

2) \( n^2 \) is not divisible by 2 or 5

Show the answer

Correct Answer: C.

GMAT Question of the Day Solution

There are a ton of number properties or number properties related questions on the GMAT (especially in the Data Sufficiency). How should you tackle these questions? It depends. But often creating some kind of chart or list of possibilities will help you make inferences from the given information and/or statements. Practice this skill so that you get a sense for when you should make a chart/list out options. Better to make mistakes in your Data Sufficiency practice than on your actual GMAT. There are bunch of # properties Atlantic GMAT Questions of Day on which you can practice this skill (links forthcoming).

For this question of the day a list will help you. One clue for using a list is when it is clear that there are a very limited amount of options. In this question of the day the options are limited to the digits 0-9. Once you have made the list narrow it down based on the statements. If you can narrow down the list to only one choice then the statement is sufficient. Simple right?

Statement (1) This tells us that \( n^2 \) and n have the same units digit. This narrows down our list to 0, 1, 5, and 6. Because there are multiple choices statement (1) is insufficient.

Statement (2) If \( n^2 \) is not divisible by 2 or 5 then neither is n. This tells us that the units digit cannot be 0, 2, 4, 5, 6, or 8. That leaves 1, 3, 7, and 9. Again, in GMAT Data Sufficiency multiple options means insufficient.

Statement (1) and (2) Putting them together leaves only a single option: 1. Sufficient.