# GMAT Question of the Day – DS – Number Properties Puzzle 3 # GMAT Question of the Day – Data Sufficiency – Number Properties

How many integers between x and 10! are divisible by 3?

(1) x^2 = x

(2) -x|x| = x

<[spoiler]strong>D.[/spoiler]

## GMAT Question of the Day Solution

This GMAT question of the day presents what seems like a giant universe of options. When you see a GMAT question similar to this you don’t need to worry because usually the universe is much smaller than it seems. Let’s just stay focused on the question. In this we’re not solving for a specific value. We just need to know about the number of numbers that are divisible by three between x and 10!. Statement (1) tells us that x is either 1 or 0. You might say insufficient because there are two possibilities for x but remember that we are not solving for x. x = 1 and x = 0 produce the same outcome because the first integer that is divisible by three is three itself. Of course 0 is divisible by three (and every other number) but zero doesn’t count because the questions use the word “between” which means non inclusive. Sufficient. Statement (2) tells us that x must be 0. Sufficient. ## More GMAT Data Sufficiency Divisibility Practice Questions

Here’s another GMAT Data Sufficiency Divisibility question from the Official Guide: A school administrator will assign each student in a group of N