Number Properties

Manhattan 1st guide deals with number properties. I dont know if you have it or not but I wouldnt even take the GMAT without going through it.

Hi Felix,

Good question - my favorite thing about number properties is that you can often learn them for yourself simply by trying to "find the pattern" when approaching a question.

For example, exponents have units digit number properties in that they repeat either every first, second, or fourth exponent. Consider the number 7:

7^1 = 7
7^2 = 49
7^3 = 49 * 7, so it will end in a 3
7^4 will end in 3*7, so its units digit is a 1
7^5 will end in 1 * 7, so its units digit is 7
7^6 --> 7*7 --> 9
7^7 --> 3
7^8 --> 1

So we know that a cycle of 7, 9, 3, 1, 7, 9, 3, 1... exists for the base of 7 and its exponential units digits.

The key is that you don't really need to memorize that, as long as you can train yourself to look for patterns when you know that questions are testing number properties. Number properties are a great topic for the GMAT to test, as they're much more a thought process than any kind of specific "knowledge". I'd suggest that you go back to any Number Properties questions you've missed and train yourself to spot the pattern.