Factoring – A Crucial Factor

(This is one of a series of GMAT tips that we offer on our blog.)

The quantitative section of the GMAT has been fascinating to follow as it has evolved; with the need to create a more difficult section that remains consistent with its goals, the GMAT authors – who are concerned much more with your analytical ability than your propensity for ‘crunching numbers” – have begun to emphasize “number theory” to a large extent.

To avoid losing time on tedious calculations – a common “bait” technique that the GMAT employs regularly – and to confidently answer correctly and efficiently, you can employ factoring techniques to test answer choices for properties that you know must be contained in the correct answer. In other words, if you can prove that a correct answer, for example, must be divisible by 3, you are not simply guessing if you eliminate all of the answer choices that are not.

A few of the quick-checks you can perform to efficiently eliminate incorrect answer choices are:

- Numbers must be even (or divisible by 2) – must end in 0, 2, 4, 6, or 8
- Numbers must be odd (not divisible by 2) – must end in 1, 3, 5, 7, or 9
- Numbers must be divisible by 3 – the sum of the digits in the number is a multiple of 3
- Numbers must be divisible by 5 – must end in 0 or 5
- Numbers must be divisible by 6 – an even number that is divisible by 3 (**this is a favorite, as it doesn’t appear to have an easy check, but is actually the combination of two easy checks, as a number divisible by 6 must be divisible by 2 and 3)
- Numbers must be divisible by 9 – the sum of the digits is a multiple of 9
- Numbers must be divisible by 10 – must end in 0

Ask yourself whether you can solve problems simply by using factorization number theory and you will undoubtedly save time over the course of the exam.

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