Happy New Year! With a new year comes a new number – even if you’re still writing 2012 on checks for the next month or two (if you write checks at all…it is 2013 after all), the year is now 2013. And if 2013 is the year that you’re going to get serious about going to business school, the number 2013 gives you a great opportunity to learn to think in terms of GMAT math.

Because you can’t use a calculator on the GMAT, being able to perform mental calculations and think in terms of properties of numbers is critical for efficiency on this test. To become an expert at mental math, you should recognize that there are numbers all around you, including 2013. A few ways that 2013 can help you are:

Know the major divisibility properties

If a number ends in 0, 2, 4, 6, or 8 it’s even, which means it’s divisible by 2. 2013 is not – it’s odd.
It the sum of the digits of a number is a multiple of 3, that number is divisible by 3. For 2013, 2 + 0 + 1 + 3 = 6, so 2013 is a multiple of 3.
If the sum of the digits of a number is a multiple of 9, that number is divisible by 9. Since 2013 sums to 6, it’s not divisible by 9.

One of the most efficient ways to perform calculations is to “find zeroes”. It’s difficult, for example, to divide 2013 by 3 in your head, but you can pretty easily divide 2100 by 3 (it’s 700). And 2013 is 87 less than 2100, so now you need to determine how many threes to subtract. 90 is 30*3, so 87 is one less than that: 29*3. So the answer is 700-29 = 671. To factor out 2013, you can break it into 671 * 3.

Now, that’s one example. How can you systematically do this over time? Break “technical” calculations in two, finding a nearby number that’s easy to calculate (usually finding something that ends in as many zeroes as possible) and taking care of that first. Let’s try that now with 671, since that will help us break down 2013 further.

671 is not divisible by 3 or 5. To see if you can break it down by 7, consider a nearby multiple of 7 that you know: 700. 700 – 671 is 29, which isn’t a multiple of 7, so you know that 671 isn’t a multiple of 7 either. But 11…11*6 is 66, so 660 must be 11*60. And to get from 660 to 671 you just add one more 11. So 671 is 61 * 11.

Now you’ve factored out 2013: It’s 3 * 11 * 61.

If you find this difficult to do in your head right now, fear not – the year is young and so is your GMAT prep. The bigger purpose of this post is this – numbers are all around you, and learning to notice their properties and calculate them mentally is something you can do just while living everyday life. Saving 5-10 seconds per math question adds up to several questions that you’re able to get to at an average of 2 minutes per question, so just small time savings can add up to an increase in your score. And the GMAT loves to test number properties and divisibility, so if you can train yourself to break down numbers mentally this way – while driving, paying bills, seeing phone numbers on infomercials, whatever – you’ll get your mind sharpened perfectly for GMAT math.

2013 is your year, and it starts with a good omen – the number itself. Learning to break down numbers like 2013 can help to ensure that this is the year you make huge strides on your GMAT score and quest for a top business school. Next stop – breaking down all the numbers on that tuition bill…

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