Working without a Calculator: Tips for Complicated GMAT and GRE Math Problems
November 21, 2014
On the integrated reasoning section of the GMAT, and the quantitative section of the GRE you are given an onscreen calculator to use. But is the calculator really helpful? Often times students will use it in cases where it really isn’t necessary. In these cases they are wasting valuable time that they could be using to solve other problems on the test.
Here are a few tips I use for complicated GMAT and GRE math problems:
1. Fractions over Decimals
Perhaps this only a deeply held belief, but using fractions on the GMAT or GRE seems to make the math far easier. Percents are a good example of this: we're used to writing 20% as .2, but it can also be written as 20/100, which in turn reduces to 1/5, which you probably already knew. If you're multiplying something by .15 and you're unwilling to do long multiplication, it can be far faster to instead multiply by 3/20. This is a particularly powerful method with Tip 2.
2. Divide then Multiply
English language trains us to begin at the left and work our way right, start at the top and work our way down. When working with fractions, this manifests as the preference to multiply the top numbers before dividing. This will almost always take more time and involve more difficult calculations. 14/9 x 15/21 is cumbersome to do by hand...until you realize you can remove a 7 and a 3 to turn the problem into 2/3 x 5/3 = 10/9.
3. Multiplication in Steps
We can do multiplication in our heads with familiar or predictable numbers – think of 5 and 10 multiples, for example. While less predictable numbers might be daunting, you can make them easier by using familiar multiples and adding from there. What I mean is: What is 26 x 31, in your head? Not so easy, but we can do something easier. 25 and 30 are easy numbers to work with, and 25 x 30 = 25 x 10 x 3 = 750. We can find 26x30 by adding 30 = 780. This represents 26 repeated 30 times, but we need it 31 times, so we add 26 for 806.
4. Prime Factors and the Properties of Integers
In general, no student feels comfortable working with factor questions, and properties of integers questions can be some of the most challenging to teach and learn. Yet time spent working on these rewards you not only by helping with properties questions in general, but on a lot of math that involves multiplying and dividing complicated numbers. A number is divisible by 12 if it is divisible by 2x2x3. If want to avoid long division, you can break the number into
Nothing is better than ballparking. Well, approximately nothing. If you're stumped on a question or even feeling a little lazy, ballparking can occasionally solve questions in seconds. The ratio of girls to boys is 5:3 and we need to know the number of girls? Are any answers half or less than half? Take a look at number 85 in the Official Guide; doing the math on the question is almost inconsequential. If we get a sense of the scale of the number, it can be solved quickly.
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