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# Solving questions involving fractions: An alternative strategy

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We recently published advice on how to solve questions involving fractions. The truth is that sometimes you will try one method to solve a question and that method does not turn out to be the right one. Don’t give up! Try another method. Of course, the trick is to select the correct method from the beginning, but let’s be realistic: This won’t happen 37 times on test day for all 37 Quant questions. Be prepared to change tack!

Consider the following problem from the Economist GMAT Tutor question database:

If 10y/(2m) is an odd integer, then y may be which of the following?

A) 2m
B) 2m+1
C) 2m-1
D) (2m)/5
E) 5 * 2m

The wrong way to solve this GMAT question

Your first reaction may be to plug in numbers for m and for y. Let’s see what happens when you do this. Let’s choose 2 for m and 6 for y.

10y/(2m) thus become 60/4 = 15, an odd integer. So far so good. But see what happens when you plug in m=2 into the answer choices to check if any of the answer choices equal 6:

A) 22 = 4
B) 22+1 = 23 = 8
C) 22-1 = 21 = 2
D) (22)/5 = 4/5 = 0.8
E) 5 * 22 = 5*4 = 20

After all that we're work, we are none the wiser.

The right way to solve this problem

Now is the time to change tack. What about using the power of the answer choices to help you? One is correct. Don’t just plug in any number for y, but plug in each answer choice for y and see what happens:

A) 10*2m / 2m = 10, not an odd integer.
B) 10*2m+1 / 2m = 10*2m+1-m = 10*21 = 10*2 = 20, not an odd integer.
C) 10*2m-1 / 2m = 10*2m-1-m = 10*2-1 = 10*(1/2) = 5, an odd integer and therefore the correct answer.

Let’s check D and E to be sure:

D) 10*(2m)/5 / 2m = 10*(2m)/5 *1/2m = 10/5 = 2, not an odd integer.
E) 10*5*2m / 2m = 10*5 = 50, not an odd integer.

As such, C is our answer.

I hope you choose the right method from the beginning. However, it may be best to accept that there are times when you may proceed on a wrong track for a while. All is not lost if you can think of another method quickly!

The article first appeared on Economist : https://gmat.economist.com/blog/quantitative/solving-questions-involving-fractions-alternative-strategy

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