Common Sense Beats Formulas in GMAT Quant

by on July 14th, 2017

1You may get into the situation on a math question in which the answer seems very difficult to calculate. When this happens, there may be a simple, common sense approach to get to the right answer quicker than any memorized formula.

Consider the following question from The Economist GMAT Tutor’s practice question database:

M and N are among the 5 runners in a race, and there can be no tie. How many possible results are there where M is ahead of N?

A) 10

B) 25

C) 35

D) 60

E) 80

Your first reaction may be to try to calculate all the possible ways M can finish ahead of N. For example, consider if M finishes first, how many ways are there to order the other runners and so on. You will be able to do this, but it is tricky and time consuming.

Instead, consider how many ways there are of ordering the five runners in total, without any conditions. This is 5! = 5*4*3*2*1 = 120

We have no information about the relative abilities of M and N. Therefore, it is likely that M beats N as it is that N beats M. Therefore, there are 60 ways for M to beat N and 60 ways for N to beat M. Answer choice D is correct.

At this stage you can pat yourself on the back and move quickly to the next question.

However, in case this method did not occur to you, we can also prove that there are 60 ways by doing some calculations:

M finishes first: M*4*3*2*1 = 24

M finishes second: 3*M*3*2*1 = 18

M finishes third: 3*2*M*2*1 = 12

M finishes fourth: 3*2*1*M*1 = 6

24 + 18 + 12 + 6 = 60

You can see that this method is much slower than considering the common sense approach that half the total ways is the answer we are looking for. The common sense approach is much faster. You may not always see it, but at least keep your eyes open for such a chance.

This post appeared first on the Economist GMAT Tutor blog.

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