Last week we covered the importance of saving time on quantitative questions, particularly problem solving questions, in order to be able to reapply seconds to the harder questions or those that require a recheck.

Quick preface – this doesn’t mean you should be rushing through 500 and 600 level problems in order to “get to” hard problems. The strategy for managing time on the GMAT is very different from a SAT or an ACT exam. Writing an email is not necessarily a difficult task, but can take up loads of time at work. The same rule applies with GMAT quantitative (and verbal) questions, meaning that there are plenty of 500-level problem solving questions you should spend more time on over a 700-level data sufficiency question.

That being said, let’s dive into a problem solving question to illustrate our point.

At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

A. 6 to 1
B. 3 to 2
C. 2 to 3
D. 1 to 5
E. 1 to 6

Plenty of you will take a variable route to solve this problem. As this is a word problem, our first step is to breakdown the problem line by line, potentially word by word. If we were to translate this problem using variables:

E = English

H = History

M = Mathematics

Step 1: At a certain college there are twice as many English majors as history majors

2E = H

Step 2: Three times at many English majors as mathematics majors

3E = M

Step 3: Answering the question, What is the ratio of the number of history majors to the number of mathematics majors?

M = H?

3E = 2E

E cancels out, leaving us with 3:2 or answer choice B.

That seems pretty easy, right? Unfortunately, many students will incorrectly set up their variables, mainly because they misunderstand the relationship of English majors to mathematics and history majors. Most will set up the variables as either:

E = 2H

And/or E = 3M

And get lucky and set up the ratio incorrectly but get to the correct answer B, or will select C or be completely lost on how to get to a relationship between history and mathematics majors, going down the mine-path of fractions or unsuccessfully backtracking on work.

If you feel 100% confident in taking this variable approach, great! This question is clearly of a 500-level, and there are similar problems with more steps and/or variables to consider.

For those that feel completely disoriented by the wording of problems like this, seconds add up to lots of minutes trying to decipher the algebraic set-up… and that’s where plugging in numbers comes into play.

If we read the problem again as:

Step 1: There are twice as many English majors as history majors

Step 2: There are three times as many English majors as mathematic majors

So, if there are 12 English majors, then there are 6 history majors. If there are still 12 English majors – stay consistent but also simple with the numbers – the 12/3 = 4, so there are 4 mathematics majors.  

What’s the question asking? The ratio of history majors to mathematics majors.

Our ratio is 6:4 which reduces to 3:2, again, giving us the correct answer of B.

Pause, reread the question, and say “did I give them what they were looking for?”

The answer is, of course, yes!

Remember: the GMAT is a battle of time management, leveraging assets, and keeping your head straight. Always think about how you can tackle a question more efficiently, shaving down seconds, but also in a way that you feel confident you’ve selected the right answer.