Read the Last Piece First on the GMAT!

Make Studying FunWhen I was in grad school, I had a writing teacher who insisted on reading the last page of a novel before she read the first. Her reasoning was that she was starting a kind of journey, and she was curious to know where she’d be going before she could decide whether she wished to embark. Now, as a devoted reader, I couldn’t find this strategy more abhorrent. Uncertainty and mystery are integral parts of the pleasure of reading fiction. Why ruin it?

However, when it comes to the GMAT, I am quite content to ruin the suspense of a question in favor of deriving a more convenient and efficient means of solving it. Interestingly, it turns out that when a question offers multiple bits of information, starting with the last piece can often be a way of dramatically simplifying the problem.

Take the following problem that a tutoring student of mine encountered on her GMATPrep test:

Mary’s income is 60 percent more than Tim’s income, and Tim’s income is 40% less than Juan’s income. What percent of Juan’s income is Mary’s income?

A) 124%

B) 120%

C) 96%

D) 80%

E) 64%

She approached the question like many test-takers would: she started with the first piece of information, and called Mary’s income $100. And then she got stuck. She realized that Tim’s income isn’t $40 here, as $100 is more than double $40, so clearly Mary’s income would not then be 60% greater than Tim’s (though Tim’s would have been 60% less than Mary’s.) So then, I suggested, why not start at the end?

The last person mentioned here is Juan, so let’s call Juan’s income $100. She then knocked out the remaining calculations in about 30 seconds. If Juan’s income is $100, and Tim’s income is 40% less than Juan’s, than Tim’s income would be $60. And if Tim’s income is $60, and Mary’s income is 60% more than Tim’s, Mary’s income would be 60 + 60% of 60 = 60 + 36 = 96. (Or 1.6 * 60 = 96.) If Mary’s income is $96 and Juan’s is $100, then clearly, Mary’s income is 96% of Juan’s, and the answer is C. Not bad.

Let’s try it again on another question:

In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 5000 have been vaccinated against both, how many have been vaccinated only against rubella?

A) 2500

B) 7500

C) 10000

D) 15000

E) 17500

First, note that this is a classic overlapping sets questions, so let’s set up a simple matrix:

DG Graph 1

 

 

 

 

 

But now, let’s start by inserting the last piece of information we’re given. 5000 have been vaccinated against both, so that goes in the Mumps/Rubella Vaccine cell. Now we’ve got:

DG Graph 2

 

 

 

 

 

Next, we’ll work backwards. We’re told that the number that have been vaccinated against both (5000) is twice the number that have been vaccinated against only mumps. So the number that have been vaccinated against only mumps must be 2500. Now our table looks like this:

DG Graph 3

 

 

 

 

 

Now we know that 7500 people have been vaccinated against Mumps. Last, we’re told that the number vaccinated against Rubella is twice the number that have been vaccinated against Mumps, which means that 15,000 people have been vaccinated against Rubella. If 15,000 total have been vaccinated against Rubella, and 5000 of those have been vaccinated against both, then, according to our table, 10,000 have been vaccinated against only Rubella. So C is our answer.


DG Graph 4

 

 

 

 

 

Takeaway: The GMAT question writer is going to provide information to you in a very strategic way. If the most useful piece of info comes at the end of a lengthier question, the question will be harder if you start at the beginning. So be like my zany grad school teacher and start at the end. It may ruin the suspense, but as a consolation, you’re more likely to get the question right, and I’m guessing that’s a trade-off most of us are more than happy to make.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

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By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here.