Working Smarter, Not Harder

What’s more valuable on the GMAT? Saving 30 seconds on a question that took you 2:30 to solve? Or 30 seconds on a question that took you 1:30 to solve? Trick question. Either way, you have the same amount of extra time to use on some other question. So with that in mind, take out a timer, pen, and paper, and let’s try out a fairly straightforward GMATPrep® problem.

 

District	Number of Votes	Percent of Votes for Candidate P	Percent of Votes for Candidate Q
1	800	60	40
2	1,000	50	50
3	1,500	50	50
4	1,800	40	60
5	1,200	30	70

 

The table above shows the results of a recent school board election in which the candidate with the higher total number of votes from the five districts was declared the winner. Which district had the greatest number of votes for the winner?

 

(A)  1

(B)  2

(C)  3

(D)  4

(E)  5

Now before we work through the problem. Ask yourself a few questions about what you just did:

1. How confident are you in your answer?
2. How much time did you take to answer?
3. Looking back on your solution, was there shortcut you could have used to eliminate some of the work you did?
4. If so, what specifically about this problem allows you to use your shortcut?

At this point, hopefully you either did the shortcut for this problem or discovered what the shortcut might be. Let’s start with the long method. If I wanted to calculate the number of votes for each candidate, it would look like this:

Twelve calculations later (ten products and two sums), we have all of our numbers calculated and can answer two questions:

1. Who won the election? (Candidate Q)
2. Which district had the most votes for that candidate? (District 4- answer D)

Let’s go back for a second though. Are there any calculations from above that we could have skipped? Let’s start by analyzing the first question from above. Who won the election?

 

District	Number of Votes	Percent of Votes for Candidate P	Percent of Votes for Candidate Q
1	800	60	40
2	1,000	50	50
3	1,500	50	50
4	1,800	40	60
5	1,200	30	70

 

Looking at the table, four out of the five districts had the same number of or more voters for Candidate Q. And District 1, the only district where Candidate P won, had the fewest number of votes. Finally, the 60-40 margin in District 1 is the same margin in District 2, but in favor of Candidate Q. Looking at the first four districts, we should be able to clearly see that Candidate Q had more votes in those four districts combined AND had more votes in District 5. Our problem is now half-solved and we can look just at Candidate Q’s votes:

 

District	Number of Votes	Percent of Votes for Candidate Q
1	800	40
2	1,000	50
3	1,500	50
4	1,800	60
5	1,200	70

 

Time to answer our second question: which district had the most votes for Candidate Q? Again, we should be able to simplify this question by comparing the first four districts; the population in the first four districts goes up as we go down the list AND the percentage of votes for Candidate Q goes up or stay even. Of the first four districts, District 4 has the largest number of votes AND the highest percentage of votes for Candidate Q. So our chart can be simplified even further and after two computations we have this:

Those twelve initial computations that we had to solve the first time we solved the problem became just two computations after some critical reasoning. This may not be a 700+ level question, but the same shortcuts that are helpful in analyzing an easy or medium question will become necessary when tackling harder problems. Those of you who have taken a Manhattan course have seen some of these shortcuts when we simplify Data Sufficiency questions before looking at the statements or identify several different splits in Sentence Correction. Whenever you review questions and skip over the ones you get right, you might be missing out on a concept, a shortcut, or, in a DS question, an earlier place to stop calculating an answer. So the next time you finish up a set of problems, spend 10 minutes going back through the questions and ask yourself how you can work smarter, not harder.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.