GMAT Quant: Reflect before you Work

Stacey Koprince —  February 25, 2014 — Leave a comment

gmat-quantStop! Before you dive in and start calculating on a math problem, reflect for a moment. How can you set up the work to minimize the number of annoying calculations?

Try the below Percent problem from the free question set that comes with your GMATPrep® software. The problem itself isn’t super hard but the calculations can become time-consuming. If you find the problem easy, don’t dismiss it. Instead, ask yourself: how can you get to the answer with an absolute minimum of annoying calculations?

 

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”

 

Ugh. We have to figure out what they’re talking about in the first place!

The first sentence of the problem describes the table. It shows 5 different districts with a number of votes, a percentage of votes for one candidate and a percentage of votes for a different candidate.

Hmm. So there were two candidates, P and Q, and the one who won the election received the most votes overall. The problem doesn’t say who that was. I could calculate that from the given data, but I’m not going to do so now! I’m only going to do that if I have to.

Let’s see. The problem then asks which district had the greatest number of votes for the winner. Ugh. I am going to have to figure out whether P or Q won. Let your annoyance guide you: is there a way to tell who won without actually calculating all the votes?

The two candidates tied in Districts 2 and 3, so ignore those votes entirely. Candidate P won District 1 while Candidate Q won Districts 4 and 5. Because both of the latter districts (4 and 5) had a lot more votes, Candidate Q must have won more votes overall. Candidate Q, then, is the overall winner. (And I didn’t have to do any math. Yay!)

Next, which district had the most votes for Q? I can actually calculate the exact number of votes in each district… but do I really want to? Glance at District 1. No way can that be the district: there are only 800 votes and Q won a low percentage. Maybe I can get away with just eye-balling the numbers or comparing districts—let’s see.

District 3 beats out District 2: both have 50% for Q, but there are more votes from District 3.

District 4 beats out District 3: Candidate Q won a larger percentage (60%) of a larger number (1800). Excellent!

Ah. Okay, District 5 has a higher percentage but a lower number of votes. I may actually have to do some calculations here.

What’s the fastest way to take a percentage of a number? “Add them up.”

In District 4, 60% of 1,800 votes were cast for Q. 50% of 1,800 is 900. 10% of 1,800 is 180. Add up the numbers: 50% + 10% = 60%, so 900 + 180 = 1,080 votes for Q.

In District 5, 70% of 1,200 votes were cast for Q. 50% of 1,200 is 600. 10% of 1,200 is 120. 50% + 10% + 10% = 600 + 120 + 120 = less than 1,000. (Don’t do any more math than you have to!)

District 4, then, beats out District 5. District 4 cast the greatest number of votes for the eventual victor, Q.

The correct answer is (D).

Want to try some other problems for which a little Reflection will help you solve? Follow this link to an article about Reorienting Your View on GMAT quant.

Key Takeaway: Reflect before you Work

(1) Often, we feel so pressed for time on this test that we dive right into a complex calculation without really thinking about what we’re doing or why we’re doing it. Break that habit! It’s crucial to consider your options before starting to solve.

(2) The official solution for this problem actually does calculate the number of votes for Q in each of the 5 districts. What a waste of time! The official explanations for real GMAT problems will always show you mathematically correct solutions—but those solutions often won’t be the best or most efficient way to solve.

(3) Let your annoyance guide you: whenever you think, “Ugh, that’s so annoying;  I wish I didn’t have to calculate this!” ask yourself, “Wait a second—can I get away with not calculating it?” Even when you get something right, review your work: if the math you did has any annoying bits, see whether an alternate approach can save you some time and mental effort. After all, who doesn’t need more of both of those precious commodities on the GMAT?

 

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

Stacey Koprince

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Stacey Koprince is an Instructor and Trainer as well as the Director of Online Community for Manhattan Prep. She also co-manages the company's GMAT curriculum and product line. She has been teaching various standardized tests for more than fifteen years and her entire teaching philosophy can be summed up in five words: teaching students how to think.

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