Testing numbers when it involves variables and inequalities

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beatgmatny1: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sat Feb 15, 2014 3:13 pm

by beatgmatny1 » Wed Feb 26, 2014 12:59 pm

Are there a set of numbers that we can test on questions that involve variables and inequalities? I tend to take longer than 2 mins and sometimes I get them wrong.

For example, During the practice test, I spent quite a bit of time testing numbers for the following DS question. I ended up getting wrong!

If M, K, X, and Y are integers, is MX + KY > KX +MY?

A. M>K
B. X>Y

What is the ideal/less time-consuming method to solve this question? Please assist.

Thanks!

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Source: Beat The GMAT — Data Sufficiency | Wed Feb 26, 2014 12:59 pm

Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Wed Feb 26, 2014 1:26 pm

First, rearrange the inequality from the stem:

MX + KY > KX + MY?

MX - MY > KX - KY?

M(X - Y) > K(X - Y)?

I started with Statement 1. M is greater than K, and since we have the common term (X - Y) on each side, that should indicate that M(X-Y) is greater than K(X-Y), right? Well, what if X - Y gives you a negative value? Let M=5 and K=3, and let X - Y = -2:

5(-2) > 3(-2) ?
-10 > -6?

No, -10 is clearly not greater than -6. So Statement says yes if X - Y is positive and no if X - Y is negative. Insufficient.

Statement 2 guarantees that X - Y is positive, but now we don't know anything about M and K. We can take our rephrased question and divide both sides by X - Y:

M(X - Y) > K(X - Y)?

M > K?

But we can't answer that question. It could be, but it doesn't have to be.

Combined, we have enough to answer the question.

When picking numbers on inequalities, the biggest trap is forgetting to consider what happens when you have negative values. Make sure you test negative numbers (if allowed by the question) to see what happens if the sign flips.

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beatgmatny1: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sat Feb 15, 2014 3:13 pm

by beatgmatny1 » Wed Feb 26, 2014 1:44 pm

Thank you so much for your explanation! simplifying the question makes this much easier to solve! Yes. I forgot to test negative numbers on this question.

Thank you for the tip!

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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Wed Feb 26, 2014 1:50 pm

It's a good technique when the inequality or equation in the stem is messy. Just because they ask the question a certain way doesn't mean you can't rephrase it to be easier to work with (as long as you're manipulating it correctly).

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Feb 27, 2014 7:34 pm

beatgmatny1 wrote:Are there a set of numbers that we can test on questions that involve variables and inequalities? I tend to take longer than 2 mins and sometimes I get them wrong.

For example, During the practice test, I spent quite a bit of time testing numbers for the following DS question. I ended up getting wrong!

If M, K, X, and Y are integers, is MX + KY > KX +MY?

A. M>K
B. X>Y

Note that the question stem can also be rephrased as follows:
MX + KY > KX + MY
MX - KX > MY - KY
X(M-K) > Y(M-K).

Question stem, rephrased: Is X(M-K) > Y(M-K)?

Statement 1: M>K
Thus, M-K>0.
Since M-K>0, we can simplify the question stem by dividing each side by M-K.
The question stem becomes:
Is X>Y?
No way to know.
INSUFFICIENT.

Statement 2: X>Y
If X=2, Y=1, and M-K=1, then X(M-K) > Y(M-K).
If X=2, Y=1, and M-K=0, then X(M-K) = Y(M-K).
INSUFFICIENT.

Statements combined:
In statement 1, the question stem becomes: Is X>Y?
Since statement 2 states that X>Y, the answer to the rephrased question stem is YES.
SUFFICIENT.

The correct answer is C.

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