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DS Geometry

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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Feb 05, 2015 11:51 am
scottchapman wrote:If L & W represent the length and width, respectively, of the rectangle above, what is the perimeter?

1). 2L+W=40
2). L+W=25
Perimeter of a rectangle with length L and width W = L+L+W+W = 2L + 2W = 2(L+W).
Question stem, rephrased:
What is L+W?

Statement 1: 2L + W = 40
Thus, W = 40 - 2L.

Case 1: L=10, implying that W = 40 - 2*10 = 20.
In this case, L+W = 10+20 = 30.

Case 2: L=15, implying that W = 40 - 2*15 = 10.
In this case, L+W = 15+10 = 25.

Since L+W can be different values, INSUFFICIENT.

Statement 2: L+W = 25
SUFFICIENT.

The correct answer is B.
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by Brent@GMATPrepNow » Thu Feb 05, 2015 11:53 am
scottchapman wrote:If L & W represent the length and width, respectively, of the rectangle above, what is the perimeter?

1). 2L + W = 40
2). L + W = 25
Target question: What is the perimeter?
This is a great candidate for REPHRASING the target question.

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

If L and W represent the rectangle's length and width, then the perimeter = 2L + 2W.
So, we can REPHRASE the target question as...

REPHRASED target question: What is the value of 2L + 2W?

Statement 1: 2L + W = 40
This statement does not FEEL sufficient to answer the rephrased target question. So, I'm going to PLUG IN numbers.
There are several values of L and W that satisfy statement 1. Here are two:
Case a: L = 5 and W = 30, in which case 2L + 2W = 70
Case b: L = 10 and W = 20, in which case 2L + 2W = 60
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: L + W = 25
If we take this equation and multiply both sides by 2, we get: 2L + 2W = 50
PERFECT - we have answered the REPHRASED target question!
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
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by MartyMurray » Thu Feb 05, 2015 12:10 pm
Scott, this is a good example of a C trap question.

C trap questions are set up to get the test taker thinking that both statements are needed to get to the answer.

In this case, one could be thinking this way. "To calculate the perimeter, I need the length and width."

That thinking might even seem somehow confirmed after working on Statement 1, which allows for multiple values of L and W.

So then you might jump to Statement 2 and find that once again you can't determine the value of L or W.

At that point maybe you notice that you can subtract Statement 2 from Statement 1 and easily calculate the values of L and W. "Ahhhh," you think. "The answer is C."

The thing is that that combining of the statements is not necessary. You don't actually need the values of L and W because P = (L + W) + (L + W). So as soon as you have L + W = 25 you are set. So Statement 2 is sufficient and the answer is B.

If you didn't see that and instead chose C, then you fell into a C trap.

So there's one thing to be aware of in order to do better on DS.
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by scottchapman » Thu Feb 05, 2015 4:57 pm
Thank you all for your responses. I struggle with DS and I think part of the reason for it is not rewording the question effectively. It makes sense after I see you guys go through the steps, but for whatever reason, I continue to make the same errors. I'm assuming I just need more practice...
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by Brent@GMATPrepNow » Thu Feb 05, 2015 5:32 pm
scottchapman wrote:Thank you all for your responses. I struggle with DS and I think part of the reason for it is not rewording the question effectively. It makes sense after I see you guys go through the steps, but for whatever reason, I continue to make the same errors. I'm assuming I just need more practice...
EVERYONE struggles with Data Sufficiency (DS) questions at first. Keep in mind that this question type is unique to the GMAT, so it's totally foreign territory.

It just takes time for the concepts and strategies to become secondary, at which point you may come to find that DS questions are actually easier than Problem Solving questions.

I could start listing dozens of DS strategies and common mistakes, but it's easier to just direct you to our free set of videos that cover everything you need to know to tackle DS questions: https://www.gmatprepnow.com/module/gmat-data-sufficiency

Cheers,
Brent
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by GMATGuruNY » Sat Feb 07, 2015 4:43 am
scottchapman wrote:Thank you all for your responses. I struggle with DS and I think part of the reason for it is not rewording the question effectively. It makes sense after I see you guys go through the steps, but for whatever reason, I continue to make the same errors. I'm assuming I just need more practice...
The geometry problem above is a VALUE DS: a DS whose question stem asks for a specific value.
One way to evaluate the statements -- and to avoid falling for a trap -- is to TEST TWO CASES.
If the desired value is THE SAME in each case, the statement is SUFFICIENT.
If the desired value is NOT the same in each case, the statement is INSUFFICIENT.
If L & W represent the length and width, respectively, of the rectangle above, what is the perimeter?

1). 2L + W = 40
2). L + W = 25
Statement 1: 2L + W = 40
Case 1: L=10, W=20, with the result that 2L + W = 2*10 + 20 = 40
The following rectangle is yielded:
Image

Case 2: L=5, W=30, with the result that 2L + W = 2*5 + 30 = 40
The following rectangle is yielded:
Image

Since the perimeter is NOT the same in each case, INSUFFICIENT.

Statement 2: L+W = 25
Case 3: L=10, W=15
The following rectangle is yielded:
Image

Case 4: L=5, W=20
The following rectangle is yielded:
Image

Since the perimeter is THE SAME in each case, SUFFICIENT.

The correct answer is B.

One advantage to this approach:
It does not require any special insight.
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by Matt@VeritasPrep » Mon Feb 09, 2015 12:43 am
scottchapman wrote:Thank you all for your responses. I struggle with DS and I think part of the reason for it is not rewording the question effectively. It makes sense after I see you guys go through the steps, but for whatever reason, I continue to make the same errors. I'm assuming I just need more practice...
You'll definitely get there. Once you get the hang of the format, you may find yourself scoring higher on DS than on PS, even if the questions seem hard. DS is MUCH more guessable than PS, so you can get away with a lot of inspiring guesswork / trial and error / risk intelligence, as opposed to PS where you often need to know the math in question.
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