SOLUTION


If l and w represent the length and width, respectively, of the rectangle above, what is the perimeter?

The perimeter is 2(l+w).

(1) 2l + w = 40. Not sufficient.

(2) l + w= 25 --> \(perimeter=2(l+w)=50\). Sufficient.

Answer: B.
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Straight B.

For Perimeter we need 2(l+b),so if we know l+b its sufficient..

Answer is B straightaway.

Explanation: The perimeter of a rectangle can be found by 2(l+w). So, if we know (l+w) or l and w separately, the perimeter can be found. Hence B.

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 (see below)

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

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

RELATED VIDEO

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I don’t think I understand how to derive that 2l + w = 40 is not right away a viable option. My initial inclination is to try to use algebra to get it into a 2(l+w) format, costing me precious time. Thoughts?

Posted from my mobile device

hi montanhaf100
Just for the learning purpose, Can you show here how to use algebra to get it into a 2(l +w) format?
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