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If p is the perimeter of rectangle Q...

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nchaswal Senior | Next Rank: 100 Posts
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If p is the perimeter of rectangle Q...

Post Tue May 10, 2016 12:54 pm
If P is the perimeter of rectangle Q, what is the value of p?

1) Each diagonal of rectangle Q has length 10
2) The area of rectangle Q is 48.

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GMAT/MBA Expert

Post Tue May 10, 2016 1:26 pm
nchaswal wrote:
If P is the perimeter of rectangle Q, what is the value of p?

1) Each diagonal of rectangle Q has length 10
2) The area of rectangle Q is 48.
Statement 1:
Here, L² + W² = 10² = 100.

Test one case that also satisfies Statement 2.
Case 1: L=6 and W=8, with the result that LW=48 and L² + W² = 6² + 8² = 36+64 = 100.
In this case, p = 6+6+8+8 = 28.
Test one case that DOESN'T also satisfy Statement 2.
Case 2: L=1 and W=√99, with the result that LW≠48 but L² + W² = 1² + √99² = 1+99 = 100.
In this case, p = 1+1+√99+√99 = 2 + 2√99.

Since p can be different values, INSUFFICIENT.

Statement 2:
Here, LW = 48.
Case 1 also satisfies Statement 2.
In Case 1, p = 28.

Case 3: L=1 and W=48, with the result that LW = 1*48 = 48
In this case, p = 1+1+48+48 = 98.

Since p can be different values, INSUFFICIENT.

Statement combined:
Case 1 satisfies both statements (L² + W² = 100 and LW = 48).
No other length and width will yield both a diagonal of 10 and an area of 48.
Thus, p = 28.
SUFFICIENT.

The correct answer is C.

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