If p is the Perimeter of Rectangle Q, What is the Value of p? GMAT Data Sufficiency

Question: 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.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“If p is the perimeter of rectangle Q, what is the value of p?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

There is only one way to find the solution to the problem statement.
Let x and y be two sides of the rectangle.
Then the perimeter p =x+y
We will now consider each statement to see if they are sufficient.
Statement 1
Length of the diagonal = 10
Hence, we get
=> x^2 + y^2 = 10^2
we cannot find p i.e. x+y using this information.
Hence the statement is NOT SUFFICIENT
Statement 2
Area of the rectangle Q = 48
=> xy =48
From this, we cannot find p.
Since using this info we cannot find p, the statement is NOT SUFFICIENT
Now, we will be combining (1) and (2)
We will get
value of x+y = sqrt (x+y)^2
= sqrt(x^2 + y^2 + 2xy)
= sqrt ( 10^2 + 2*48)
=> sqrt(196)
= 14
Hence, the statement is SUFFICIENT

Correct Answer: C

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