Question: If equation |x| + |y| = 5 encloses a certain region on the graph, what is the area of that region?

1. 5
2. 10
3. 25
4. 50
5. 100

“If equation |x| + |y| = 5 encloses a certain region on the graph, what is the area of that region?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer

Approach Solution 1

There is only one approach to solving this problem.

X and Y intercepts are (0,5), (0,-5), (5,0), and (-5,0) (just make x = 0 and find y and then make y equal to zero and find x). Now if we join these points we will get the following region:

The diagonals of the quadrilateral are equal (10,10), and also perpendicular bisectors of each other (as they are on X and Y axis), so the figure must be a square.

Area of a square equals to \(\frac{Diagonal^2}{2}=\frac{10^2}{2}\) =50

Correct option: D

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