Question: What is the area of a region enclosed by \(|\frac{x}{3}|+|\frac{y}{9}=10|\)?

1. 675
2. 1350
3. 2700
4. 5400
5. 10800

Answer:
Solution with Explanation:
Approach Solution (1):

Find the x and y intercepts

When y = 0, then x = 30 or x = -30
When x = 0, then y = 90 or x = -90
So, we have 4 points: (30, 0), (-30, 0), (0, 90), (0, -90). When joining these points we get the rhombus:

The area of a rhombus is \(\frac{d_1*d_2}{2}\) where (\(d_1,d_2\)are lengths of the diagonals), thus the area of the enclosed figure is \(\frac{60*180}{2}=5,400\)

Correct Option: D

Approach Solution (2):

In case you don’t have the equation for the area of a rhombus memorized, you could have also multiplied the area of a triangle by 4. This figure is made up of 4 equal triangles
Area of triangle = ½ bh
Area of our figure = 4 * (½ * 30 * 90) = 5400

Correct Option: D

Approach Solution (3):

We can make 4 triangles each with height = 90 units, and base = 30 units
Now, Area of triangle = 0.5 * base * height = 90 * 30 / 2 = 1350 sq units
For 4 triangles, we get 4 * 1350 = 5400 sq units

Correct Option: D

“What is the area of a region enclosed by \(|\frac{x}{3}|+|\frac{y}{9}=10|\)?”- 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.

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