In the rectangular coordinate system above, for which of the shaded regions is the area 2?

AAPL wrote: ↑

Sat Feb 29, 2020 11:39 am

GMAT Prep

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In the rectangular coordinate system above, for which of the shaded regions is the area 2?

A. None
B. Q Only
C. Q and R
D. P, Q, and R only
E. P, Q, R and S

OA D

Let's calculate the areas of each figure.

• Figure P: 1/2*1*4 = 2; The correct answer must be between D and E.

Since figure Q and R common in both options, let's calculate the area of figure S.

• Figure S: 1/2*1*3 = 1.5 ≠ 2.

The correct answer is D.

The correct answer: D

Hope this helps!

-Jay
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AAPL wrote: ↑

Sat Feb 29, 2020 11:39 am

GMAT Prep

Untitled.png

In the rectangular coordinate system above, for which of the shaded regions is the area 2?

A. None
B. Q Only
C. Q and R
D. P, Q, and R only
E. P, Q, R and S

OA D

Observe that the area of each small square formed by the gridlines is 1.

The area of region P is 2 since P is a triangle with base = 4 and height = 1. Thus, the area of P is (1/2)(4)(1) = 2.

The area of region Q is 2 since Q is a rectangle with length = 2 and width = 1. Thus, the area of Q is (2)(1) = 2.

The area of region R is 2 since R can be broken into four right triangles, each of which has an area of exactly 1/2.

The area of region S, however, is not 2. We can see that S is a triangle with base = 3 and height = 1. Thus, the area of S is (1/2)(3)(1) = 3/2.

Answer: D