If vertices of a triangle are A (5, 0), B (x, y), and C (25, 0), what GMAT Data Sufficiency

Question: If vertices of a triangle are A (5, 0), B (x, y), and C (25, 0), what is the area of the triangle?

Statement (1) |x| = y = 10
Statement (2) x = |y| = 10

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: D

Approach Solution (1):
Area = ½ * Base * Height = ½ * 20 * h
Where h is the length of the perpendicular from (x, y) to x axis
1. x >= 0
x = y = 10
(x, y) = (10, 10)
x < 0
-x = y = 10
(x, y) = (-10, 10)
Both the above points results in the height of 10
Sufficient
2. y >= 0
x = y = 10
(x, y) = (10, 10)
y < 0
x = -y = 10
(x, y) = (10, -10)
Both of the above points result in the height of 10
Sufficient
Correct option: D

Approach Solution (2):

The answer will be D; both pairs of triangle have the same base and height

Correct option: D

Approach Solution (3):

1. B can be two points B1 (10, 10) or B2 (-10, 10)
Therefore S abc is certain
2. B can be B1 (10, 10) or B2 (10, -10)
AC is certain
Correct option: D

“If vertices of a triangle are A (5, 0), B (x, y), and C (25, 0), what is the area of the triangle?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". 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 sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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