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The line y = ax - 1 passes through (1/3, 0). On the line, t

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The line y = ax - 1 passes through (1/3, 0). On the line, t

by Max@Math Revolution » Tue Jan 07, 2020 12:53 am
[GMAT math practice question]

The line y = ax - 1 passes through (1/3, 0). On the line, there is a point whose x-coordinate and y-coordinate are the same. What is this point?

A. (1/5 , 1/5)
B. (1/3 , 1/3)
C. (1/2 , 1/2)
D. (- 1/4 , - 1/4)
E. (- 1/5 , - 1/5)
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by Max@Math Revolution » Wed Jan 08, 2020 11:36 pm
=>

Since the line y = ax - 1 passes through (1/3, 0), we have 0 = a/3 - 1 or a = 3.
To figure out the point with the same x-coordinate and y-coordinate on the line y = 3x - 1, we make y = x, which gives us x = 3x - 1 or 2x = 1.
Thus we have x = 1/2, y = 1/2, and the point is (1/2, 1/2).

Therefore, C is the answer.
Answer: C
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