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If 2x = 3y(xy ≠ 0), what is (5x^2+xy)/(3x^2 -4xy)?

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by Max@Math Revolution » Tue Sep 24, 2019 12:31 am
[GMAT math practice question]

If 2x = 3y(xy ≠ 0), what is (5x^2+xy)/(3x^2 -4xy)?

A. 14
B. 16
C. 17
D. 19
E. 21
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by Max@Math Revolution » Wed Sep 25, 2019 11:23 pm
=>

Since 2x=3y, we have y = (2/3)x.
(5x^2+xy)/(3x^2 -4xy)
= (5x^2+x*(2/3)x)/(3x^2 -4x*(2/3)x)
= (5x^2+(2/3)x^2)/(3x^2 -4(2/3)x^2)
= ((17/3)x^2)/((1/3)x^2)
= 17.

We can also substitute x = 3 and y = 2 for a short-cut and get 17.

Therefore, C is the answer.
Answer: C
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