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Two inequalities (2x - 3)/2 > (5x - 6)/3 and 5x - 3 >

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Two inequalities (2x - 3)/2 > (5x - 6)/3 and 5x - 3 >

by Max@Math Revolution » Tue Nov 26, 2019 4:48 am
[GMAT math practice question]

Two inequalities (2x - 3)/2 > (5x - 6)/3 and 5x - 3 < (3x + a)/2 have same solution. What is the value of a?

A. 3/4
B. 1/4
C. 0
D. - 3/4
E. - 1/4
Last edited by Max@Math Revolution on Fri Nov 29, 2019 8:40 am, edited 1 time in total.
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Fixed

by Max@Math Revolution » Wed Nov 27, 2019 11:55 pm
=>

Since we have (2x - 3)/2 > (5x - 6)/3, if we cross multiply we get 3(2x - 3) > 2(5x - 6) or -4x > -3. Then, we have x < 3/4.
Since we have 5x - 3 < (3x + a)/2, if we cross multiply we get 10x - 6 < 3x + a or 7x < a + 6. Then we have x < (a + 6)/7.
Since those two inequalities are equivalent each other, we have (a + 6)/7 = 3/4 or 4a + 24 = 21. Then we have a = -3/4.

Therefore, D is the answer.
Answer: D
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