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Updated on: 29 Nov 2019, 09:46
Originally posted by MathRevolution on 26 Nov 2019, 06:07.
Last edited by MathRevolution on 29 Nov 2019, 09:46, edited 1 time in total.
Last edited by MathRevolution on 29 Nov 2019, 09:46, edited 1 time in total.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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72% (02:36) correct
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[GMAT math practice question]
Two inequalities \(\frac{(2x - 3)}{2} > \frac{(5x - 6)}{3}\) and \(5x - 3 < \frac{(3x + a)}{2}\) have same solution. What is the value of \(a\)?
A. \(\frac{3}{4}\)
B. \(\frac{1}{4} \)
C. \(0 \)
D. \(\frac{- 3}{4 }\)
E. \(\frac{- 1}{4}\)
Two inequalities \(\frac{(2x - 3)}{2} > \frac{(5x - 6)}{3}\) and \(5x - 3 < \frac{(3x + a)}{2}\) have same solution. What is the value of \(a\)?
A. \(\frac{3}{4}\)
B. \(\frac{1}{4} \)
C. \(0 \)
D. \(\frac{- 3}{4 }\)
E. \(\frac{- 1}{4}\)
26 Nov 2019, 07:06
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MathRevolution
\(\frac{(2x - 3)}{2} > \frac{(5x - 6)}{3}.......6x-9>10x-12......4x<3...x<\frac{3}{4}\)
\(5x - 3 > \frac{(3x + a)}{2}.....10x-6>3x+a.....7x>a+6.....x>\frac{a+6}{7}\)
Add the two inequalities
\(\frac{3}{4}+x>\frac{a+6}{7}+x...........\frac{3}{4}>\frac{a+6}{7}......21>4a+24....4a<-3......a<\frac{-3}{4}\)
Had your Inequality been \(\frac{(2x - 3)}{2}
Please correct your question.
Updated on: 29 Nov 2019, 09:47
Originally posted by MathRevolution on 28 Nov 2019, 01:20.
Last edited by MathRevolution on 29 Nov 2019, 09:47, edited 1 time in total.
Last edited by MathRevolution on 29 Nov 2019, 09:47, edited 1 time in total.
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=>
Since we have \(\frac{(2x - 3)}{2} > \frac{(5x - 6)}{3}\), if we cross multiply we get \(3(2x - 3) > 2(5x - 6)\) or \(-4x > -3.\) Then, we have \(x < \frac{3}{4}.\)
Since we have \(5x - 3 < \frac{(3x + a)}{2}\), if we cross multiply we get \(10x - 6 < 3x + a\) or \(7x < a + 6.\) Then we have \(x < \frac{(a + 6)}{7}.\)
Since those two inequalities are equivalent each other, we have \(\frac{(a + 6)}{7} = \frac{3}{4}\) or \(4a + 24 = 21\). Then we have \(a = \frac{-3}{4}.\)
Therefore, D is the answer.
Answer: D
Since we have \(\frac{(2x - 3)}{2} > \frac{(5x - 6)}{3}\), if we cross multiply we get \(3(2x - 3) > 2(5x - 6)\) or \(-4x > -3.\) Then, we have \(x < \frac{3}{4}.\)
Since we have \(5x - 3 < \frac{(3x + a)}{2}\), if we cross multiply we get \(10x - 6 < 3x + a\) or \(7x < a + 6.\) Then we have \(x < \frac{(a + 6)}{7}.\)
Since those two inequalities are equivalent each other, we have \(\frac{(a + 6)}{7} = \frac{3}{4}\) or \(4a + 24 = 21\). Then we have \(a = \frac{-3}{4}.\)
Therefore, D is the answer.
Answer: D
