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25 May 2020, 05:18
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
41% (02:12) correct
59%
(02:22)
wrong
based on 229
sessions
History
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If \(0.7^{(2x^2 - 3x + 4)} < 0.343\), then which of the following must be true?
A. x < -1/2
B. -1/2 < x < 1/2
C. 1/2 < x < 1
D. x > 1
E. x < 1/2 or x > 1
Are You Up For the Challenge: 700 Level Questions
A. x < -1/2
B. -1/2 < x < 1/2
C. 1/2 < x < 1
D. x > 1
E. x < 1/2 or x > 1
Are You Up For the Challenge: 700 Level Questions
Updated on: 29 Jun 2020, 19:49
Originally posted by GMATinsight on 25 May 2020, 05:34.
Last edited by GMATinsight on 29 Jun 2020, 19:49, edited 2 times in total.
Last edited by GMATinsight on 29 Jun 2020, 19:49, edited 2 times in total.
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Bunuel
RULE:
If \(0 < a < 1\), then \(a^x < a^y\) if \(x > y\)
If \(0 < a < 1\), then \(a^x < a^y\) if \(x > y\)
i.e. \(0.7^{(2x^2 - 3x + 4)} < 0.343\)
i.e. \(0.7^{(2x^2 - 3x + 4)} < (0.7)^3\)
i.e. \((2x^2 - 3x + 4) > 3\)
i.e. \((2x^2 - 3x + 1) > 0\)
i.e. \((2x^2 - 2x - x + 1) > 0\)
i.e. \((2x - 1)*(x - 1) > 0\)
i.e. either both (2x - 1)*(x - 1) should be positive or both should be Negative
For both positive, x>1
For both negative, x<1/2
i.e. Answer: Option E
General Discussion
Updated on: 25 May 2020, 06:32
Originally posted by GMATWhizTeam on 25 May 2020, 05:48.
Last edited by GMATWhizTeam on 25 May 2020, 06:32, edited 1 time in total.
Last edited by GMATWhizTeam on 25 May 2020, 06:32, edited 1 time in total.
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Bunuel
Solution
- • \(0.7^{(2x^2 – 3x + 4)} < 0.342\)
\(⟹0.7^{(2x^2 – 3x + 4)} < 0.7^3\)
• Since, 0.7 < 1 , so higher power of 0.7 will result in lower value.
- o Therefore, \(2x^2 – 3x + 4 > 3\)
\(⟹ 2x^2 – 3x + 1 > 0\)
\(⟹ 2x^2 – 2x -x + 1> 0\)
\(⟹ 2x(x – 1) – 1(x – 1)> 0\)
\(⟹ (x – 1)(2x – 1) > 0\)
o Thus, \(x < \frac{1}{2}\) or \(x > 1\)
Thus, the correct answer is Option E.
