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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
If 0 < x < 1, which of the following inequalities must be true?
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29 Nov 2022, 08:26
29 Nov 2022, 08:26
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Question Stats:
61% (01:37) correct
38% (01:48) wrong based on 18 sessions
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If 0 < x < 1, which of the following inequalities must be true ?
I. \(x^5 < x^3\)
II. \(x^4 + x^5 < x^3 + x^2\)
III. \(x^4 - x^5 < x^2 - x^3\)
A. None
B. I only
C. II only
D. I and II only
E. I, II and III
I. \(x^5 < x^3\)
II. \(x^4 + x^5 < x^3 + x^2\)
III. \(x^4 - x^5 < x^2 - x^3\)
A. None
B. I only
C. II only
D. I and II only
E. I, II and III
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: If 0 < x < 1, which of the following inequalities must be true?
[#permalink]
30 Nov 2022, 23:06
30 Nov 2022, 23:06
1
Expert Reply
0 < x < 1 => Improper Fractions. Property: x > x^2 > x^3 ...
1) x^5 < x^3 => MBT
2) x^4 (1+x) < x^2 (1+x)
Since 1+x > 0, we can cancel it off from both sides
x^4 < x^2 => MBT
3) x^4 (1-x) < x^2 (1-x)
Since 1-x > 0, we can cancel it off from both sides
x^4 < x^2 => MBT
Answer: E
1) x^5 < x^3 => MBT
2) x^4 (1+x) < x^2 (1+x)
Since 1+x > 0, we can cancel it off from both sides
x^4 < x^2 => MBT
3) x^4 (1-x) < x^2 (1-x)
Since 1-x > 0, we can cancel it off from both sides
x^4 < x^2 => MBT
Answer: E
Re: If 0 < x < 1, which of the following inequalities must be true?
[#permalink]
08 Jun 2024, 00:36
08 Jun 2024, 00:36
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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