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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
If -1 < x < 0, which of the following must be true?
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19 Mar 2020, 22:07
19 Mar 2020, 22:07
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Question Stats:
40% (00:44) correct
60% (00:31) wrong based on 25 sessions
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If \(-1 < x < 0\), which of the following must be true?
I. \(x < x^2\)
II. \(x^2 < x^3\)
III. \(x < x^3\)
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
I. \(x < x^2\)
II. \(x^2 < x^3\)
III. \(x < x^3\)
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
If -1 < x < 0, which of the following must be true?
[#permalink]
10 Mar 2021, 10:04
10 Mar 2021, 10:04
1
This is a numbers theory question. Since -1 < x < 0, it follows that x is a negative fraction (e.g., -1/3). To make things easy, pick your favorite negative fraction--mine is -1/2.
I) x < x^2: TRUE
x is always negative, x^2 is always positive. To ensure that we are correct, test with -1/2
-1/2 < 1/4
II) x^2 < x^3: FALSE
x^2 is always positive, and x^3 is always negative.
III) x < x^3: TRUE
Now, this is the tricky part, and it is the reason why I spending precious time testing a fraction. To avoid traps, test immediately:
-1/2 ? (-1/2)^3
-1/2 < -1/8
Notice that -1/8 is bigger because it is less negative and closer to zero. You can also draw the number line if you are having trouble seeing this.
My answer is D.
Posted from my mobile device
I) x < x^2: TRUE
x is always negative, x^2 is always positive. To ensure that we are correct, test with -1/2
-1/2 < 1/4
II) x^2 < x^3: FALSE
x^2 is always positive, and x^3 is always negative.
III) x < x^3: TRUE
Now, this is the tricky part, and it is the reason why I spending precious time testing a fraction. To avoid traps, test immediately:
-1/2 ? (-1/2)^3
-1/2 < -1/8
Notice that -1/8 is bigger because it is less negative and closer to zero. You can also draw the number line if you are having trouble seeing this.
My answer is D.
Posted from my mobile device
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
Re: If -1 < x < 0, which of the following must be true?
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20 Nov 2021, 04:01
20 Nov 2021, 04:01
2
If \(-1 < x < 0\), which of the following must be true?
I. \(x < x^2\) --> 1>x and 1<x, true as can't be false
II. \(x^2 < x^3\) --> 1<x and 1>x, not true as can be false
III. \(x < x^3\) --> 1>\(x^2\) and 1<\(x^2\), true as can't be false
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
answer is D
I. \(x < x^2\) --> 1>x and 1<x, true as can't be false
II. \(x^2 < x^3\) --> 1<x and 1>x, not true as can be false
III. \(x < x^3\) --> 1>\(x^2\) and 1<\(x^2\), true as can't be false
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
answer is D
