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# If −1<x<5, which is the following could be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
If −1<x<5, which is the following could be true?  [#permalink]

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04 Feb 2015, 08:53
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Difficulty:

25% (medium)

Question Stats:

77% (02:03) correct 23% (01:50) wrong based on 134 sessions

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If −1<x<5, which is the following could be true?

A. 2x > 10
B. x > 17/3
C. x^2 > 27
D. 3x + x^2 < −2
E. 2x – x^2 < 0

Kudos for a correct solution.

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Re: If −1<x<5, which is the following could be true?  [#permalink]

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04 Feb 2015, 09:46
1
1
−1<x<5

A. 2x > 10 divide both sides by 2 and x > 5 [False]
B. x > 17/3 17/3 > 5 so x > 5 [False]
C. x^2 > 27 $$\sqrt{27}$$ is $$3\sqrt{3}$$ or $$-3\sqrt{3}$$ which is approximately 5.1 or -5.1 [False]
D. 3x + x^2 < −2 = x*(3+x) < -2. For this to be true, x would have to be negative and 3+x would have to be positive. If we test values between -1 and 0, we see the statement is [False]. For example, -0.5*(3-0.5) < -2 so -0.5*2.5 < -2 so -1.25 < -2
E. 2x – x^2 < 0 = x*(2-x) < 0 For this to be true, either x or 2-x would have to be negative and the other value would have to be positive. If we test x = 3 we get 3*(2-3) < 0 so 3*(-1) < 0 so -3 < 0 [True]
Math Expert
Joined: 02 Sep 2009
Posts: 59587
Re: If −1<x<5, which is the following could be true?  [#permalink]

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09 Feb 2015, 05:19
Bunuel wrote:
If −1<x<5, which is the following could be true?

A. 2x > 10
B. x > 17/3
C. x^2 > 27
D. 3x + x^2 < −2
E. 2x – x^2 < 0

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Simplify each inequality.
(A) says x>5, which contradicts the question stem.
(B) says x>a number greater than 5: also a contradiction.
(C) says x^2>27 , so x>√27, which is > 5; impossible.
(D) says x<−1; impossible.
(E) says x>2, which is possible.
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Re: If −1<x<5, which is the following could be true?  [#permalink]

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17 Mar 2019, 11:08
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Re: If −1<x<5, which is the following could be true?   [#permalink] 17 Mar 2019, 11:08
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