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# Is x positive? (1) x^2 + 10 x > 0 (2) 3^x > 1

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
Is x positive? (1) x^2 + 10 x > 0 (2) 3^x > 1  [#permalink]

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29 Oct 2017, 00:41
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:14) correct 27% (01:17) wrong based on 137 sessions

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Is x positive?

(1) x^2 + 10 x > 0
(2) 3^x > 1

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Retired Moderator
Joined: 25 Feb 2013
Posts: 1216
Location: India
GPA: 3.82
Is x positive? (1) x^2 + 10 x > 0 (2) 3^x > 1  [#permalink]

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29 Oct 2017, 10:37
2
Bunuel wrote:
Is x positive?

(1) x^2 + 10 x > 0
(2) 3^x > 1

Statement 1: implies $$x(x+10)>0$$

$$=> x<-10$$ or $$x>0$$. clearly $$x$$ can be negative or positive. Hence insufficient

Statement 2: $$3^x>3^0 => x>0$$. Sufficient

Option B
CEO
Joined: 11 Sep 2015
Posts: 3440
Is x positive? (1) x^2 + 10 x > 0 (2) 3^x > 1  [#permalink]

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29 Nov 2018, 17:07
Top Contributor
Bunuel wrote:
Is x positive?

(1) x² + 10x > 0
(2) 3^x > 1

Target question: Is x positive?

Statement 1: x² + 10x > 0
Let's TEST some values
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 1. In this case, the answer to the target question is YES, x IS positive
Case b: x = -20. In this case, the answer to the target question is NO, x is NOT positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3^x > 1
We know that 3^0 = 1
If x < 0, then 3^x < 1
And if x > 0, then 3^x > 1
So, statement 2 indirectly tells us that x IS positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Is x positive? (1) x^2 + 10 x > 0 (2) 3^x > 1   [#permalink] 29 Nov 2018, 17:07
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# Is x positive? (1) x^2 + 10 x > 0 (2) 3^x > 1

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