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# If f(x) = x^3 + 9, is f(x) positive?

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If f(x) = x^3 + 9, is f(x) positive?  [#permalink]

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08 Feb 2017, 00:46
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Difficulty:

55% (hard)

Question Stats:

58% (01:30) correct 42% (00:52) wrong based on 160 sessions

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If f(x) = x^3 + 9, is f(x) positive?

(1) x < −1

(2) x > −3

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If f(x) = x^3 + 9, is f(x) positive?  [#permalink]

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08 Feb 2017, 01:47
1
1
Bunuel wrote:
If f(x) = x^3 + 9, is f(x) positive?

(1) x < −1

(2) x > −3

St I
x < -1
if x = -2 we have $$(-2)^3+9$$ = 1 f(x) is positive.
if x = -3 we have $$(-3)^3+9$$ = -18 f(x) is negative ----------Insufficient.

St II
x > -3
if x = -2 we have $$(-2)^3+9$$ = 1 f(x) is positive.
if x = -2.5 we have $$(-2.5)^3+9$$ = -6.25 f(x) is negative. ----------Insufficient.

St. I and II ----------Insufficient.

Hence Option E is correct.
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Re: If f(x) = x^3 + 9, is f(x) positive?  [#permalink]

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08 Feb 2017, 10:10
Bunuel wrote:
If f(x) = x^3 + 9, is f(x) positive?

(1) x < −1

(2) x > −3

1) If x is -2 f(x) is +ve. If x is -3 f(x) is -ve. Not suff.
2) If x is -2 f(x) is +ve. If x is -2.9 f(x) is -ve. Not suff.
1)&2) Constraints for 2) still apply. Not suff. E.
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If f(x) = x^3 + 9, is f(x) positive?  [#permalink]

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11 Feb 2017, 20:06
Bunuel wrote:
If $$f(x) = x^3 + 9$$, is $$f(x)$$ positive?

(1) $$x < −1$$

(2) $$x > −3$$

Official solution from Veritas Prep.

If $$x<−1$$, then x could be $$−2$$ in which case $$f(x)$$ is positive or $$x$$ could be $$−3$$ in which case $$f(x)$$ is negative. Therefore, Statement 1 alone is not sufficient.

If $$x>−3$$, the x could be $$−2$$ in which case $$f(x)$$ is positive. However, the problem never stated that $$x$$ is an integer. Then, $$x$$ could be $$-2.99999$$, that is almost $$-3$$. In this case, $$f(x)$$ will be a negative. $$f(x)=(-2.99999)^3+9 = -17.99973$$ Therefore, Statement 2 is not sufficient.

Combining Statement 1 and Statement 2, $$f(x)$$ could still either be positive or negative. Therefore, the answer is $$E$$.
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Re: If f(x) = x^3 + 9, is f(x) positive?  [#permalink]

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13 Feb 2017, 00:48
I think it should be B.

(-2.9999)^3 is less than 9 and therefor -899999+9 >0

Hence it should be B
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Re: If f(x) = x^3 + 9, is f(x) positive?  [#permalink]

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13 Feb 2017, 01:28
deepthit wrote:
I think it should be B.

(-2.9999)^3 is less than 9 and therefor -899999+9 >0

Hence it should be B

(-2.9999)^3 = -26.997300 < 0.
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Re: If f(x) = x^3 + 9, is f(x) positive?  [#permalink]

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04 Apr 2018, 22:08
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Re: If f(x) = x^3 + 9, is f(x) positive? &nbs [#permalink] 04 Apr 2018, 22:08
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