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If f(x) = x^3 + 9, is f(x) positive? 08 Feb 2017, 01:46
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

58% (01:34) correct 42% (00:59) wrong based on 433 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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E
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If f(x) = x^3 + 9, is f(x) positive? 08 Feb 2017, 02:47
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Bunuel
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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If f(x) = x^3 + 9, is f(x) positive? 08 Feb 2017, 11:10
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Bunuel
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? 11 Feb 2017, 21:06
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Bunuel
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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If f(x) = x^3 + 9, is f(x) positive? 13 Feb 2017, 01:48
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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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If f(x) = x^3 + 9, is f(x) positive? 13 Feb 2017, 02:28
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deepthit
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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If f(x) = x^3 + 9, is f(x) positive? 14 Nov 2020, 09:59
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Quote:
If f(x) = x^3 + 9, is f(x) positive?
Step 1: Understanding the question
When f(x) = 0
x^3 + 9 = 0
x = \((-9)^{1/3}\)
x ~ -2.1
When x = -3; f(x) is negative
When x = -1; f(x) is positive
ie. on left side of -2.1, the function is negative, and on right side of -2.1 the function is positive

Step 2: Understanding statement 1 alone
(1) x < −1
When x = -1.5; f(x) is positive
When x = -2.5; f(x) is negative
Insufficient

Step 3: Understanding statement 2 alone
(2) x > −3
from above reasoning; Insufficient

Step 4: Combining
x lies between -3 and -1 ie -3<x<-1. Still sign of f(x) is unknown.
Insufficient

E is correct
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If f(x) = x^3 + 9, is f(x) positive? 18 Feb 2025, 00:10
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