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Function data sufficiency

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Jul 28, 2014 2:50 am
alexandrabiorka wrote: Is f(x) < 0?

(1) f(x) = (x^3)^3(x^5)
(2) x = -2
Target question: Is f(x) less than 0?

Statement 1: f(x) = (x^3)^3(x^5)
Simplify to get: f(x) = (x^9)(x^5) = x^14
Since x is raised to an EVEN power, x^14 will be greater than or equal to zero for ANY x value.
If that's the case, then we can be certain that f(x) is NOT less than 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = -2
Here, we don't know anything about the function f(x)
Consider these two conflicting cases:
Case a: f(x) = x + 3, in which case f(-2) = -2 + 3 = 1. Here, f(x) is NOT less than 0
Case b: f(x) = x - 3, in which case f(-2) = -2 - 3 = -5. Here, f(x) IS less than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Sat Oct 08, 2016 7:09 am, edited 1 time in total.
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by GMATinsight » Mon Jul 28, 2014 8:23 am
alexandrabiorka wrote:Here is a data suffic problem I have been stumbling on.

Is f(x) < 0?

(1) f(x) = (x^3)^3(x^5)
(2) x=-2
Question : Is f(x) < 0?

Statement 1) f(x) = (x^3)^3(x^5)

Value of x is unknown, therefore,
INSUFFICIENT

Statement 2) x=-2

'How Function f(x) is related to x' is unknown therefore,
INSUFFICIENT

Combining the two statements
Both x and how f(x) is related to x are known, therefore
SUFFICIENT

Answer: Option C
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by dassabyasachi14 » Sat May 07, 2016 12:00 pm
Is f(x) < 0?

(1) f(x) = (x^3)^3(x^5)
(2) x=-2

I think the answer to this question is (A)- Statement (1) alone is sufficient.

Reason:
1) f(x)= x^14

So, if x=0==> f(x)=0

In this case, is f(x)<0?? ---> No, f(x)= 0

2) For x=-1==> f(x)= 1.

Again is f(x)<0?? ---> No

3) For x=1==> f(x)= 1.

Again is f(x)<0?? ---> No

All the previous answers to this question is (C).

Please clarify if my answer- "Statement (1) alone is sufficient" is incorrect??
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by emilytay23 » Sun Aug 28, 2016 10:37 pm
I also think that it should indeed be A. Since the question asks Is f(x) < 0?

To which we can safely answer yes with the info in Statement 1. Since the exponent of 14 is even, it will never f(x) will never be negative.

Although the we dont know for sure what the value is f(x) is, the target question is phrased in a way that requires only a yes or no answer.

Please help!
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by harmeen19 » Sat Oct 08, 2016 2:18 am
Hi @Brent, I think the question stem says: "Is f(x)<0?" And not "Is f(x) greater than 0?" as mentioned in your response.

With this, Statement A: SUFFICIENT
Taking x=1, f(x) = (1)^14 = 1 , so answer to the question stem is NO
Taking x=0, f(x) = (0)^14 = 0 , so answer to the question stem is NO
We can answer the target question with certainty, so SUFFICIENT

Statement B: INSUFFICIENT since we dont know about the function f(x).

OA: a
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by harmeen19 » Sat Oct 08, 2016 2:23 am
Brent@GMATPrepNow wrote:
alexandrabiorka wrote: Is f(x) < 0?

(1) f(x) = (x^3)^3(x^5)
(2) x = -2
Target question: Is f(x) greater than 0?

Statement 1: f(x) = (x^3)^3(x^5)
Simplify to get: f(x) = (x^9)(x^5) = x^14
Since there are no restrictions on the value of x, there are several possible cases. Here are two:
Case a: x = 1, in which case f(x) = 1^14 = 1. In this case, f(x) is GREATER than 0
Case b: x = 0, in which case f(x) = 0^14 = 0. In this case, f(x) is NOT GREATER than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = -2
Here, we don't know anything about the function f(x)
Consider these two conflicting cases:
Case a: f(x) = x + 3, in which case f(-2) = -2 + 3 = 1. Here, f(x) is GREATER than 0
Case b: f(x) = x - 3, in which case f(-2) = -2 - 3 = -5. Here, f(x) is NOT GREATER than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that f(x) = x^14
Statement 2 tells us that x = -2
f(-2) = (-2)^14 = SOME POSITIVE VALUE
In other words, f(x) is definitely GREATER then 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Hi @Brent, I think the question stem says: "Is f(x)<0?" And not "Is f(x) greater than 0?" as mentioned in your response.

With this, Statement A: SUFFICIENT
Taking x=1, f(x) = (1)^14 = 1 , so answer to the question stem is NO
Taking x=0, f(x) = (0)^14 = 0 , so answer to the question stem is NO
We can answer the target question with certainty, so SUFFICIENT

Statement B: INSUFFICIENT since we dont know about the function f(x).

OA: a
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by Brent@GMATPrepNow » Sat Oct 08, 2016 7:11 am
harmeen19 wrote:Hi @Brent, I think the question stem says: "Is f(x)<0?" And not "Is f(x) greater than 0?" as mentioned in your response.

With this, Statement A: SUFFICIENT
Taking x=1, f(x) = (1)^14 = 1 , so answer to the question stem is NO
Taking x=0, f(x) = (0)^14 = 0 , so answer to the question stem is NO
We can answer the target question with certainty, so SUFFICIENT

Statement B: INSUFFICIENT since we dont know about the function f(x).

OA: a
You're absolutely right. I misread the question.
The correct answer is, indeed, A.
I have edited my response accordingly.

Cheers and thanks,
Brent
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