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
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Function data sufficiency
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alexandrabiorka
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Target question: Is f(x) less than 0?alexandrabiorka wrote: Is f(x) < 0?
(1) f(x) = (x^3)^3(x^5)
(2) x = -2
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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Question : Is f(x) < 0?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
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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dassabyasachi14
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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??
(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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emilytay23
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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!
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!
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
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
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.Brent@GMATPrepNow wrote:Target question: Is f(x) greater than 0?alexandrabiorka wrote: Is f(x) < 0?
(1) f(x) = (x^3)^3(x^5)
(2) x = -2
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
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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You're absolutely right. I misread the question.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
The correct answer is, indeed, A.
I have edited my response accordingly.
Cheers and thanks,
Brent
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