If s4v3x7 < 0, is svx < 0?
(1) v < 0
(2) x > 0
all is raise to i.e is s4 v3 x7
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Since s�v³x� < 0, svx≠0.Abhijit K wrote:If s�v³x� < 0, is svx < 0?
(1) v < 0
(2) x > 0
Implication:
If s, v or x is raised to ANY EVEN POWER, the result will be POSITIVE.
Implication:
Each side of s�v³x� < 0 can safely be divided by any even power of s, v, or x.
Thus:
(s�v³x�)/(s�v²x�) < 0/(s�v²x�)
vx < 0.
Question stem: Is svx < 0?
Since vx < 0, svx < 0 only if s>0.
Question stem, rephrased:
Is s>0?
Even when the statements are combined, it is possible that s<0 or s>0.
The correct answer is E.
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Hi Abhijit K,
This DS question is loaded with Number Property rules and you have to be thorough with your thinking to get the correct answer.
First, since s�v³x� < 0 we have to think about what S, V and X COULD be....
Since the product is less than 0, NONE of those variables can equal 0.
s� will always be positive, but S COULD be positive or negative
v³ will be positive IF V is positive.
v³ will be negative IF V is negative
x� will be positive IF X is positive
x� will be negative IF X is negative
So, knowing that s�v³x� < 0, that means....
We don't know whether S is positive or negative
Between V and X, one is positive and one is negative.
(+)(+)(-) = less than 0
(+)(-)(+) = less than 0
Knowing all of this, we can now work on the question itself: Is (S)(V)(X) < 0? This is a YES/NO question.
Fact 1: V < 0
Knowing that V is negative, we also know that X is positive. HOWEVER, we don't know whether S is positive OR negative...
IF....S is positive, we have (+)(-)(+) = negative and the answer to the question is YES.
IF....S is negative, we have (-)(-)(+) = negative and the answer to the question is NO.
Fact 1 is INSUFFICENT
Fact 2: X > 0
Here, we have the same situation that we had in Fact 1. We know that X is positive, so we know that V is negative, but we don't know about S. The same two examples in Fact 1 fit here as well.
Fact 2 is SUFFICIENT.
Combined, we know...
V < 0
X > 0
And all of the deductions that we made form the prompt itself.
We end up with the same 2 examples that we had before - one YES and one NO answer.
Combined, INSUFFICIENT.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
This DS question is loaded with Number Property rules and you have to be thorough with your thinking to get the correct answer.
First, since s�v³x� < 0 we have to think about what S, V and X COULD be....
Since the product is less than 0, NONE of those variables can equal 0.
s� will always be positive, but S COULD be positive or negative
v³ will be positive IF V is positive.
v³ will be negative IF V is negative
x� will be positive IF X is positive
x� will be negative IF X is negative
So, knowing that s�v³x� < 0, that means....
We don't know whether S is positive or negative
Between V and X, one is positive and one is negative.
(+)(+)(-) = less than 0
(+)(-)(+) = less than 0
Knowing all of this, we can now work on the question itself: Is (S)(V)(X) < 0? This is a YES/NO question.
Fact 1: V < 0
Knowing that V is negative, we also know that X is positive. HOWEVER, we don't know whether S is positive OR negative...
IF....S is positive, we have (+)(-)(+) = negative and the answer to the question is YES.
IF....S is negative, we have (-)(-)(+) = negative and the answer to the question is NO.
Fact 1 is INSUFFICENT
Fact 2: X > 0
Here, we have the same situation that we had in Fact 1. We know that X is positive, so we know that V is negative, but we don't know about S. The same two examples in Fact 1 fit here as well.
Fact 2 is SUFFICIENT.
Combined, we know...
V < 0
X > 0
And all of the deductions that we made form the prompt itself.
We end up with the same 2 examples that we had before - one YES and one NO answer.
Combined, INSUFFICIENT.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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Brent@GMATPrepNow
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The above solutions are great, so I won't delve into in the solution.
I just want to note that, at the heart of this question lie the following (important) properties:
Two important rules:
ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE
An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE
Cheers,
Brent
I just want to note that, at the heart of this question lie the following (important) properties:
Two important rules:
ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE
An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
