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Inequalities & Powers

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Inequalities & Powers

by sparkle6 » Tue Sep 20, 2011 8:09 am
If s^4 * v^3 * x^7 < 0, is s*v*x < 0?

1) v < 0

2) x > 0


[spoiler]Answer: E, but I feel it is D because if v < 0, then x must be positive, hence s*v*x is < 0. If x > 0, then v must be negative, and s*v*x is negative.[/spoiler]
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Source: — Data Sufficiency |
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by cans » Tue Sep 20, 2011 8:30 am
s^4 * v^3 * x^7 <0
s^4 >=0
thus v^3 * x^7 <0
v^2*x^6 * vx<0
thus vx<0.
is svx<0??
we know vx<0, thus we have to find whether s>0??
A and b are both insufficient as nothing is given about s...
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by knight247 » Tue Sep 20, 2011 9:28 am
@sparkle6. Ur logic does make sense. However, there is one thing u've overlooked. If v is -ve then v^3 is -ve and the only other logical deduction is that x and therefore x^7 is positive as s^4 is always +ve. But s^4 is always positive irrespective of whether s is +ve or -ve. We still don't have any indication of s's sign in either of the two statements. Even after we combine both statements we only know that s^4 is +ve and hence s could be either negative or positive. Hope that clarifies ur doubt.
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by saketk » Tue Sep 20, 2011 10:13 am
sparkle6 wrote:If s^4 * v^3 * x^7 < 0, is s*v*x < 0?

1) v < 0

2) x > 0


[spoiler]Answer: E, but I feel it is D because if v < 0, then x must be positive, hence s*v*x is < 0. If x > 0, then v must be negative, and s*v*x is negative.[/spoiler]

Since the product given to us is <0 we know for sure that either V or X is NEGATIVE. S^4 will always be positive. BUT, S can be a negative number

From Statement 1 we get to know the sign of X.
From Statement 2 we get to know the sign of V..

BUT we still don't have any information about the sign of S. Therefore the product of these 3 numbers can be either Greater than zero or less than zero.

Hence, the answer should be E.
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by Brian@VeritasPrep » Tue Sep 20, 2011 5:40 pm
Great explanation, guys!

And one thing that comes up in this problem that you could use (I'm not sure how often it would come up, but here it's a nice clue) is this:

If you're saying that the answer is D, then there's really no use for the statements. You'd be able to get D even if the statements were pure gibberish. From the stimulus we know that s^4 must be positive (it's an even exponent so it can't be negative, and the whole product is less than 0, so it's not 0). Which means that one of v and x is positive and the other is negative, because we have:

+ * ? * ? = negative

They can't share the same sign.

When I first looked at this, my initial inclination was D...but that was before I even looked at the statements. And that was my clue to think "wait a second...how can I solve the problem even before I get to the statements?", reconsider the setup and realize that while s^4 must be positive, s could be either positive or negative. s is the linchpin - v * x is definitely going to be negative, so it all hinges on s. And noting that the statements didn't matter in my incorrect-assumption view of the original stimulus gave me that clue that I should read it again more closely.


Like I said, I don't know how often that will come up, but if it does it's a nice clue that you need to go back and reconsider...
Brian Galvin
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Chief Academic Officer
Veritas Prep

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