Data Sufficiency

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]

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...

@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.

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.

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...