Data Sufficiency

Brent@GMATPrepNow wrote:

alex.gellatly wrote:If s^4v^3x^7<0, is svx<0?

1. v<0
2 x>0

thanks

Two important rules:

Odd exponents preserve the sign of the base.
That is, a positive number raised to an odd power will remain positive. A negative number raised to an odd power will remain negative.

An even exponent always yields a positive result. (Proviso: As long as the base does not equal zero.)
In other words, any non-zero number raised to an even power will result in a positive value.

Since we're told that s^4v^3x^7 < 0, we can conclude that s, v and x do not equal zero. Furthermore, we can conclude that s^4 is positive (from the rule above).

So, we get (some positive number)(v^3)(x^7) < 0
We also know that v^3 has the same sign (positive or negative) as v, and we know that x^7 has the same sign as x (from the rule above).

Since (some positive number)(v^3)(x^7) is negative, there are only two possible cases:
case a) v is positive and x is negative
case b) v is negative and x is positive

Target question: Is svx<0?

Statement 1: v is negative
This means that case b is true, and we can rule out case a.
If case b is true, then v is negative and x is positive, which means (s^4)(v^3)(x^7) = (positive)(negative)(positive) = some negative number.
In other words, (s^4)(v^3)(x^7) must be less than 0
SUFFICIENT


Statement 2: x is positive
This means that case b is true, and we can rule out case a.
Same logic as before . . . (s^4)(v^3)(x^7) must be less than 0
SUFFICIENT

Answer = D

Cheers,
Brent