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
Brent you have made a mistake. The correct answer should be
E. Let me explain:
We are given s^4*v^3*x^7<0 which tells us two things.
1. None of s, v, x are 0.
2. s^4*v^3*x^7 = (s^2*v*x^3)^2*(vx) <0
anything squared is positive (since none of s,v,x equals 0), hence vx<0.
We are looking for svx. We know that vx<0, so
we need to find a statement that tells us whether s is greater than or less than 0.
Now we have the two conditions. :
1. v<0 , doesn't tell whether s is positive or negative, INSUFFICIENT.
2 x>0, doesn't tell whether s is positive or negative, INSUFFICIENT.
Together, it tells us that v<0, x>0 tell us that vx<0, which we already knew. Hence we still don't know the sign of s. Still INSUFFICIENT. Hence
E
Let me know if this helps
