Nina1987 wrote:
VeritasPrepKarishma wrote:
When is z greater than z^2? When z lies between -1 and 1
VeritasPrepKarishma :
Except for z=0 right?
This actually tripped me up, I ended up way overthinking this problem. Luckily, it isn't actually an issue here because statements 1) & 2) explicitly rule out 0 for x and y. In a more difficult problem I could easily see either case 1 or case 2 being viable and thus changing the answer to E.
Is |xy| > x^2*y^2 ?The question is asking if the product of 2 numbers is more than the product of the two numbers squared.
What the question is testing is the properties of exponents around -1,0,1
There are 4 cases:1. If either x,y = 0 then they are equal (Answer = No)
2. If both x,y are between -1, and 1, then the exponent fractions are smaller (Answer = Yes)
3. If both are less or greater than -1 and 1, then the exponent fractions are bigger (Answer = No)
4. If one is bigger and the other is between then it becomes a question of individual values, as product of fractions could cancel out to make them equal, e.g. x=1/2, y=2 so 1/2 * 2 = 1/4 * 4 = 1 (Answer = Yes/No)
(1) 0 < x^2 < 1/4This means that x^2 is positive (obviously, since it's squared)
x^2 < 1/4
But, taking the square root gives us back the negative side of the inequality...
-1/2 < x < 1/2
We know that x≠0 because the LHS of the original statement was 0 < x^2 and NOT 0 ≤ x^2
We have no info about y so we can't make a determination, insufficient.
(2) 0 < y^2 < 1/9 The same idea as above, -1/3 < y < 1/3, y≠0
No information about x, insufficient.
(3)y≠0, x≠0
This rules out case 1.
-1/3 < y < 1/3
-1/2 < x < 1/2
Both are between -1 and 1 which rules out case 3 and 4, and we're left with only case 2, definite Yes, C is sufficient!