1. Good post? |

If x and y are real numbers, is (x^2 -y^2)^5>0?
(1) (x+y)^2 =25
(2) x-y>0

OA: Later

2. Good post? |
LHS = (x+y)^5*(x-y)^5

(1) x+y=+5 or -5. And do not know which one is greater: x or y? Insufficient.
(2) x>y. Do not know whether they are (+, +) or (-,-). Insufficient.

Combining: Insufficient. Suppose x=3, y=2. LHS>0.
Suppose x=-2, y = -3. LHS<0.

E

3. Good post? |
(x^2 -y^2)^5 = ((x-y)(x+y))^5=(x-y)^5*(x+y)^5

Statement 1 Alone not enough
Statement 2 Alone not enough
Togetherx-y)^5>0 Also (x+y)^4>0 But we do not know if the remaining term (x+y)>0 since x+y can +0r -5 derving from (1).

4. Good post? |

5. Good post? |
Originally Posted by nazar
If x and y are real numbers, is (x^2 -y^2)^5>0?
(1) (x+y)^2 = 25
(2) x-y>0
r
Target question:Is (x^2 - y^2)^5 > 0?

IMPORTANT: (x^2 - y^2)^5 will be positive (i.e., > 0) if and only if (x^2 - y^2) > 0.
So, we can REPHRASE the target question....

REPHRASED target question:Is x^2 - y^2 > 0?

Statement 1: (x+y)^2 = 25
This tells us that EITHER x+y = 5 or x+y = -5
There are several possible values for x and y that satisfy this condition. Here are two:
case a: x = 3 and y = 2, in which case x^2 - y^2 > 0
case b: x = 0 and y = -5, in which case x^2 - y^2 < 0
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - y > 0
In other words, x is GREATER than y
There are several possible values for x and y that satisfy this condition. Here are two:
case a
: x = 3 and y = 2, in which case x^2 - y^2 > 0
case b: x = 0 and y = -5, in which case x^2 - y^2 < 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are still several possible values for x and y that satisfy BOTH conditions. Here are two:
case a
: x = 3 and y = 2, in which case x^2 - y^2 > 0
case b: x = 0 and y = -5, in which case x^2 - y^2 < 0
Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent