ajaysingh24 wrote:If the product of x and y is a positive number, is the sum of x and y a negative number?
(1) x > y^5
(2) x > y^6
IMPORTANT CONCEPTS:
An ODD power preserves the sign of the base.
For example, (-5)^3 = -125 and 2^5 = 32
An EVEN power always yields a positive number (as long as the base ≠0
For example, (-5)^4 = 625 and 2^6 = 64
Target question: Is the sum of x and y negative?
Given: the product xy is positive
This tells us that EITHER
x and y are both positive, OR
x and y are both negative
Also, if the product xy is positive, we know that x ≠0 and y ≠0
Statement 1: x > y^5
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = -1 and y = -2, in which case
the sum of x and y IS negative
Case b: x = 10 and y = 1, in which case
the sum of x and y is NOT negative
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x > y^6
Since y ≠0 we know that y^6 must be positive
[since we have an EVEN exponent]
If x > y^6, then we know that x MUST BE POSITIVE
So, there are only 2 possible scenarios to consider:
Scenario #1: x is positive and y is positive
Scenario #2: x is positive and y is negative
HOWEVER, scenario #2 CANNOT OCCUR because it is given that the product xy is positive, and the product cannot be positive in scenario #2.
So, scenario #1 is the only possible scenario, which means x is positive and y is positive, which means
the sum of x and y is definitely NOT negative
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
