Data Sufficiency

M7MBA wrote:Is kw>0?

(1) k - w = 10

(2) k^2 = w^2

Statement 1:
Case 1: k=10 and w=0
In this case, kw=0, so the answer to the question stem is NO.
Case 2: k=11 and w=1
In this case, kw=11, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statement 2:
Case 3: k=0 and w=0
In this case, kw=0, so the answer to the question stem is NO.
Case 2: k=1 and w=1
In this case, kw=1, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statements combined:
Statement 2 can be rephrased as follows:
k² - w² = 0
(k+w)(k-w) = 0.
Since Statement 1 indicates that k-w=10, the equation in blue requires that k+w=0.
Since we have two variables (k and w) and two distinct linear equations (k-w=10 and k+w=0), we can solve for the two variables, enabling us to determine whether kw>0.
SUFFICIENT.

The correct answer is C.

The values of k and w can be determined by ADDING together k-w=10 and k+w=0:
(k-w) + (k+w) = 10+0
2k = 10
k = 5.
Substituting k=5 into k+w = 0, we get:
5+w = 0
w = -5.