There are 2 variables in the original condition, Hence, since we need 2 equations, the correct answer is C.
The line of reasoning is typically valid for a DS with two distinct linear equations and two variables.
But if a DS problem is constrained to positive integers, one equation with two variables can be sufficient:
https://www.beatthegmat.com/to-find-the- ... 73004.html).
Here, Statement 1 is not an equation but an inequality -- and a NONLINEAR inequality at that.
As a result, we cannot conclude that the two statements are sufficient simply because they offer two variables and two distinct relationships with these variables.
Consider the following variation:
Is y > 0?
1) x² > y²
2) x+y = 1
Statement 1:
It's possible that x=2 and y=1, in which case y>0.
It's possible that x=2 and y=-1, in which case y<0.
INSUFFICIENT.
Statement 2:
It's possible that x=0 and y=1, in which case y>0.
It's possible that x=2 and y=-1, in which case y<0.
INSUFFICIENT.
Statements combined:
Statement 2 implies that x = 1-y.
Substituting x = 1-y into x² > y², we get:
(1-y)² > y²
1² + y² - 2y > y²
1 > 2y
1/2 > y
y < 1/2.
If y=1/4, then the answer to the question stem is YES.
If y=-1, then the answer to the question stem is NO.
INSUFFICIENT.
Virtually the same set of facts, yet the correct answer is not C but
E.
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