Does ∛b = ∛(2b-a)?
1. a+b=0
2. a=2b
Does ∛b = ∛(2b-a)?
Cubing both sides, we get:
(∛b)³ = [∛(2b-a)]³
b = 2b-a
a = b.
Question stem, rephrased:
Does a=b?
Statement 1: a+b = 0
Case 1: a=0, b=0
In this case, a=b, so the answer to the question stem is YES.
Case 2: a=1, b=-1
In this case, a≠b, so the answer to the question stem is NO.
INSUFFICIENT.
Statement 2: a=2b
Case 1: a=0, b=0
In this case, a=b, so the answer to the question stem is YES.
Case 3: a=2, b=1
In this case, a≠b, so the answer to the question stem is NO.
INSUFFICIENT.
Statements combined:
Since we have two distinct linear equations -- a=2b and a+b=0 -- we can solve for a and b.
Since we can solve for a and b, we can determine whether a=b.
SUFFICIENT.
The correct answer is
C.
As noted above, there is no reason to solve for a and b when we combine the two statements.
If we HAD to solve for a and b, we could proceed by substituting a=2b into a+b = 0:
2b+b = 0
3b=0
b=0
a = 2b = 2*0 = 0.
Since a=0 and b=0, a=b.
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