Bunuel wrote:
If 2^(x + y) = 4^8, what is the value of y?
(1) x^2 = 81
(2) x − y = 2
Kudos for a correct solution.
Target question: What is the value of y? Given: 2^(x + y) = 4^8 Notice that 4^8 = (2^2)^8 = 2^16
In other words, 2^
(x + y) = 2^
16, which means
x + y = 16 Statement 1: x^2 = 81 This tells us that x = 9 OR x = -9
Let's examine each possible case
Case a: x = 9. If
x + y = 16, then we can conclude that
y = 7Case b: x = -9. If
x + y = 16, then we can conclude that
y = 25Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x − y = 2 When we combine this information with
x + y = 16, we see that we have TWO different equations and TWO variables.
So, we COULD solve this system to find one unique value of y (incidentally, we get
y = 7)
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
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