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Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE DS
Solution:
Since we want to find the value of y, let’s isolate y in the equation:
2^(x + y) = 4^8
2^(x + y) = (2^2)^8
2^(x + y) = 2^16
x + y = 16
y = 16 – x
If we can find the value of x, we can find the value of y.
Statement One Alone:
x^2 = 81
This means x = 9 or x = -9. If x = 9, then y = 16 – x = 16 – 9 = 7. However, if x = -9, then y = 16 – x = 16 – (-9) = 25. Since we have two different values for y, statement one alone is not sufficient. We can eliminate choices A and D.
Statement Two Alone:
x – y = 2
Since y = 16 – x, we can substitute 16 – x for y into the equation x – y = 2:
x – (16 – x) = 2
x – 16 + x = 2
2x = 18
x = 9
Since x = 9, then y = 16 – 9 = 7. Statement two alone is sufficient to answer the question.
Answer: B
