Bunuel wrote:
For positive integers x and y, x^y*8^3=2(10^8). What is the value of y?
(1) x > y
(2) y is a prime number
Let’s first simplify the given expression:
x^y(8^3) = 2(10^8)
x^y(2^9) = 2^1(2^8 x 5^8)
x^y(2^9) = 2^9 x 5^8
x^y = 5^8
We need to determine the value of y. At this point, it’s tempting to conclude that x = 5 and y = 8. However, this is not always the case; it can be one of the following 4 cases:
1) x = 5, y = 8
2) x = 5^2 = 25, y = 4
3) x = 5^4 = 625, y = 2
4) x = 5^8, y = 1
Statement One Alone:
x > y
Although x is greater than y, we still do not have enough information to determine the value of y. For example, we could have x = 25 and y = 4, or we could have x = 625 and y = 2.
Statement Two Alone:
y is a prime number.
Since y is a prime number, x must be 625 and y must be 2. Statement two alone is sufficient to answer the question.
Answer; B
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