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02 Jun 2015, 07:03
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B
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Difficulty:
35%
(medium)
Question Stats:
71% (02:08) correct
29%
(02:27)
wrong
based on 659
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If x and y are integers, and x ≠ 0, what is the value of \(x^y\)?
(1) |x| = 2
(2) \(64^x*6^{(2x + y)} = 48^{(2x)}\)
(1) |x| = 2
(2) \(64^x*6^{(2x + y)} = 48^{(2x)}\)
08 Jun 2015, 03:34
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Bunuel
MANHATTAN GMAT OFFICIAL SOLUTION:
Since x ≠ 0, we know that xy does not equal 0y or 0. To determine the exact non-zero value of xy, we need either the values of both x and y, or if y is even, the values of |x| and y (an even exponent “hides the sign” of the base, so we wouldn't need to know x's sign).
(1) INSUFFICIENT: This statement tells us that x is equal to 2 or –2. However, we know nothing about y and cannot determine the value of xy.
(2) SUFFICIENT: Simplify using exponent rules, noting the common factors of 6 and 8 on each side of the equation:
\(64^x*6^{2x + y} = 48^{2x}\)
\((8^2)^x *6^{2x + y} = (6*8)^{2x}\)
\(8^{2x}* (6^{2x}*6^y) = 6^{2x}*8^{2x}\)
\(6^y = 1\)
\(y = 0\)
Since y = 0 and x ≠ 0 (as stated in the question stem), this information is sufficient to conclude that \(x^y = x^0 = 1\).
The correct answer is B.
General Discussion
02 Jun 2015, 07:13
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Bunuel
Question : what is the value of x^y?
Statement 1: |x| = 2
i.e. x = +2
but the value of y is unknown in absence of which the value of x^y is indeterminable
Hence NOT SUFFICIENT
Statement 2: 64^x*6^(2x + y) = 48^(2x)
i.e. 2^(6x) * 2^(2x+y) * 3^ (2x+y) = 2^(8x) * 3^(2x)
i.e. 2^(8x+y) * 3^ (2x+y) = 2^(8x) * 3^(2x)
Comparing the powers
i.e. (8x+y) = 8x and (2x+y) = 2x
i.e. y=0
Therefore for any value of x, the value of x^y is always 1 [Because, x^0 = 1]
Hence SUFFICIENT
Answer: Option
