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If x and y are integers, and x ≠ 0, what is the value of x^y?

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If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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New post 02 Jun 2015, 06:03
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72% (02:04) correct 28% (02:22) wrong based on 351 sessions

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Re: If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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New post 02 Jun 2015, 06:13
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Bunuel wrote:
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)


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
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Re: If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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New post 08 Jun 2015, 02:34
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Bunuel wrote:
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)


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.
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Re: If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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New post 13 Mar 2017, 03:17
If x and y are integers, and x ≠ 0, what is the value of x^y?
(1) |x| = 2

(2) 64^x6^(2x + y) = 48^2x
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Re: If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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New post 13 Mar 2017, 03:33
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Re: If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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New post 25 Sep 2017, 17:27
Bunuel wrote:
If x and y are integers, and x ≠ 0, what is the value of \(x^y\)?

(1) |x| = 2

(2) \(64^x*6^{(2x + y)} = 48^{(2x)}\)


St 1

Too many possibilities...and no info about y

insuff

St 2

2^6x * 6^2x+y= 2^6x * 6^2x

2^6x * 6^2x+y=2^6x * 6^2x

6^(2x+y)= 6^(2x)
2x +y =2x
y= 0

This just basically tells us that x^y will always be 1 since x cannot be 0

B
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Re: If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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New post 26 Jan 2019, 03:35
Bunuel wrote:
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
Tells nothing about x

2) \(64^x*6^{(2x + y)} = 48^{(2x)}\)

\(2^{6x} * 2^{(2x + y)} * 3^{(2x + y)} = 2^{8x} * 3^{2x}\)

\(2^{(8x + y)} * 3^{(2x + y)} = 2^{8x} * 3^{2x}\)

Compare the similar terms to get value of y as 0

Now anything raised to power 0 is 1

B
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Re: If x and y are integers, and x ≠ 0, what is the value of x^y?   [#permalink] 26 Jan 2019, 03:35
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