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

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Math Expert
Joined: 02 Sep 2009
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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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02 Jun 2015, 07:03
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75% (01:42) correct 25% (02:04) wrong based on 260 sessions

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

(1) |x| = 2

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

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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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02 Jun 2015, 07:13
3
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

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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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08 Jun 2015, 03:34
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1
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 $$x^y = x^0 = 1$$.

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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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13 Mar 2017, 04:17
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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13 Mar 2017, 04:33
anairamitch1804 wrote:
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

Merging topics. Please refer to the discussion above.
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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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25 Sep 2017, 18:27
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
Re: If x and y are integers, and x ≠ 0, what is the value of x^y? &nbs [#permalink] 25 Sep 2017, 18:27
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# If x and y are integers, and x ≠ 0, what is the value of x^y?

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