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Math Expert V
Joined: 02 Sep 2009
Posts: 58417
If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 70% (02:07) correct 30% (02:27) wrong based on 359 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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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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Math Expert V
Joined: 02 Sep 2009
Posts: 58417
Re: If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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3
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 $$x^y = x^0 = 1$$.

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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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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Anaira Mitch
Math Expert V
Joined: 02 Sep 2009
Posts: 58417
Re: If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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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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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
Director  G
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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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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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Intern  B
Joined: 21 Jan 2019
Posts: 5
Re: If x and y are integers, and x ≠ 0, what is the value of x^y?  [#permalink]

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Any tips for reducing solving time? I understand the mechanics of how to solve but can't manage to complete (2) in the requisite time.
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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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sfoo wrote:
Any tips for reducing solving time? I understand the mechanics of how to solve but can't manage to complete (2) in the requisite time.

Hey sfoo

You have to get comfortable with playing around exponents, solve questions pertaining to this topic, this can actually help you on improving on this question type.

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Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: If x and y are integers, and x ≠ 0, what is the value of x^y?   [#permalink] 24 Feb 2019, 07:43
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