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# If x is a non-zero integer, what is the value of xy?

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Math Expert
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If x is a non-zero integer, what is the value of xy?  [#permalink]

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06 Nov 2014, 09:20
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Difficulty:

45% (medium)

Question Stats:

70% (02:20) correct 30% (02:27) wrong based on 211 sessions

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Tough and Tricky questions: Algebra.

If x is a non-zero integer, what is the value of xy?

(1) x = 2

(2) $$128^x*6^{(x + y)} = 48^{(2x)}*3^{(-x)}$$

Kudos for a correct solution.

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Re: If x is a non-zero integer, what is the value of xy?  [#permalink]

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06 Nov 2014, 10:24
2
Statement 1 is clearly insufficient.
Statement 2: You can combine all the bases with the exponent "x". They all end up cancelling out and yielding 6^y=1^x. Here, 1^x is always equal to 1, so 6^y=1 and that should be sufficient.

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Re: If x is a non-zero integer, what is the value of xy?  [#permalink]

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06 Nov 2014, 13:15
1
Statement 1 not sufficient since we clearly dont know value of y
Statement 2 can be simplified to reach 2^y*3^y=1, 6^y=1
This means y=0
This is enough to find xy that is 0

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Re: If x is a non-zero integer, what is the value of xy?  [#permalink]

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06 Nov 2014, 20:06
Statement 1 is clearly insufficient, since we don't know the value of y

Statement 2:
128^x*6^(x + y) = 48^(2x)*3^(-x)

This can be simplified as

2^8x * 2^y * 3^x*3^y = 2^8x*3^x
=> 2^y *3^y=1
Only possible if y = 0

Therefore xy = 0. Sufficient

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Re: If x is a non-zero integer, what is the value of xy?  [#permalink]

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06 Nov 2014, 23:58
1
Bunuel wrote:

Tough and Tricky questions: Algebra.

If x is a non-zero integer, what is the value of xy?

(1) x = 2
(2) 128^x*6^(x + y) = 48^(2x)*3^(-x)

Kudos for a correct solution.

Statmnt1) Nothing we know about Y...Insuff

Statmnt2)
2^7x * 2^(x+y) * 3^(x+y) = 3^2x*2^8x*3^(-x)
2^8x+y * 3^(x+y) = 3^x * 2^8x

so y=0 -> xy=0

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Re: If x is a non-zero integer, what is the value of xy?  [#permalink]

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20 Jan 2017, 22:10
There is another thread on this post which is actually locked. In that question says to find the value of x^y and here it says to find xy though it doesn't matter which one you find as answer will be same. I just want to clarify which question is correct.

if-x-is-a-non-zero-integer-what-is-the-value-of-x-y-1-x-30817.html
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Re: If x is a non-zero integer, what is the value of xy?  [#permalink]

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21 Jan 2017, 01:06
anairamitch1804 wrote:
There is another thread on this post which is actually locked. In that question says to find the value of x^y and here it says to find xy though it doesn't matter which one you find as answer will be same. I just want to clarify which question is correct.

if-x-is-a-non-zero-integer-what-is-the-value-of-x-y-1-x-30817.html

Hi,

Both the questions are correct.

If you solve the equation in statement 2. You get y=0
This is sufficient to get the value of xy and x^y, as we are already given that x is a non zero integer in both the questions.
Given y=0, xy = 0 and x^y = 1.
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Re: If x is a non-zero integer, what is the value of xy?  [#permalink]

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29 Jan 2017, 03:50
If x is a non-zero integer, what is the value of xy?

x could negative or positive integer. y could be any number

(1) x = 2

Insufficient

(2) 128^x*6^(x + y) = 48^(2x)*3^(-x)

Simplifying the equation above keeping an eye of 3 as it has x & y......... 3^(x+y) = 3^x

x+y=x............then y=0

xy=0

Sufficient

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Re: If x is a non-zero integer, what is the value of xy?  [#permalink]

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29 Nov 2018, 17:19
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Re: If x is a non-zero integer, what is the value of xy?   [#permalink] 29 Nov 2018, 17:19
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