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# If x is an integer, is y an integer?

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Math Expert
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If x is an integer, is y an integer? [#permalink]

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28 Feb 2014, 03:01
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x, y, and y - 2 is x.
(2) The average (arithmetic mean) of x and y is not an integer.

Data Sufficiency
Question: 118
Category: Arithmetic Statistics; Properties of numbers
Page: 161
Difficulty: 600

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If x is an integer, is y an integer? [#permalink]

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28 Feb 2014, 03:02
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SOLUTION

If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x, y and y – 2 is x --> $$\frac{x+y+(y-2)}{3}=x$$ --> $$x+2y-2=3x$$ --> $$y=x+1=integer+integer=integer$$. Sufficient.

(2) The average (arithmetic mean) of x and y is not an integer --> if $$x=1$$ and $$y=2$$ the answer is YES but $$x=1$$ and $$y=\frac{1}{2}$$ the answer is NO. not sufficient.

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Re: If x is an integer, is y an integer? [#permalink]

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28 Feb 2014, 06:25
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KUDOS

Statement 1 is sufficient because if we perform algebra we get :

x+y-2+y/3=x
=2x= 2y-2
=x-1=y so if X is and integer Y is definitely an integer !!!

Statement 2 is insufficient because Y could be an Odd integer which results in a non integer
or Y could be a decimal and will result in a non integer.

Therefore "A" is the answer !!
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Re: If x is an integer, is y an integer? [#permalink]

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02 Mar 2014, 22:28
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KUDOS
[quote="Bunuel"]The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x, y, and y -2 is x.
(2) The average (arithmetic mean) of x and y is not an integer.

Statement I is sufficient:

(x + y + y - 2) = 3x
x +2y - 2 = 3x
2y = 2x + 2
y = x + 1

If x is an integer then x + 1 will also be an integer

Statement II is insufficient:
x = 1, y = 2 - the average of x and y is not an integer however y is an integer
x = 1, y = 1.5, the average of x and y is not an integer and y is also not an integer

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Joined: 16 Oct 2017
Posts: 25
Re: If x is an integer, is y an integer? [#permalink]

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01 Feb 2018, 11:36
Bunuel wrote:
SOLUTION

If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x, y and y – 2 is x --> $$\frac{x+y+(y-2)}{3}=x$$ --> $$x+2y-2=3x$$ --> $$y=x+1=integer+integer=integer$$. Sufficient.

(2) The average (arithmetic mean) of x and y is not an integer --> if $$x=1$$ and $$y=2$$ the answer is YES but $$x=1$$ and $$y=\frac{1}{2}$$ the answer is NO. not sufficient.

With the limited time constraints, how can you tell if it's best to try out alegebra or to plug in numbers?

I tried to plug in numbers for statement 1, but didn't seem to plug in correctly. I then proceeded to plug in #'s for number #2, and this one was much easier to solve!
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Re: If x is an integer, is y an integer? [#permalink]

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02 Feb 2018, 10:21
OCDianaOC wrote:
Bunuel wrote:
SOLUTION

If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x, y and y – 2 is x --> $$\frac{x+y+(y-2)}{3}=x$$ --> $$x+2y-2=3x$$ --> $$y=x+1=integer+integer=integer$$. Sufficient.

(2) The average (arithmetic mean) of x and y is not an integer --> if $$x=1$$ and $$y=2$$ the answer is YES but $$x=1$$ and $$y=\frac{1}{2}$$ the answer is NO. not sufficient.

With the limited time constraints, how can you tell if it's best to try out alegebra or to plug in numbers?

I tried to plug in numbers for statement 1, but didn't seem to plug in correctly. I then proceeded to plug in #'s for number #2, and this one was much easier to solve!

Hi

I think this comes best with practice. The more we practice various questions and the more you try to apply both algebra and number plug-in methodology in those questions, the more our understanding will increase steadily.
Eg., in this question only substitution works better in statement 2 but algebra works better in statement 1.

Sometimes we will see that when there are only 1/2 variables, substitution works out well and when more variables are given in a question, generally algebra or some conceptual application fits in better towards a solution. (That is not true all the time though)
Re: If x is an integer, is y an integer?   [#permalink] 02 Feb 2018, 10:21
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