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

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If x is an integer, is y an integer? [#permalink]  28 Apr 2012, 21:25
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67% (01:26) correct 32% (01:17) wrong based on 17 sessions
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.
[Reveal] Spoiler: OA

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Re: If x is an integer, is y an integer? [#permalink]  28 Apr 2012, 23:50
1)the average arithmatic mean is (x+y+y-2)/3 = x which simplies to x= y-1 => y is an integer.
1) if x=2 , y=1 mean = 1.5 not an integer, x=2 , y=2.5 mean = 2.25 not an integer => not sufficient
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Re: If x is an integer, is y an integer? [#permalink]  29 Apr 2012, 03:18
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=3y --> y=x-2=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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QR DS #112 [#permalink]  01 May 2013, 11:22
If X is an integer, is Y an integer?

1. The average (mean) of x, y & y-2 is equal to x.
2. The average (mean) of x and y is not an integer.
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Re: QR DS #112 [#permalink]  01 May 2013, 11:26
Guys As i try addressing statement #1, my approach was:
x+y+y-2 /3 = x
thus, x+2y-2 = 3x i.e. ( integer + integer - integer = integer)
Now we know that 2y is an integer however, y may or may not be an integer eg: y=2.5, thus 2y = 5 (integer)

I therefore concluded that option E ( neither statements make sense) Obviously i am wrong. Can some one tell me where my thought process is flawed?
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Re: QR DS #112 [#permalink]  01 May 2013, 11:35
Option A:

from stmt 1:
x+y+y-2 =3x or 2y-2=2x or y=x+1. since X is an integer Y = X+1 will be an integer. Sufficient.

from stmt 2:

let x=2 and y=1 then mean of x+y si 1.5 which is not an integer, while y is an integer.
let x=2 and y=1.4 then mean of x and y is 1.7 which is again not an integer, and y is not an integer.

hence insufficnent.
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Re: QR DS #112 [#permalink]  01 May 2013, 11:38
vibhav wrote:
Guys As i try addressing statement #1, my approach was:
x+y+y-2 /3 = x
thus, x+2y-2 = 3x i.e. ( integer + integer - integer = integer)
Now we know that 2y is an integer however, y may or may not be an integer eg: y=2.5, thus 2y = 5 (integer)

I therefore concluded that option E ( neither statements make sense) Obviously i am wrong. Can some one tell me where my thought process is flawed?

What is wrong in the logic above is that for 2y=5, we get x = 1.5,a non-integral value for x, which is not valid for the given problem.

From F.S 1, we know that (x+y+y-2)/3 = x

or 2x = 2y-2
or y = x+1. Thus, as x is an integer, y IS an integer.Sufficient.

From F.S 2, for x=1,y=2, we get the mean as a non-integral value. Thus, we get a YES for the question stem. However for x=1, y=2.5 also, we get a non-integral value of mean and a NO for the question stem. Insufficient.

A.
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Re: QR DS #112 [#permalink]  01 May 2013, 11:41
mdbharadwaj, that's exactly the solution given in the QR. However, Whats wrong in my line of analysis of stmt 1?
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Re: QR DS #112 [#permalink]  01 May 2013, 11:44
vibhav wrote:
If X is an integer, is Y an integer?

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

For me, Just follow the basics.....

Is Y an integer ?? when x is an Integer ...

As Given in statement 1 , The average (mean) of x, y & y-2 is equal to x .

Therefore, \frac{x+y+y-2}{3}=x \Rightarrow y-1 = x .

\Rightarrow y = x+1 & as we know x is an integer & Integer + Integer = Integer.

Hence, Y is an Integer.

Statement 2 :: The average (mean) of x and y is not an integer.
This clearly means that the value of Both x & Y can be integer or non-integer to yield a Non- integer as their average.

Hence, A alone is sufficient.
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Re: QR DS #112 [#permalink]  01 May 2013, 11:47
vibhav wrote:
mdbharadwaj, that's exactly the solution given in the QR. However, Whats wrong in my line of analysis of stmt 1?

Vinay has succinctly put it in his post.
your assumption of values for Y is going against the information given in the question stem. X has to be an integer.

So i guess it will be easier and correct if you assume values of X first instead of Y,
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Re: QR DS #112 [#permalink]  01 May 2013, 18:28
vibhav wrote:
Guys As i try addressing statement #1, my approach was:
x+y+y-2 /3 = x
thus, x+2y-2 = 3x i.e. ( integer + integer - integer = integer)
Now we know that 2y is an integer however, y may or may not be an integer eg: y=2.5, thus 2y = 5 (integer)

I therefore concluded that option E ( neither statements make sense) Obviously i am wrong. Can some one tell me where my thought process is flawed?

From Stmnt 1 we can conclude easily that y-2, x and y are consecutive integers since mean =x --> x =y-1
Therefore sufficient.

Stmnt 2--> clearly insufficient

Therefore Option A is correct.
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Re: QR DS #112 [#permalink]  02 May 2013, 02:27
vibhav wrote:
If X is an integer, is Y an integer?

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

Merging similar topics.
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Re: If x is an integer, is y an integer? [#permalink]  03 May 2013, 21:28
ood question and quite a learning...

Out of curiousity, can this sum be solved in less than 2mins that too under "GMAT exam" conditions that too at first sight??
Re: If x is an integer, is y an integer?   [#permalink] 03 May 2013, 21:28
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