If x is an integer, is y an integer?

Question

(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.

Bunuel · Accepted Answer

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.

Answer: A.

Zatmah · Answer

My Answer is "A"

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 !!

CrackverbalGMAT · Answer

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

Hence answer is A

OCDianaOC · Answer

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!

amanvermagmat · Answer

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)

LeoN88 · Answer

Statement# 2
Let x be 3, now
Case 1 (3+2)/2 is not I
Case 2 But (3+.5) is also not I, so y can be 2 or .5

Statement# 1
x+2y-2=3x
2y-2=2x
y-1=x
y=x+1

On the number line y is one unit ahead of x, must be Integer as x is integer. A

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If x is an integer, is y an integer?

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