Fraction: Reduced (Simplest) Form

[work.hard]

Will the GMAT assume that a fraction is in its reduced form when it is expressed as X/Y (where X and Y are positive integers)? The GMAT seemed to make this assumption in OG Quant 2 DS #119.

Because discussion is not allowed on OG problems, let me give an alternative example for consideration:

QUESTION: In the fraction X/Y, both X and Y are positive integers. The least common denominator of X/Y and 1/2 is 6. What is the value of Y?

ANSWER: The answer in Quant 2 (for DS 119, a very similar problem) would lead me to believe that the only possible values for Y would be 3 or 6 (in other words, X/Y can be X/3 or X/6) but that it is impossible to determine whether y=3 or y=6.

MY ANSWER: I would contend that there are an infinite number of possible values for Y based on the information in the question. For this to be the case, I am considering that X/Y may not be in the reduced (simplest) form. For instance, all of the following fractions will have an LCD of 6 when compared with 1/2: 1/3, 2/6, 3/9, 4/12, 5/15, .... AND 1/6, 2/12, 3/18, .... (Am I right on this?) Therefore, Y could potentially take values of 3, 6, 9, 12, 15.... (any multiple of 3) depending what X is. I think the GMAT would be wrong to assume that Y could only take values of y=3 or y=6.

Please note that regardless of whose answer is correct, a singular answer for Y is clearly not possible to obtain with this information.

This is going to bug me. I'm taking the GMAT on Friday... So if someone would be kind to answer this question, I would really appreciate it! Thanks in advance!

[RonPurewal]

the short answer is that you should only consider fractions in reduced form.

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the long answer: it doesn't matter anyway.

your analysis is flawed, because you're not being consistent here.
specifically, you can't simultaneously do both of the following:
(i) view the fraction as 6/18 (unreduced), rather than as 1/3 (reduced);
(ii) view the common denominator as 6.
you can't do both of these things. if you're going to call the fraction 6/18 (which you shouldn't be doing anyway), then the common denominator would be 18, not 6. if you want the common denominator to be 6 then you have to reduce the fraction, thus obviating the complaint.

[work.hard]

Thanks. Reduced form it is.

[jlucero]

Glad it helped.