In the fraction x/y, where x and y are positive integers, what is the

Bunuel, I couldn't follow what this sentence means: "The least common denominator of x/y and 1/3 is 6 " . What is the Least common denominator?! So, are they just saying that the least common multiple between y and 3 is 6?

Bunuel can I have more math questions link (PS+DS) like this to practice?

Could not find questions similar to this one but the links below should help to master divisibility/multiples/factors questions.

5. Divisibility/Multiples/Factors

• Theory
  Divisibility and Remainders on the GMAT
  Tips and hints: Divisibility/Multiples/Factors
  3 Deadly Mistakes you must avoid in LCM-GCD Questions
  How Well Do You Know Your Factors?
  THE MOST EFFICIENT WAY TO STUDY LEAST COMMON MULTIPLES ON THE GMAT
  
  • Questions
    The E-GMAT Primes Trio - 3 Ques on No. of factors & Prime factors
    DS Questions
    PS Questions

For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

(1) The least common denominator of x/y and 1/3 is 6.
Bunuel VeritasKarishma chetan2u IanStewart or other experts, can you explain why we read this statement to mean "y and 3 have LCM of 6" and not "x/y times 1/3 is x/6?"

I read it as the latter... so I got C (see below)

For (1):
1/3*1/2 = 1/6
1/3*3/6 = 1/6
multiple values for x (1,3) and for y (2,6), insufficient

(2) x = 1 no info about y, insufficient

(1&2)
if x=1, y=2 ... (1/3)*(1/2) = 1/6, Ok
x can't be 3 so (1/3)*(3/6) is not possible now.
Sufficient since there's a definite value for x, y

Because that's not what that sentence means. You might think of what the same sentence would mean if you had numbers everywhere, instead of letters. If I were to talk about the "least common denominator of the fractions 1/4 and 1/6", I wouldn't be talking about the product of 1/4 and 1/6, or of 4 and 6. The answer would not be 24. Instead I'd be talking about the smallest common denominator we could make, if we wanted to, say, add those two fractions -- and that's exactly what the Least Common Multiple is. The answer would be 12, the LCM of 4 and 6.

Thanks Ian, that clears it up.

If it was worded "the least common denominator of the product of x/y and 1/3 is 6" then it would be solved as I wrote above?

this article will help you:-

https://www.mathsisfun.com/definitions/ ... nator.html

That sentence wouldn't mean anything - it would be like saying "the least common multiple of 6 is 6". If you are talking about the "least common multiple", you are talking about a multiple that is common to two (or more) numbers. In the same way, if you talk about a least common denominator, you are talking about a denominator common to two or more fractions. In your sentence, you're only talking about the denominator of a single fraction, the product of the fractions you mention.

But I think I may now understand how you're interpreting the wording. I think you're interpreting it to mean something like "the lowest possible denominator (if everything stays an integer) of the product of x/y and 1/3 is 6", or "if (x/y)(1/3) were completely reduced, its denominator would be 6". But if that's what the question meant, they would need to use different phrasing - they would need to talk about reducing that fraction completely, and not about "least common denominators".

Solution:

Statement One Only:

The least common denominator of x/y and 1/3 is 6.

If the least common denominator of x/y and 1/3 is 6, then y could be either 2 or 6. Since y does not have a unique value, statement one is not sufficient.

Statement Two Only:

x = 1

This does not tell us anything about the value of y; statement two is not sufficient.

Statements One and Two Together:

Using the two statements, we have: the least common denominator of 1/y and 1/3 is 6. However, again, y could be either 2 or 6. The two statements together are not sufficient.

Answer: E

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