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

Question

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

(1) The least common denominator of x/y and 1/3 is 6.
(2) x = 1

Bunuel · Accepted Answer

SOLUTION

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

(1) The least common denominator of x/y and 1/3 is 6 --> LCM of y and 3 is is 6 --> y=2 or y=6. Not sufficient.

(2) x = 1 --> no info about y. Not sufficient.

(1)+(2) y can still be 2 or 6. Not sufficient.

Answer: E.

Bunuel · Answer

The least common denominator is the least common multiple of the denominators of a set of fractions. For example, the least common denominator of 1/2 and 1/3 is 6.

herbgatherer · Answer

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?

sadikabid27 · Answer

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

Bunuel · Answer

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

energetics · Answer

(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

IanStewart · Answer

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.

energetics · Answer

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?

LeoN88 · Answer

this article will help you:- https://www.mathsisfun.com/definitions/ ... nator.html

IanStewart · Answer

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".

ScottTargetTestPrep · Answer

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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