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

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New post Updated on: 06 Feb 2019, 04:21
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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


Data Sufficiency
Question: 119
Category: Arithmetic Properties of numbers
Page: 161
Difficulty: 650


The Official Guide For GMAT® Quantitative Review, 2ND Edition

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Originally posted by Bunuel on 28 Feb 2014, 04:04.
Last edited by Bunuel on 06 Feb 2019, 04:21, edited 1 time in total.
Updated.
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Re: In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 28 Feb 2014, 04:05
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New post 01 Mar 2014, 02:50
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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


Statement 1: LCM of y and 3 is 6. Which means y can be 2 or 6. Not sufficient.
Statement 2: Only talks about value of x. Not sufficient.

Both statements combined together is also not sufficient as y can still be 2 or 6.

Answer: Option E
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Re: In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 18 May 2014, 09:59
IMO it is E.

least common denominator is 6 from stmt 1.

then it can be x/2 or x/6 when compared with 1/3 both will give 6 as the lease common denominator.

INSUFF

stmt 2. no info bout Y.. Insuff
together...same problem as stmt 1.
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Re: In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 30 Oct 2016, 16:16
Bunuel wrote:
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, 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?
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New post 30 Oct 2016, 23:51
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herbgatherer wrote:
Bunuel wrote:
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, 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?


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.
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Re: In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 09 Dec 2017, 23:57
Bunuel can I have more math questions link (PS+DS) like this to practice?
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Re: In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 10 Dec 2017, 00:02
sadikabid27 wrote:
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



For other subjects:
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Ultimate GMAT Quantitative Megathread
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Re: In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 07 May 2018, 04:41
Bunuel wrote:
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.


Hi Bunuel,

The way your question is phrased as seems to make it more accurate for interpretation but some sources have statement I phrased as "The LCM of x/y and 1/3 is 6".
In that case, we would proceed to say LCM of (x,1) is 6 and GCD of (y,3) is 1?
Here since we're interested in the value of y, and y,3 have only 1 as common factor that means y and 3 are co-prime but y could then have any value.

Statement 2 is anyway insufficient so 1 +2 would still yield E?
Is this correct?
Thanks in anticipation.
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Re: In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 07 May 2018, 11:42
Aditi10 wrote:
Bunuel wrote:
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.


Hi Bunuel,

The way your question is phrased as seems to make it more accurate for interpretation but some sources have statement I phrased as "The LCM of x/y and 1/3 is 6".
In that case, we would proceed to say LCM of (x,1) is 6 and GCD of (y,3) is 1?
Here since we're interested in the value of y, and y,3 have only 1 as common factor that means y and 3 are co-prime but y could then have any value.

Statement 2 is anyway insufficient so 1 +2 would still yield E?
Is this correct?
Thanks in anticipation.


Hello

My perspective - Yes, you are right in that if we were given LCM of x/y and 1/3 (rather than least common denominator...) then the resultant LCM would have been: x/(GCD of y&3) = 6, which can only happen if x = 6 and GCD of y/3 = 1.
But then second statement wouldn't have made any sense at all, because from first statement x=6 and in second statement x=1. Such inconsistency cannot be there in GMAT.

So, for this particular question, the word LCM would not be used I think. Also, I think LCM of fractions is probably something that is NOT tested on the GMAT (experts can intervene to correct if I am wrong)
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In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 14 May 2019, 13:42
(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
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Re: In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 14 May 2019, 15:31
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energetics wrote:
(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?"


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.
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New post 14 May 2019, 20:03
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?
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Re: In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 14 May 2019, 22:36
herbgatherer wrote:
Bunuel wrote:
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, 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?



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https://www.mathsisfun.com/definitions/ ... nator.html
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Re: In the fraction x/y, where x and y are positive integers, what is the  [#permalink]

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New post 15 May 2019, 08:24
energetics wrote:
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?


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".
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New post 15 May 2019, 09:43
Yes, that's exactly it. My point of confusion was thinking it meant that multiplying those two fractions would lead something/6 when it is fully reduced.

I understand the concept when it's worded as LCM: x is divisible by 6 and x is divisible by 4, so x must be at least 12 (this would be the LCM of 6 and 4).

I think the particular phrasing in this problem is not something I saw much previously (or at least not recently), so I managed to completely obfuscate what it was actually asking me to do... I suppose from being tired and assuming that some mathematical operation was required because of variables.
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Re: In the fraction x/y, where x and y are positive integers, what is the   [#permalink] 15 May 2019, 09:43
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