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

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In the fraction x/y, where x and y are positive integers [#permalink]

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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
[Reveal] Spoiler: OA

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Re: Least common denominator [#permalink]

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New post 07 Sep 2010, 13:41
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metallicafan wrote:
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


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 \(y=6\) (the least common denominator of \(\frac{x}{2}\) and \(\frac{1}{3}\) is 6 and the least common denominator of \(\frac{x}{6}\) and \(\frac{1}{3}\) is also 6). Not sufficient.

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

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

Answer: E.
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GMAT PREP LCM [#permalink]

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New post 26 Jan 2011, 08:27
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
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QR DS 119. The fraction [#permalink]

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New post 23 Feb 2011, 21:10
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
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Re: QR DS 119. The fraction [#permalink]

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New post 24 Feb 2011, 01:20
From 1) y can be 2 or 6 ,so Insufficient.
From 2) nothing can be inferred about y, so insufficient.

Combining (1) and (2), sill nothing can be said conclusively about y, so the answer is E.
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Re: Least common denominator [#permalink]

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New post 20 Sep 2012, 07:10
Bunuel wrote:
metallicafan wrote:
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


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 \(y=6\) (the least common denominator of \(\frac{x}{2}\) and \(\frac{1}{3}\) is 6 and the least common denominator of \(\frac{x}{6}\) and \(\frac{1}{3}\) is also 6). Not sufficient.

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

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

Answer: E.



Hi Bunuel,

This time i am not able to understand the explanation given by you.
Assuming x=1 & y can be either 2 or 6, I want to know how come the LCM of (1/2 , 1/3) & (1/6, 1/3) can be 6. As per me the LCM has to be 1 & 1/3 respectively.

Kindly enlighten me.
Waiting for reply
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Re: Least common denominator [#permalink]

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New post 20 Sep 2012, 07:47
Expert's post
fameatop wrote:
Bunuel wrote:
metallicafan wrote:
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


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 \(y=6\) (the least common denominator of \(\frac{x}{2}\) and \(\frac{1}{3}\) is 6 and the least common denominator of \(\frac{x}{6}\) and \(\frac{1}{3}\) is also 6). Not sufficient.

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

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

Answer: E.



Hi Bunuel,

This time i am not able to understand the explanation given by you.
Assuming x=1 & y can be either 2 or 6, I want to know how come the LCM of (1/2 , 1/3) & (1/6, 1/3) can be 6. As per me the LCM has to be 1 & 1/3 respectively.

Kindly enlighten me.
Waiting for reply


We are told that "The least common denominator of x/y and 1/3 is 6" not LCM of 1/2 and 1/3.
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Re: Least common denominator [#permalink]

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New post 20 Sep 2012, 08:38
Hi Bunuel,
Ok, Forget the question. Can you tell me what is the LCM of (1/2 , 1/3) & (1/6, 1/3) or how to calculate the LCM of two fractions.
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Re: Least common denominator [#permalink]

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New post 20 Sep 2012, 08:43
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fameatop wrote:
Hi Bunuel,
Ok, Forget the question. Can you tell me what is the LCM of (1/2 , 1/3) & (1/6, 1/3) or how to calculate the LCM of two fractions.


The least common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b.
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Re: In the fraction x/y, where x and y are positive integers [#permalink]

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In the fraction x/y, where x and y are positive integers [#permalink]

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New post 17 Nov 2015, 11:43
Having a bit of a hard time grasping this one. I chose A, but im trying to reason out the right answer (E)

(2) - NS

(1) - S because

x/y and 1/3 LCM is 6

So

x/2 and 1/3 works for a LCM of 6, because 1/2 and 1/3

also x/6 and 1/3 works for a LCM of 6 because say 5/6 and 1/3 the LCM will be 6 or 1/6 and 1/3 will be 6

so NS

(1)+(2)

with x=1 we still have the two cases of 1/3 and 1/6 for x/y therefore we do not know what y is.



Hope this is the right reasoning. I missed the multiple values of y the first time .
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Re: In the fraction x/y, where x and y are positive integers [#permalink]

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New post 17 Nov 2015, 12:30
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GMATDemiGod wrote:
Having a bit of a hard time grasping this one. I chose A, but im trying to reason out the right answer (E)

(2) - NS

(1) - S because

x/y and 1/3 LCM is 6

So

x/2 and 1/3 works for a LCM of 6, because 1/2 and 1/3

also x/6 and 1/3 works for a LCM of 6 because say 5/6 and 1/3 the LCM will be 6 or 1/6 and 1/3 will be 6

so NS

(1)+(2)

with x=1 we still have the two cases of 1/3 and 1/6 for x/y therefore we do not know what y is.



Hope this is the right reasoning. I missed the multiple values of y the first time .


One thing I will mention here is that statement 1 mentions Least Common DENOMINATOR and not multiple. There is a difference between the 2 but not for this question though!!

As for your reasoning, yes it is correct. LCM/GCDs are tricky so do make sure to test all the possible cases.
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Re: In the fraction x/y, where x and y are positive integers   [#permalink] 17 Nov 2015, 12:30
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