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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

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.

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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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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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.
_________________

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.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

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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12 Aug 2015, 13:35

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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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