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# If y 3 and 3x/y is a prime integer greater than 2, which of

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Director
Joined: 01 Apr 2008
Posts: 811
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
If y 3 and 3x/y is a prime integer greater than 2, which of  [#permalink]

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Updated on: 11 Sep 2013, 13:01
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If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?

I. x = y
II. y = 1
III. x and y are prime integers.

(A) None
(B) I only
(C) II only
(D) III only
(E) I and III

Guys, I am sure this might have come earlier, but I am kind of confused about these MUST be true questions.

Here, if 3x/y is a prime number greater than 2 then x and y should always be equal so that they can cancel out. We cant have any other factor of 3x/y!!

Originally posted by Economist on 30 Mar 2009, 05:02.
Last edited by Bunuel on 11 Sep 2013, 13:01, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: DS: Must be true  [#permalink]

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30 Mar 2009, 09:38
Economist wrote:
If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ

Guys, I am sure this might have come earlier, but I am kind of confused about these MUST be true questions.

Here, if 3x/y is a prime number greater than 2 then x and y should always be equal so that they can cancel out. We cant have any other factor of 3x/y!!

There are other possibilities here: 3 might be a factor of y, and might therefore cancel in the fraction, leaving us with a prime that comes from the factors of x. For example, if x = 10, and y = 6, then 3x/y = 5. So we can see that none of I, II, or III need to be true.
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Joined: 12 Oct 2008
Posts: 481
Re: DS: Must be true  [#permalink]

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09 May 2009, 11:35
what about the case x=y? if x=y then x will cancel Y and answer will be 3, which is greater than 2 and it is prime number

IanStewart wrote:
Economist wrote:
If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ

Guys, I am sure this might have come earlier, but I am kind of confused about these MUST be true questions.

Here, if 3x/y is a prime number greater than 2 then x and y should always be equal so that they can cancel out. We cant have any other factor of 3x/y!!

There are other possibilities here: 3 might be a factor of y, and might therefore cancel in the fraction, leaving us with a prime that comes from the factors of x. For example, if x = 10, and y = 6, then 3x/y = 5. So we can see that none of I, II, or III need to be true.
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Posts: 1344
Re: DS: Must be true  [#permalink]

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10 May 2009, 11:28
1
what about the case x=y? if x=y then x will cancel Y and answer will be 3, which is greater than 2 and it is prime number

Yes, it *could* be true that x = y, but the question doesn't ask what could be true; it asks what *must* be true. As I pointed out above, it doesn't need to be true that x = y.
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Joined: 06 Sep 2013
Posts: 1801
Concentration: Finance
Re: If y 3 and 3x/y is a prime integer greater than 2, which of  [#permalink]

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11 Sep 2013, 12:51
1
1
Tricky question. Took 1.50min to solve it.

But this is what I did.

1st Statement: From first looking at the expression, 'x=y' is the easiest way to have a Prime Integer greater > 2 (3 in this case) from the original question stem. Now we must ask ourselves, is there anyway that this number is a prime number greater than 2 and different from 3? Say for example 5. First look at the denominator, to have 5 as the answer we need to get rid of the 3 so 'y=3', could be an option. Then if 'x = 5, we have that the expression is in fact 5.

So x/y = 5/3 could be an option.

2nd Statement: Does 'y=1" ? We just found out that 'y=3' is an option so this one is out.

3rd Statement: This is a bit more difficult. We need to ask ourselves again, do they both have to be prime integers? Let's start with the denominator, we used 'y=3' in the last example but 'y' could be in fact any multiple of 3, lets say we picked 6. Now, to have '5' (Prime>2) as an answer we could use 10 in the numerator. Since both 'x' and 'y' are 10 and 6 they don't both have to be prime numbers.

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Re: If y 3 and 3x/y is a prime integer greater than 2, which of  [#permalink]

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11 Sep 2013, 13:06
jlgdr wrote:
Tricky question. Took 1.50min to solve it.

But this is what I did.

1st Statement: From first looking at the expression, 'x=y' is the easiest way to have a Prime Integer greater > 2 (3 in this case) from the original question stem. Now we must ask ourselves, is there anyway that this number is a prime number greater than 2 and different from 3? Say for example 5. First look at the denominator, to have 5 as the answer we need to get rid of the 3 so 'y=3', could be an option. Then if 'x = 5, we have that the expression is in fact 5.

So x/y = 5/3 could be an option.

2nd Statement: Does 'y=1" ? We just found out that 'y=3' is an option so this one is out.

3rd Statement: This is a bit more difficult. We need to ask ourselves again, do they both have to be prime integers? Let's start with the denominator, we used 'y=3' in the last example but 'y' could be in fact any multiple of 3, lets say we picked 6. Now, to have '5' (Prime>2) as an answer we could use 10 in the numerator. Since both 'x' and 'y' are 10 and 6 they don't both have to be prime numbers.

The only issue with your response is the prompt explicitly says that y≠3
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Re: If y 3 and 3x/y is a prime integer greater than 2, which of  [#permalink]

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11 Sep 2013, 13:36
1
Nwsmith11 wrote:
jlgdr wrote:
Tricky question. Took 1.50min to solve it.

But this is what I did.

1st Statement: From first looking at the expression, 'x=y' is the easiest way to have a Prime Integer greater > 2 (3 in this case) from the original question stem. Now we must ask ourselves, is there anyway that this number is a prime number greater than 2 and different from 3? Say for example 5. First look at the denominator, to have 5 as the answer we need to get rid of the 3 so 'y=3', could be an option. Then if 'x = 5, we have that the expression is in fact 5.

So x/y = 5/3 could be an option.

2nd Statement: Does 'y=1" ? We just found out that 'y=3' is an option so this one is out.

3rd Statement: This is a bit more difficult. We need to ask ourselves again, do they both have to be prime integers? Let's start with the denominator, we used 'y=3' in the last example but 'y' could be in fact any multiple of 3, lets say we picked 6. Now, to have '5' (Prime>2) as an answer we could use 10 in the numerator. Since both 'x' and 'y' are 10 and 6 they don't both have to be prime numbers.

The only issue with your response is the prompt explicitly says that y≠3

You are right appologies, my bad.

So we could just use x=10 and y=6 for all the Statements and there we go.
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Re: If y 3 and 3x/y is a prime integer greater than 2, which of  [#permalink]

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19 Jul 2014, 07:25
Economist wrote:
If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?

I. x = y
II. y = 1
III. x and y are prime integers.

(A) None
(B) I only
(C) II only
(D) III only
(E) I and III

Guys, I am sure this might have come earlier, but I am kind of confused about these MUST be true questions.

Here, if 3x/y is a prime number greater than 2 then x and y should always be equal so that they can cancel out. We cant have any other factor of 3x/y!!

Must be true should hold in all the cases

3x/y can be = 3 in this case, Option A) and Option B) comes. It doesn't satisfy Option C) as x= y = 1 is a possibility
If 3x/y = 5, in this case, Option A) and Option B) goes out of the way and it satisfies option C)
Hence None.
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Joined: 20 Apr 2018
Posts: 169
Concentration: Technology, Nonprofit
WE: Analyst (Non-Profit and Government)
Re: If y 3 and 3x/y is a prime integer greater than 2, which of  [#permalink]

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26 Jun 2018, 03:51
I think the best way to go is to try to break the statements. I tried taking irrational nos as x and y, and made 3x/y prime
For example: x = 7*sqrt(3); y = 3*sqrt(3), 3x/y = 7.

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Joined: 04 Aug 2010
Posts: 277
Schools: Dartmouth College
Re: If y 3 and 3x/y is a prime integer greater than 2, which of  [#permalink]

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26 Jun 2018, 05:02
1
Economist wrote:
If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?

I. x = y
II. y = 1
III. x and y are prime integers.

(A) None
(B) I only
(C) II only
(D) III only
(E) I and III

Make a list of options for $$\frac{3x}{y}$$ and solve for x:
$$\frac{3x}{y}$$ = 3, 5, 7, 11...
3x = 3y, 5y, 7y, 11y...
x = y, $$\frac{5y}{3}$$, $$\frac{7y}{3}$$, $$\frac{11y}{3}$$...

If $$x = \frac{5y}{3}$$, then it's possible that $$y=4$$ and that $$x=\frac{20}{3}$$, with the result that I, II, and III are all NOT true.

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Re: If y 3 and 3x/y is a prime integer greater than 2, which of &nbs [#permalink] 26 Jun 2018, 05:02
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# If y 3 and 3x/y is a prime integer greater than 2, which of

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