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If y 3 and 3x/y is a prime integer greater than 2, which of
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Updated on: 11 Sep 2013, 12:01
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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!!
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Originally posted by Economist on 30 Mar 2009, 04:02.
Last edited by Bunuel on 11 Sep 2013, 12:01, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



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Re: DS: Must be true
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30 Mar 2009, 08:38
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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Re: DS: Must be true
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09 May 2009, 10:35
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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Re: DS: Must be true
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10 May 2009, 10:28
reply2spg wrote: 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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Re: If y 3 and 3x/y is a prime integer greater than 2, which of
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11 Sep 2013, 11:51
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.
So answer is (a) None



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Re: If y 3 and 3x/y is a prime integer greater than 2, which of
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11 Sep 2013, 12:06
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.
So answer is (a) None 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
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11 Sep 2013, 12:36
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.
So answer is (a) None 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
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19 Jul 2014, 06:25
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 cases3x/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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Re: If y 3 and 3x/y is a prime integer greater than 2, which of
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26 Jun 2018, 02:51
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.
Answer: A



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Re: If y 3 and 3x/y is a prime integer greater than 2, which of
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26 Jun 2018, 04:02
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
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