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

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If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink] New post   Updated on: 21 Aug 2019, 09:16
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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

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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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Official Answer
A

Originally posted by Economist on 30 Mar 2009, 05:02.
Last edited by Bunuel on 21 Aug 2019, 09:16, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink] New post   12 Oct 2009, 11:49
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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

Answer to this question is A. None of the statements (I,II,III) must be true.

This Q. can be solved by number plugging in a minute but it's quite tricky, so let's generalize it so to understand the concept, as there are many similar problems in GMAT:

Q. says that: y≠3 and that 3x/y IS a prime integer. Then it asks which of the statements MUST be true?

First note that it's not stated that x and y are integers or positive/negative.

Generally, the expression 3x/y is always prime in two cases:

When x is a multiple of prime and y is same multiple of three: x=pn and y=3n (p prime >2, n ANY number but 1), so we have 3(pn)/3n=p.

AND

When x=y ≠1 then 3x/y=3=p>2

Note that first formula also gives us the p=3 but only when x and y are the multiples of three (n ANY number but 1, can be -6 or 75 but not 1), thus it exclude all possibilities when x=y and ARE not multiples of three, for instance x=8 and y=8.

So from above it's not necessary x=y or y=1 or x,y to be primes.

Let's look:

I. x = y --> not necessarily true: x=25 y=15 3x/y=5

II. y=1 --> not necessarily true: x=8 y=8 3x/y=3

III. x and y are prime integers --> x=21 y=9 3x/y=7
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Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink] New post   30 Mar 2009, 09:38
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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: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink] New post   09 May 2009, 11:35
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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: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink] New post   10 May 2009, 11:28
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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 [#permalink] New post   11 Sep 2013, 12:51
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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 [#permalink] New post   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.

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 [#permalink] New post   11 Sep 2013, 13:36
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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 [#permalink] New post   14 Jan 2014, 20:42
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TooLong150 wrote:
Can you explain your reasoning to (I)?


If a prime number is written as a product of two numbers, one of them must be prime and the other must be 1.
3x/y would be prime if 'x/y is 1' (in which case 3x/y = 3) or '3 gets canceled off from a 3 in y and the leftover is a prime number'

So some solutions are:
x = y = 1
x = y = Anything other than 0
y is a multiple of 3, say 3n and x/n is a prime number.

We are given that y is not 3 but we are not given that it is not a multiple of 3. Say, y = 6 = 3n. In that case x/n can be a prime number. e.g. x = 10 or 14 or 26 etc
3x/y = 3*10/6 = 5
3x/y = 3*14/6 = 7
etc

So x = 14, y = 6 is a solution. So it not NECESSARY (but it is possible) that x=y, y = 1, x and y are prime

Answer (A)
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Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink] New post   26 Jun 2018, 05:02
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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 [#permalink] New post   21 Aug 2019, 09:10
Bunuel can you help us here
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Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink] New post   21 Aug 2019, 09:16
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ShivamoggaGaganhs wrote:
Bunuel can you help us here


Check here: https://gmatclub.com/forum/if-y-3-and-3 ... ml#p638293
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Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink] New post   22 Aug 2019, 11:14
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

Show Spoiler
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!!





Since this is a ‘Must be true’ kind of question, the best strategy to adopt would be that of trying to falsify each statement once and simultaneously eliminate the corresponding answer options.

Remember that any statement which is false ONCE, cannot be true ALWAYS. In a ‘Must be true’ question, the objective is to identify a statement/statements which is/are true ALWAYS/under all cases.

To make a statement false, we take a few simple cases i.e. simple values for the variables.
The question says that y≠3 and 3x/y is a prime number greater than 2. This means that the possible value for 3x/y can be 3,5,7 and so on.

If 3x/y = 3, then x and y can be any value, but both are equal, since x/y = 1. Statement I is true in this case, so we hold on to options containing statement I i.e. options B and E.

If 3x/y = 5, then x/y = 5/3. One possible value that satisfies this ratio is x = 10 and y = 6. Clearly, all 3 statements are false in this case.

This means that none of them are ALWAYS true. So, the correct answer options is A.

Hope this helps!
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Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink] New post   14 Jun 2021, 09:03
given that y ≠ 3
3x/y is prime >2
must be true
1. x=y yes & no
yes when x=y=3 and no when x=7 & y = 3
2. y=1
yes when x= 1 or any value same as y so not sufficient
3
x & y are prime integers
x=y=3
x=7 ; y = 3
x=35 & y = 5
insufficient
option A none is correct

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

Show Spoiler
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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Re: If y 3 and 3x/y is a prime integer greater than 2, which [#permalink] New post   09 Apr 2024, 23:22
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

 

­
i solved in a different way (someone might have posted, not sure!)
3x/y = prime no. > 2 => 3,5,7,11,13......
3x/y = 3 --> x/y = 1 --> x=y (I. is true. But is it "must be true for all cases"?)
3x/y = 5,7,11,13...
=> x/y = 5/3 , 7/3, 11/3, 13/3, ....... (but y not equals to 3 as given)
=> x/y = 10/6, 14/6, 22/6, 26/6........ (multiplied by 2/2 here). We can also multiply by 3/3 and so on!!!
==> All these combinations of x & y (10,6) , (14,6) are ordered pairs for (x,y)

Now analyyse the options.
I. x=y --> True only for 3x/y = 3. Not true for other cases.
II. y=1 -> Not true as seen for ordered pair solutions.
III. x & y are prime nos. --> No, x and y can be 10 & 6!

Hence (A) none.
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Re: If y 3 and 3x/y is a prime integer greater than 2, which [#permalink]
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