Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

20. 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 _________________

Re: PS Number property [#permalink]
12 Oct 2009, 10:49

3

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

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 _________________

Re: PS section 1 q20 [#permalink]
08 Jun 2010, 11:28

1

This post received KUDOS

Expert's post

sunland wrote:

20. If y ≠ 3 and 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

the solution booklet says answer is A but shouldnt x=y making B the answer if the number is prime and greater than 2, then the number has to be 3. which is possible only if x=y.

First of all the question misses important part (\frac{3x}{y}=prime). Second this question is MUST be true question not COULD be true.

Refer to the solutions above to see that it's not necessary x=y to be true for 3x/y to be a prime integer greater than 2. For example x=25 and y=15 --> \frac{3x}{y}=5=prime.

Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink]
15 Dec 2013, 18:58

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink]
03 Jan 2014, 06:11

Done by Plugging in y#3 and 3x/y = prime number > 2 ,so 3,5,7,11...

1. x = y , x,y = 2 answer is 3 ; x,y = 3 or 4 or 5... answer is 3 which is a prime number then why this option is wrong 2. y = 1 its straight away wrong 3. x,y both prime any prime numbers so wrong

why 1 option is wrong?? but after seeing with other numbers and bunnel post i realized that

even if x= 35 , y = 15 the prime number is 7 even though which is >2

Re: Number properties: [#permalink]
14 Jan 2014, 19:42

Expert's post

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

Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink]
19 Apr 2014, 20:28

y !=3

x * (3/y)

I. x = y

x * 3/x > 2 3> 2

Hence Must be true for the inequality to hold

II. y = 1

x * 3/1 > 2

Could be true if x=1

III. x and y are prime integers.

Then the expression itself wont be an integer except when x=y

Could be true

Hence only (1) is must be true _________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

gmatclubot

Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which
[#permalink]
19 Apr 2014, 20:28

Wow...I'm still reeling from my HBS admit . Thank you once again to everyone who has helped me through this process. Every year, USNews releases their rankings of...

I had an interesting conversation with a friend this morning, and I realized I need to add a last word on the series of posts on my application process. Five key words:...