Last visit was: 17 Jul 2024, 05:33 It is currently 17 Jul 2024, 05:33
Toolkit
GMAT Club Daily Prep
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

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.

# If y is a positive integer, is y prime?

SORT BY:
Tags:
Show Tags
Hide Tags
Senior Manager
Joined: 03 Sep 2006
Posts: 445
Own Kudos [?]: 6900 [32]
Given Kudos: 33
Director
Joined: 22 Mar 2011
Posts: 518
Own Kudos [?]: 2159 [5]
Given Kudos: 43
WE:Science (Education)
General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 94371
Own Kudos [?]: 641616 [4]
Given Kudos: 85627
Math Expert
Joined: 02 Sep 2009
Posts: 94371
Own Kudos [?]: 641616 [1]
Given Kudos: 85627
Re: If y is a positive integer, is y prime? [#permalink]
1
Kudos
LM wrote:
If y is a positive integer, is y prime?

(1) y>4!

(2) 11!-12<y<11!-2

Another similar question:

If x is an integer, does x have a factor n such that 1 < n < x?

Question basically asks: is $$x$$ a prime number? If it is, then it won't have a factor $$n$$ such that $$1<n<x$$ (definition of a prime number).

(1) $$x>3!$$ --> $$x$$ is more than some number (3!). $$x$$ may or may not be a prime. Not sufficient.

(2) $$15!+2\leq{x}\leq{15!+15}$$ --> $$x$$ can not be a prime. For instance if $$x=15!+8=8*(2*3*4*5*6*7*9*10*11*12*13*14*15+1)$$, then $$x$$ is a multiple of 8, so not a prime. Same for all other numbers in this range: $$x=15!+k$$, where $$2\leq{k}\leq{15}$$ will definitely be a multiple of $$k$$ (as weould be able to factor out $$k$$ out of $$15!+k$$). Sufficient.

Discussed here: if-x-is-an-integer-does-x-have-a-factor-n-such-that-100670.html

Hope it helps.
Intern
Joined: 25 Oct 2012
Posts: 5
Own Kudos [?]: 1 [1]
Given Kudos: 2
Concentration: Economics, Finance
Re: If y is a positive integer, is y prime? [#permalink]
1
Kudos
EvaJager wrote:
LM wrote:
If y is a positive integer, is y prime?
1.$$y>4!$$

2.$$11!-12<y<11!-2$$

(1) obviously not sufficient. There are many primes greater than 4! as well as non-primes.

(2) y can be one of the integers 11! - 11, 11! - 10, 11! - 9, ... , 11! - 2, 11! - 3.
It is easy to see that all the numbers on the above list are certainly not primes. 11! = 2x3x4x5x6x7x8x9x10x11, and between 11! and the term subtracted, there is in each case a common factor. So, the first number on the list is divisible by 11, the second by 10,..., the last number is divisible by 3.
Sufficient.

Hi Eva, can you help to explain me why B is the answer? you mentioned that, "y can be one of the integers 11! - 11, 11! - 10, 11! - 9, ... , 11! - 2, 11! - 3." and "the first number on the list is divisible by 11, the second by 10,..., the last number is divisible by 3", can you help to discuss it in more detail? thanks.
Director
Joined: 22 Mar 2011
Posts: 518
Own Kudos [?]: 2159 [0]
Given Kudos: 43
WE:Science (Education)
Re: If y is a positive integer, is y prime? [#permalink]
ss58146 wrote:
EvaJager wrote:
LM wrote:
If y is a positive integer, is y prime?
1.$$y>4!$$

2.$$11!-12<y<11!-2$$

(1) obviously not sufficient. There are many primes greater than 4! as well as non-primes.

(2) y can be one of the integers 11! - 11, 11! - 10, 11! - 9, ... , 11! - 2, 11! - 3.
It is easy to see that all the numbers on the above list are certainly not primes. 11! = 2x3x4x5x6x7x8x9x10x11, and between 11! and the term subtracted, there is in each case a common factor. So, the first number on the list is divisible by 11, the second by 10,..., the last number is divisible by 3.
Sufficient.

Hi Eva, can you help to explain me why B is the answer? you mentioned that, "y can be one of the integers 11! - 11, 11! - 10, 11! - 9, ... , 11! - 2, 11! - 3." and "the first number on the list is divisible by 11, the second by 10,..., the last number is divisible by 3", can you help to discuss it in more detail? thanks.

The integers between x - 12 and x - 2 are x - 11, x - 10, ..., x - 3. In our case x =11!.

Take common factor between 11! and the term that is subtracted from it:
For example, 11! - 11 = 2x3x4x5x6x7x8x9x10x11 - 11 = 11(2x3x4x5x6x7x8x9x10 - 1) is divisible by 11, so it is not a prime, as the number in the parentheses is greater than 1.
Intern
Joined: 25 Oct 2012
Posts: 5
Own Kudos [?]: 1 [0]
Given Kudos: 2
Concentration: Economics, Finance
Re: If y is a positive integer, is y prime? [#permalink]
it is not a prime, as the number in the parentheses is greater than 1. I get it now .. Thank you..
Intern
Joined: 03 Dec 2013
Posts: 42
Own Kudos [?]: 231 [0]
Given Kudos: 35
If y is a positive integer, is y prime? [#permalink]
If y is a positive integer, is y prime?

1) y > 4!
2) 11! – 12 < y < 11! – 2
Math Expert
Joined: 02 Sep 2009
Posts: 94371
Own Kudos [?]: 641616 [0]
Given Kudos: 85627
Re: If y is a positive integer, is y prime? [#permalink]
riskietech wrote:
If y is a positive integer, is y prime?

1) y > 4!
2) 11! – 12 < y < 11! – 2

Merging similar topics. Please refer to the discussion above.

Hope it helps.

Similar questions to practice:
does-the-integer-k-have-a-factor-p-such-that-1-p-k-126735.html
if-z-is-an-integer-is-z-prime-128732.html
if-x-is-an-integer-does-x-have-a-factor-n-such-that-100670.html
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30824 [1]
Given Kudos: 799
Re: If y is a positive integer, is y prime? [#permalink]
1
Kudos
Top Contributor
LM wrote:
If y is a positive integer, is y prime?

(1) y > 4!

(2) 11! - 12 < y < 11! - 2

Target question: is y prime?

Statement 1: y > 4!
In other words, y > 24
This does not help us determine whether or not y is prime. Consider these two conflicting cases:
Case a: y = 29, in which case y IS prime
Case b: y = 25, in which case y is NOT prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 11! – 12 < y < 11! – 2
Let's examine a few possible values for y.

y = 11! – 11
y = (11)(10)(9)....(5)(4)(3)(2)(1) - 11
y = 11[(10)(9)....(5)(4)(3)(1) - 1]
Since y is a multiple of 11, y is NOT prime

y = 11! – 10
y = (11)(10)(9)....(5)(4)(3)(2)(1) - 10
y = 10[(11)(9)....(5)(4)(3)(1) - 1]
Since y is a multiple of 10, y is NOT prime

y = 11! – 9
y = (11)(10)(9)....(5)(4)(3)(2)(1) - 9
y = 9[(11)(10)....(5)(4)(3)(1) - 1]
Since y is a multiple of 9, y is NOT prime

As you can see, this pattern can be repeated all the way up to y = 11! - 1. In EVERY case, y is NOT prime
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
Tutor
Joined: 04 Aug 2010
Posts: 1325
Own Kudos [?]: 3228 [2]
Given Kudos: 9
Schools:Dartmouth College
Re: If y is a positive integer, is y prime? [#permalink]
1
Kudos
1
Bookmarks
LM wrote:
If y is a positive integer, is y prime?

(1) y>4!

(2) 11!-12<y<11!-2

Statement 1:
Clearly, many values greater than 4! will be prime, while most will not be prime.
Thus, the answer to the question stem can be YES or NO.
INSUFFICIENT.

Statement 2:
Since the GMAT cannot expect us to prove that any of the integers within the given range ARE prime, all of the integers within the given range must NOT be prime.
Thus, the answer to the question stem is NO.
SUFFICIENT.

Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 233 [0]
Given Kudos: 432
Location: United States
Re: If y is a positive integer, is y prime? [#permalink]
If y is a positive integer, is y prime?

(1) y>4!

Clearly insufficient.

(2) 11!-12<y<11!-2

11! - 11 = not prime
y = a multiple of 11

11! - 4 = not prime
y = multiple of 4

SUFFICIENT.
Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 233 [0]
Given Kudos: 432
Location: United States
Re: If y is a positive integer, is y prime? [#permalink]
GMATGuruNY wrote:
LM wrote:
If y is a positive integer, is y prime?

(1) y>4!

(2) 11!-12<y<11!-2

Statement 1:
Clearly, many values greater than 4! will be prime, while most will not be prime.
Thus, the answer to the question stem can be YES or NO.
INSUFFICIENT.

Statement 2:
Since the GMAT cannot expect us to prove that any of the integers within the given range ARE prime, all of the integers within the given range must NOT be prime.
Thus, the answer to the question stem is NO.
SUFFICIENT.

That's an incredible approach.

Is it safe to say that if a question asks for us to determine if a very large number is prime, we can assume the answer is no?
Non-Human User
Joined: 09 Sep 2013
Posts: 34000
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: If y is a positive integer, is y prime? [#permalink]
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 is a positive integer, is y prime? [#permalink]
Moderator:
Math Expert
94371 posts