It is currently 17 Nov 2017, 11:06

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If Z is an integer, is Z prime?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 10 Feb 2012
Posts: 72

Kudos [?]: 111 [0], given: 41

Location: India
Concentration: Marketing, Strategy
GMAT 1: 640 Q48 V31
GPA: 3.45
WE: Marketing (Pharmaceuticals and Biotech)
If Z is an integer, is Z prime? [#permalink]

### Show Tags

07 Mar 2012, 11:51
7
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

65% (00:58) correct 35% (01:16) wrong based on 399 sessions

### HideShow timer Statistics

If Z is an integer, is Z prime?

(1) 15! < Z
(2) 17! + 2 < Z < 17! + 17
[Reveal] Spoiler: OA

Kudos [?]: 111 [0], given: 41

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132499 [6], given: 12323

If Z is an integer, is Z prime? [#permalink]

### Show Tags

07 Mar 2012, 12:01
6
KUDOS
Expert's post
6
This post was
BOOKMARKED
If Z is an integer, is Z prime?

(1) $$15!<z$$ --> $$z$$ is more than some number ($$15!$$). $$z$$ may or may not be a prime. Not sufficient.

(2) $$17!+2\leq{z}\leq{17!+17}$$ --> $$z$$ cannot be a prime. For instance if $$z=17!+13=13*(2*3*4*5*6*7*8*9*10*11*12*14*15*16*17+1)$$, then $$z$$ is a multiple of 13, so not a prime. Same for all other numbers in this range. So, $$z=17!+x$$, where $$2\leq{x}\leq{17}$$ will definitely be a multiple of $$x$$ (as we would be able to factor out $$x$$ out of $$17!+x$$, the same way as we did for 13). Sufficient.

Similar questions to practice:
if-x-is-an-integer-does-x-have-a-factor-n-such-that-100670.html
does-the-integer-k-have-a-factor-p-such-that-1-p-k-126735.html

Hope it's clear.
_________________

Kudos [?]: 132499 [6], given: 12323

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132499 [0], given: 12323

Re: If Z is an integer, is Z prime? [#permalink]

### Show Tags

12 Jun 2013, 04:27
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Number Properties: math-number-theory-88376.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

_________________

Kudos [?]: 132499 [0], given: 12323

Intern
Joined: 21 Dec 2013
Posts: 24

Kudos [?]: 25 [1], given: 21

Concentration: General Management, Technology
WE: Project Management (Computer Software)
Re: If Z is an integer, is Z prime? [#permalink]

### Show Tags

08 Jan 2014, 03:25
1
KUDOS
If the statement B was rephrased to ===> 17! + 2 < Z < 17! + 19 then will the answer to this question change to E ?

Kudos [?]: 25 [1], given: 21

Intern
Joined: 23 Aug 2014
Posts: 42

Kudos [?]: 11 [0], given: 28

GMAT Date: 11-29-2014
Re: If Z is an integer, is Z prime? [#permalink]

### Show Tags

09 Nov 2014, 11:03
For the above question, this will help (its a matched question and all the posts there make things clearer)
if-x-is-an-integer-does-x-have-a-factor-n-such-that
regards

Kudos [?]: 11 [0], given: 28

Non-Human User
Joined: 09 Sep 2013
Posts: 15705

Kudos [?]: 281 [0], given: 0

Re: If Z is an integer, is Z prime? [#permalink]

### Show Tags

12 Sep 2016, 03:17
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.
_________________

Kudos [?]: 281 [0], given: 0

Intern
Joined: 12 Nov 2016
Posts: 45

Kudos [?]: [0], given: 17

Location: Kazakhstan
Concentration: Entrepreneurship, Finance
GMAT 1: 620 Q36 V39
GPA: 3.2
Re: If Z is an integer, is Z prime? [#permalink]

### Show Tags

15 Nov 2016, 09:02
I read the Kaplan explanation and read explanations above in the thread and I can't find a clue....
For instance, why 17!+13 is equal to 13∗(2∗4∗5∗6∗7∗8∗9∗10∗11∗12∗14∗15∗16∗17+1)? Isn't (2∗4∗5∗6∗7∗8∗9∗10∗11∗12∗14∗15∗16∗17+1) = 17!? So, why 17! multiplied by 13 would be equal to 17! + 13?

Kudos [?]: [0], given: 17

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132499 [1], given: 12323

Re: If Z is an integer, is Z prime? [#permalink]

### Show Tags

15 Nov 2016, 09:08
1
KUDOS
Expert's post
Erjan_S wrote:
I read the Kaplan explanation and read explanations above in the thread and I can't find a clue....
For instance, why 17!+13 is equal to 13∗(2∗4∗5∗6∗7∗8∗9∗10∗11∗12∗14∗15∗16∗17+1)? Isn't (2∗4∗5∗6∗7∗8∗9∗10∗11∗12∗14∗15∗16∗17+1) = 17!? So, why 17! multiplied by 13 would be equal to 17! + 13?

17! + 13 = 2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17 + 13

Factor out 13: 13*(2*3*4*5*6*7*8*9*10*11*12*14*15*16*17 + 1)
_________________

Kudos [?]: 132499 [1], given: 12323

Intern
Joined: 12 Nov 2016
Posts: 45

Kudos [?]: [0], given: 17

Location: Kazakhstan
Concentration: Entrepreneurship, Finance
GMAT 1: 620 Q36 V39
GPA: 3.2
Re: If Z is an integer, is Z prime? [#permalink]

### Show Tags

15 Nov 2016, 09:30
Ok, now I can see.. But honestly, it is kind of hard question for somebody who did not specialize in math...

Kudos [?]: [0], given: 17

Manager
Joined: 12 Oct 2015
Posts: 209

Kudos [?]: 131 [0], given: 105

GMAT 1: 700 Q47 V39
GPA: 3.3
WE: Accounting (Accounting)
Re: If Z is an integer, is Z prime? [#permalink]

### Show Tags

02 May 2017, 07:20
Amazing question & Amazing explanation by Bunuel!
_________________

Winners dont make excuses.

350--> 700

https://gmatclub.com/forum/700-q47-v39-ir-7-awa-246682.html

Kudos [?]: 131 [0], given: 105

Re: If Z is an integer, is Z prime?   [#permalink] 02 May 2017, 07:20
Display posts from previous: Sort by