Find all School-related info fast with the new School-Specific MBA Forum
Learn more about the recent changes... close

It is currently 22 May 2013, 20:55
Customize  |  Hide

Search
Register
New posts
Unanswered

If p and q are two different prime numbers and n is the

  Question banks Downloads My Bookmarks Reviews  
  Oldest Best Reply
Search for:
 
Print view
First unread post
Author Message
TAGS:
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1278
Location: Madrid
Followers: 9

Kudos [?]: 69 [0], given: 0

If p and q are two different prime numbers and n is the [#permalink] New post 12 Apr 2007, 07:18
00:00

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
If p and q are two different prime numbers and n is the difference between their product and their sum, what is the remainder when n is divided by 4?

(1) Both p and q have a units digit of 1.
(2) p-q= 10
Intern
Intern
Joined: 29 Aug 2005
Posts: 4
Followers: 0

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

 [#permalink] New post 12 Apr 2007, 07:38
Statement (1) Both p and q have a units digit of 1.
31, 41, 61, 71 ... So not sufficient

Statement (2) p-q= 10
23-13 = 10
41-31 = 10
71-61 = 10
So not sufficient

edit...
Statements 1 and 2 together
n=31*41-(31+41) = 1199
or
n=61*71-(61+71) = 4199

Reminder is 3 when n is devided by 4 for both the values of n.

So Answer should be C. (Please correct me if I am wrong.)

Last edited by newgmater on 12 Apr 2007, 07:47, edited 2 times in total.
Director
Director
Joined: 13 Nov 2003
Posts: 811
Location: BULGARIA
Followers: 1

Kudos [?]: 6 [0], given: 0

GMAT Tests User
 [#permalink] New post 12 Apr 2007, 07:40
Hi
Stmnt 1 is not SUFF
N would be an integer that ends with 9. But a n integer is divisible by 4 if last 2 digits are divisible by 4. If N is 9 rem is 1, If N is 19 rem is 3 so Stmnt 1 is NOT suff

sTMNT 2 is SUFF

ANS B
CEO
CEO
User avatar
Joined: 20 Nov 2005
Posts: 2934
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 7

Kudos [?]: 37 [0], given: 0

GMAT Tests User
 [#permalink] New post 12 Apr 2007, 08:13
B

St1: Clearly INSUFF
St2:
If p-q = 10
pq-(p+q) can be written as q^2+8q-10
or (q^2 - 1) + (8q-9)
8q-9 will give a remainder of 3 when divided by 4
now lets see q^2 - 1
q^2 - 1 = (q-1) (q+1)
since q is odd both (q-1) and (q+1) are divisible by 2 hence it is divisible by 4.
Final remainder = 3: SUFF
Intern
Intern
Joined: 29 Aug 2005
Posts: 4
Followers: 0

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

 [#permalink] New post 12 Apr 2007, 08:38
ps_dahiya. I am missing something. Could you please explain how you are writing pq - (p+q) = q^2+8q-10 (provided p-q=10)

Thank you.
CEO
CEO
User avatar
Joined: 20 Nov 2005
Posts: 2934
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 7

Kudos [?]: 37 [0], given: 0

GMAT Tests User
 [#permalink] New post 12 Apr 2007, 08:55
newgmater wrote:
ps_dahiya. I am missing something. Could you please explain how you are writing pq - (p+q) = q^2+8q-10 (provided p-q=10)

Thank you.

n = pq-(p+q)
substitute p= q+10 in above equation and you get q^2+8q-10

hope this helps...
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1278
Location: Madrid
Followers: 9

Kudos [?]: 69 [0], given: 0

 [#permalink] New post 12 Apr 2007, 10:30
ps_dahiya wrote:
B

St1: Clearly INSUFF
St2:
If p-q = 10
pq-(p+q) can be written as q^2+8q-10
or (q^2 - 1) + (8q-9)
8q-9 will give a remainder of 3 when divided by 4
now lets see q^2 - 1
q^2 - 1 = (q-1) (q+1)
since q is odd both (q-1) and (q+1) are divisible by 2 hence it is divisible by 4.
Final remainder = 3: SUFF


Why is (1) clearly insufficient? Shouldn't you know me better by now? :wink:
CEO
CEO
User avatar
Joined: 20 Nov 2005
Posts: 2934
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 7

Kudos [?]: 37 [0], given: 0

GMAT Tests User
 [#permalink] New post 12 Apr 2007, 11:27
kevincan wrote:
ps_dahiya wrote:
B

St1: Clearly INSUFF
St2:
If p-q = 10
pq-(p+q) can be written as q^2+8q-10
or (q^2 - 1) + (8q-9)
8q-9 will give a remainder of 3 when divided by 4
now lets see q^2 - 1
q^2 - 1 = (q-1) (q+1)
since q is odd both (q-1) and (q+1) are divisible by 2 hence it is divisible by 4.
Final remainder = 3: SUFF


Why is (1) clearly insufficient? Shouldn't you know me better by now? :wink:


Oops... :wall
Answer should be D.
St1:
p = 10x +1
q = 10y+1
where x and y are positive integers

Now pq-(p+q) can be written as
(10x+1) (10y+1) - 10x-1-10y-1
100xy +10x+10y +1 - 10x-1-10y-1
100xy - 1 so the remainder will always be 3: SUFF

A little out of practice...
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1278
Location: Madrid
Followers: 9

Kudos [?]: 69 [0], given: 0

 [#permalink] New post 13 Apr 2007, 02:56
Very nice! Also note that for prime numbers p and q, n=pq-p-q=(p-1)(q-1)-1
Intern
Intern
Joined: 10 Mar 2007
Posts: 4
Followers: 0

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

 [#permalink] New post 13 Apr 2007, 17:41
My first post. :-D

Sorry, how did you get the reminder 3?

Thanx
CEO
CEO
User avatar
Joined: 20 Nov 2005
Posts: 2934
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 7

Kudos [?]: 37 [0], given: 0

GMAT Tests User
 [#permalink] New post 13 Apr 2007, 22:26
jaspetrovic wrote:
My first post. :-D

Sorry, how did you get the reminder 3?

Thanx

If something is divisible by 4 and then you subtract 1 from that then we need to subtract 3 more from that to again make it divisible by 4. Hence remainder = 3

Same way if something is divisible by 4 and then you subtract 9 from that then we need to subtract 3 more from that to again make it divisible by 4. Hence remainder = 3
  [#permalink] 13 Apr 2007, 22:26
    Similar topics Author Replies Last post
Similar
Topics:
 New posts if n and p are different positive prime number, which of the ftoor 4 09 Nov 2003, 14:10
New posts if n and p are different positive prime numbers, which of carsen 6 08 Jul 2004, 00:09
New posts If n and p are different positive prime numbers, which of Avis 9 26 Feb 2006, 10:39
New posts If r and p are two different prime numbers, which of the ldpedroso 4 07 Jun 2008, 15:31
Popular new posts 5 EXPERTS_POSTS_IN_THIS_TOPIC p and q are different two-digit prime numbers with the same cvsmech 10 28 Sep 2011, 14:06
Display posts from previous: Sort by

If p and q are two different prime numbers and n is the

  Question banks Downloads My Bookmarks Reviews  
Print view
First unread post

Moderators: Bunuel, VeritasPrepKarishma, IanStewart

Search for:


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com