GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 29 Jan 2020, 03:30

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60772
If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ?  [#permalink]

Show Tags

New post 15 Nov 2019, 02:16
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

70% (01:55) correct 30% (02:37) wrong based on 46 sessions

HideShow timer Statistics

Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8324
Re: If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ?  [#permalink]

Show Tags

New post 15 Nov 2019, 06:34
1
If P and Q are positive integers, is \((P + 1)(Q + 1) = 12\) ?
\((P + 1)(Q + 1) = 12=1*12=(0+1)(11+1)\).. But P and Q are positive...Discard
\((P + 1)(Q + 1) = 12=2*6=(1+1)(5+1)\).. P and Q are 1 and 5 in any order...
\((P + 1)(Q + 1) = 12=3*4=(2+1)(3+1)\).. P and Q are 2 and 3 in any order...

(1) \((P – 1) (Q – 1) = 2\)
\((P - 1)(Q - 1) = 2=2*1=(3-1)(2-1)\).. So, P and Q are 2 and 3 in any order.....ans is YES
As 2 is prime, no other way that product of two positive integer is 2.
Suff


(2) \(P^2 + Q^2 = 13\)
P an q have to be less than 4 as \(4^2=16\)..
P as 1 gives Q as non-integer
P as 2 gives Q as 3 as \(2^2+3^2=13\)
P as 3 gives Q as 2 as \(3^2+2^2=13\)
Again P and Q are 2 and 3 in any order
Suff

D
_________________
Manager
Manager
avatar
S
Joined: 14 Aug 2017
Posts: 59
Location: India
Concentration: Other, General Management
GMAT 1: 640 Q48 V29
CAT Tests
Re: If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ?  [#permalink]

Show Tags

New post 16 Nov 2019, 00:55
Ooption D: I would suggest as we know they are positive int values . only one possible value fits into them.
Intern
Intern
avatar
B
Joined: 18 Jul 2019
Posts: 28
Re: If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ?  [#permalink]

Show Tags

New post 19 Nov 2019, 03:42
Statement 1 ) (P-1) (Q-1) = 2 ==> EITHER P-1 & Q-1 is a one and the other a 2 with same positive or negative sign.
Therefore, P = +/- 2 if P-1 = (+/-)1 or P= (+/-) 3 if P-1 = +/-2. Similarly Q will have the same values . In any case (P+1)(Q+1) = 12. Hence statement 1 is sufficient.

Statement 2 ) P^2 + Q^2 = 13 . P & Q can hold values of (+/-) 2 and (+/ -) 3. Again (P+1)(Q+1) = 12.

Both statement s are sufficient individually.
GMAT Club Bot
Re: If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ?   [#permalink] 19 Nov 2019, 03:42
Display posts from previous: Sort by

If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne