Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 01 May 2016, 16:19

### 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 P, Q, and R are positive integers, what is the remainder

Author Message
TAGS:

### Hide Tags

Manager
Status: Fighting hard
Joined: 04 Jul 2011
Posts: 72
GMAT Date: 10-01-2012
Followers: 2

Kudos [?]: 48 [1] , given: 84

If P, Q, and R are positive integers, what is the remainder [#permalink]

### Show Tags

27 Oct 2012, 19:48
1
KUDOS
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:30) correct 33% (01:39) wrong based on 101 sessions

### HideShow timer Statictics

If P, Q, and R are positive integers, what is the remainder when R – Q is divided by 3?

(1) R = P^3
(2) Q = (P – 2)^3
[Reveal] Spoiler: OA

_________________

I will rather do nothing than be busy doing nothing - Zen saying

Last edited by Bunuel on 29 Oct 2012, 05:35, edited 1 time in total.
Renamed the topic.
Moderator
Joined: 02 Jul 2012
Posts: 1230
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 105

Kudos [?]: 1137 [3] , given: 116

### Show Tags

27 Oct 2012, 23:14
3
KUDOS
1
This post was
BOOKMARKED
Pansi wrote:
If P, Q, and R are positive integers, what is the remainder when R – Q is divided by 3?

(1) R = P^3
(2) Q = (P – 2)^3

2) No information about R. Insufficient

1 & 2 together. $$R-Q = P^3 - (P-2)^3$$

So $$P^3$$gets cancelled out and we only have multiples of 3 and a constant remaining.

Sufficient

Kudos Please... If my post helped.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Math Expert
Joined: 02 Sep 2009
Posts: 32549
Followers: 5639

Kudos [?]: 68390 [0], given: 9797

### Show Tags

29 Oct 2012, 05:37
Expert's post
2
This post was
BOOKMARKED
If P, Q, and R are positive integers, what is the remainder when R – Q is divided by 3?

(1) R = P^3. No info about Q. Not sufficient.
(2) Q = (P – 2)^3. No info about R. Not sufficient.

(1)+(2) Important tip: x^3-y^3 can be factored as follows: $$x^3-y^3=(x-y)(x^2+xy+y^2)$$. Apply this factoring to $$R-Q$$ --> $$R-Q=P^3-(P-2)^3=(P-P+2)(P^2+P^2-2P+P^2-4P+4)=2(3P^2-6P+4)=6c^2-12c+8=6(c^2-2c+1)+2$$ --> remainder upon division this expression by 3 is 2. Sufficient.

Similar questions to practice:
if-a-b-and-c-are-positive-integers-what-is-the-remainder-140495.html
if-a-b-and-c-are-positive-integers-what-is-the-remainder-127028.html

Hope it helps.
_________________
Current Student
Joined: 03 Aug 2012
Posts: 915
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 19

Kudos [?]: 518 [0], given: 322

Re: If P, Q, and R are positive integers, what is the remainder [#permalink]

### Show Tags

10 Aug 2013, 08:39
Hi folks,

Both are insufficient without any doubts checking for option (C).

P=3 , P-2 =1 27-1 = 26/3 =2

P=4 , P-2 = 2 64-8 = 56/3 =2

P=5 , P-2 = 3 125-27 , Rem=2

P=6, P-2 = 4 Rem =2

Hence (C)
_________________

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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9248
Followers: 454

Kudos [?]: 115 [0], given: 0

Re: If P, Q, and R are positive integers, what is the remainder [#permalink]

### Show Tags

24 Oct 2015, 13:05
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 P, Q, and R are positive integers, what is the remainder   [#permalink] 24 Oct 2015, 13:05
Similar topics Replies Last post
Similar
Topics:
3 If p, q, and r are different positive integers such that p + q + r = 6 2 04 May 2015, 05:55
5 If r, s, and t are all positive integers, what is the remainder of 2^p 2 23 Oct 2014, 00:40
4 If P, Q, R, and S are positive integers, and P/Q = R/S, is R 9 01 Feb 2011, 11:01
15 x, q, r are positive integers. x/17 = q and remainder is r. 6 21 Nov 2010, 17:49
2 If P, Q, R, and S are positive integers, and P/Q=R/S, is R 6 01 Sep 2006, 06:21
Display posts from previous: Sort by