GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2019, 17:35 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 p and q are positive integers, and the remainder obtained when p is

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

Hide Tags

Senior Manager  Joined: 18 Aug 2009
Posts: 303
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
If p and q are positive integers, and the remainder obtained when p is  [#permalink]

Show Tags

1
18 00:00

Difficulty:   25% (medium)

Question Stats: 78% (01:57) correct 22% (02:01) wrong based on 210 sessions

HideShow timer Statistics

If p and q are positive integers, and the remainder obtained when p is divided by q is the same as the remainder obtained when q is divided by p, which of the following is a possible value of pq?

(A) 62
(B) 55
(C) 42
(D) 36
(E) 24

_________________
Never give up,,,
Retired Moderator Joined: 20 Dec 2010
Posts: 1572
Re: If p and q are positive integers, and the remainder obtained when p is  [#permalink]

Show Tags

1
1
I am not too sure on this. I guess it is possible only when p and q are both same. If they are both same, pq must be a perfect square.

36 is a perfect square.

Ans: "D"
_________________
Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 654
Re: If p and q are positive integers, and the remainder obtained when p is  [#permalink]

Show Tags

62=2*31
55=5*11
42=2*21=6*7=3*14
24=2*12=3*8=4*6
36=2*18=3*12=4*9=6*6
hence D

Posted from my mobile device
Manager  Joined: 09 Feb 2011
Posts: 202
Concentration: General Management, Social Entrepreneurship
Schools: HBS '14 (A)
GMAT 1: 770 Q50 V47 Re: If p and q are positive integers, and the remainder obtained when p is  [#permalink]

Show Tags

1
Answer should be D
Two numbers giving the same remainder when divided by each other should be same- and remainder zero. 36 only perfect square.
Senior Manager  Joined: 08 Apr 2012
Posts: 326
Re: If p and q are positive integers, and the remainder obtained when p is  [#permalink]

Show Tags

Does anyone have an algebraic way to solve this?
Current Student D
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If p and q are positive integers, and the remainder obtained when p is  [#permalink]

Show Tags

Hey Bunuel here is my approach
could you help with this
here => the only condition that will make the scenario possible is when the numbers are equal
hence = D
_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4015
Re: If p and q are positive integers, and the remainder obtained when p is  [#permalink]

Show Tags

Top Contributor
1
gmatjon wrote:
If p and q are positive integers, and the remainder obtained when p is divided by q is the same as the remainder obtained when q is divided by p, which of the following is a possible value of pq?

(A) 62
(B) 55
(C) 42
(D) 36
(E) 24

The remainder obtained when p is divided by q is the same as the remainder obtained when q is divided by p
This information is indirectly telling us that p = q
To explain why, let's see what happens if p does NOT equal q
If that's the case, then one value must be greater than the other value.
Let's see what happens IF it were the case that p < q.

What is the remainder when p is divided by q?
Since p < q, then p divided by q equals 0 with remainder p

IMPORTANT RULE: When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0

What is the remainder when q is divided by p?
Based on the above rule, we know that the remainder must be a number such that 0 ≤ remainder < p

Hmmmmm. In our first calculation (p ÷ q), we found that the remainder = p
In our second calculation (q ÷ p), we found that 0 ≤ remainder < p
Since it's IMPOSSIBLE for the remainder to both EQUAL p and BE LESS THAN p, we can conclude that it's impossible for p to be less than q.

Using similar logic, we can see that it's also impossible for q to be less than p.

So, it MUST be the case that p = q
So, pq = p² = the square of some integer

Check the answer choices . . . only D is the square of an integer.

RELATED VIDEO FROM OUR COURSE

_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13317
Re: If p and q are positive integers, and the remainder obtained when p is  [#permalink]

Show Tags

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 and q are positive integers, and the remainder obtained when p is   [#permalink] 20 Oct 2019, 12:46
Display posts from previous: Sort by

If p and q are positive integers, and the remainder obtained when p is

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

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