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

It is currently 20 Oct 2014, 02:32

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If p is a positive odd integer, what is the remainder when p

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Intern
Intern
User avatar
Joined: 20 Feb 2012
Posts: 41
Followers: 1

Kudos [?]: 72 [2] , given: 6

If p is a positive odd integer, what is the remainder when p [#permalink] New post 23 Feb 2012, 07:09
2
This post received
KUDOS
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (02:07) correct 59% (01:01) wrong based on 484 sessions
If p is a positive odd integer, what is the remainder when p is divided by 4 ?

(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.
[Reveal] Spoiler: OA
Expert Post
12 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23326
Followers: 3599

Kudos [?]: 28587 [12] , given: 2803

Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 23 Feb 2012, 07:57
12
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
If p is a positive odd integer, what is the remainder when p is divided by 4 ?

(1) When p is divided by 8, the remainder is 5 --> p=8q+5=(8q+4)+1=4(2q+1)+1 --> so the remainder upon division of p by 4 is 1 (since first term is divisible by 4 and second term yields remainder of 1 upon division by 4). Sufficient.

(2) p is the sum of the squares of two positive integers --> since p is an odd integer then one of the integers must be even and another odd: p=(2n)^2+(2m+1)^2=4n^2+4m^2+4m+1=4(n^2+m^2+m)+1 --> the same way as above: the remainder upon division of p by 4 is 1 (since first term is divisible by 4 and second term yields remainder of 1 upon division by 4). Sufficient.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 06 Jun 2012
Posts: 150
Followers: 0

Kudos [?]: 43 [0], given: 37

GMAT ToolKit User
If p is a positive odd integer, what is the remainder when p [#permalink] New post 26 Jul 2012, 07:05
I am not sure if this is discussed, tried to find it but couldn't find easily.

If p is a positive odd integer, what is the remainder when p is divided by 4 ?
(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.

I need help, here i thought the answer was A but the official answer given is D. Here's how i did it

(1) P = 8Q + 5, so for all values of Q starting from 1, 4 divided by P results in remainder 1. So sufficient
(2) P = X^2+ Y^2, ex X=Y=1, P= 2, remainder 2. ex X=1,Y=2, P=5, remainder 1. Hence Not Sufficient.

Confused? :shock:
_________________

Please give Kudos if you like the post

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23326
Followers: 3599

Kudos [?]: 28587 [1] , given: 2803

Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 26 Jul 2012, 07:09
1
This post received
KUDOS
Expert's post
summer101 wrote:
I am not sure if this is discussed, tried to find it but couldn't find easily.

If p is a positive odd integer, what is the remainder when p is divided by 4 ?
(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.

I need help, here i thought the answer was A but the official answer given is D. Here's how i did it

(1) P = 8Q + 5, so for all values of Q starting from 1, 4 divided by P results in remainder 1. So sufficient
(2) P = X^2+ Y^2, ex X=Y=1, P= 2, remainder 2. ex X=1,Y=2, P=5, remainder 1. Hence Not Sufficient.

Confused? :shock:


Merging similar topics.

Please hide OA under the spoiler.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 15 Jun 2010
Posts: 363
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Followers: 8

Kudos [?]: 172 [0], given: 50

Reviews Badge
Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 26 Jul 2012, 07:11
Hi Summer101

For St 2: U have to make P an odd Integer. If u select X = Y = 1, Then P become 2 i.e. even. Thats why D is the correct answer.
_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Director
Director
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 550
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 32 [0], given: 562

Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 25 Jan 2013, 20:43
number plugging is the fastest approach for remainder problems.. because there emerges a definite pattern.. that can make the stem sufficient.
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Intern
Intern
avatar
Joined: 27 Dec 2012
Posts: 12
Followers: 0

Kudos [?]: 1 [0], given: 4

Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 31 Jan 2013, 04:03
OK..
Let me quote here something..

Let's consider x=1 and y=2...
square of two number is 5 (a positive odd integer) and leaves remainder 5 when divided by 8
Again..consider x=1 and y = 6, square of two numbers is 37 (a positive odd integer) and leaves remainder 5 when divided by 8
hence, both the statements are either sufficient to ans this problem..
Intern
Intern
avatar
Joined: 11 Aug 2013
Posts: 5
Followers: 0

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

Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 03 Sep 2013, 09:02
BANON wrote:
If p is a positive odd integer, what is the remainder when p is divided by 4 ?

(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.


I think if you would work straight with digits you would get same result, reminder 1.
Just try 9 and 16, or 4 and 9
1 KUDOS received
Intern
Intern
User avatar
Status: active
Joined: 13 May 2013
Posts: 11
Followers: 0

Kudos [?]: 7 [1] , given: 7

Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 03 Sep 2013, 15:32
1
This post received
KUDOS
Nice one, second part is tricky and needs more focus.
_________________

Press Kudos if I was able to help you with questions/solutions/resources :-)

Useful Resources:
FlashCards: manhattangmat[dot]com/pdf/FlashCards_Complete_2009.pdf

Manager
Manager
avatar
Status: Persevering
Joined: 15 May 2013
Posts: 224
Location: India
Concentration: Technology, Leadership
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 1

Kudos [?]: 53 [0], given: 34

GMAT ToolKit User
Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 04 Sep 2013, 10:12
D

1) Is sufficient 5,13 all give 1 as remainder.
2) sum of squares of any two positive integers, but one of them has to be odd and other an even number because p is an odd integer. So consider any pair 3,2 (3^2+2^2) (9+4)/4 1 as remainder. Or 5,2 =>29/4 =>1 as remainder.
_________________

--It's one thing to get defeated, but another to accept it.

Intern
Intern
avatar
Joined: 19 Sep 2013
Posts: 2
Followers: 0

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

If P is a positiv [#permalink] New post 19 Sep 2013, 08:47
If P is a positive odd integer, what is the remainder when P is divided by 4 ?

S1) When P is divided by 8, the remainder is 5.

S2) P is the sum of the squares of two positive integers.




Please pay attention to the following rules.....

1) Always type the question and post. Do not attach mere a screen shot of the question.

2) Always Post the question along with OA. (OA should be in spoiler)

3) Always post the Question in RELEVANT Forum. (e.g. This Quant (DS) question was posted in Verbal Forum)

Thanks.
Attachments

File comment: It contains a screenshot of the question.
gmat prep.doc [94 KiB]
Downloaded 33 times

To download please login or register as a user


Last edited by Narenn on 22 Sep 2013, 05:17, edited 1 time in total.
Topic Moved. Always post the topic in relevant forum
Intern
Intern
avatar
Joined: 26 Apr 2013
Posts: 49
Location: United States
Concentration: Marketing, Nonprofit
GPA: 3.5
WE: Marketing (Telecommunications)
Followers: 0

Kudos [?]: 27 [0], given: 2

GMAT ToolKit User
Re: Gmatprep quant question [#permalink] New post 20 Sep 2013, 19:24
m4ch1n3 wrote:
I believe answer is wrong:


The question asks what will be the remainder when P is divided by 4.

Statement 1 says: p=8n+5…..which is when P is divided by 8 we get remainder 5.
Now from here on you can do two things.
1. think logically 8n is divided by 4 so we won't have any remainder if we divide 8n by 4 but if we divide 5 by 4 we always get remainder 1. The value of N doesn't really matter because 8N will always be divisible by 4 and 5 will always give remainder 1.
2. plug in number and see what happens. If we put n=1,2,3,4 or so on….we get 13,21,29 respectively. Now in each case we get remainder 1.

So statement 1 is sufficient. Answer should be either A or D. So cross out B C and E.

Statement 2 says: p is sum of square of two integers
just plug in numbers and see you will always get remainder 1. So statement 2 is sufficient and Answer is D.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23326
Followers: 3599

Kudos [?]: 28587 [0], given: 2803

Re: If P is a positiv [#permalink] New post 22 Sep 2013, 05:33
Expert's post
m4ch1n3 wrote:
If P is a positive odd integer, what is the remainder when P is divided by 4 ?

S1) When P is divided by 8, the remainder is 5.

S2) P is the sum of the squares of two positive integers.




Please pay attention to the following rules.....

1) Always type the question and post. Do not attach mere a screen shot of the question.

2) Always Post the question along with OA. (OA should be in spoiler)

3) Always post the Question in RELEVANT Forum. (e.g. This Quant (DS) question was posted in Verbal Forum)

Thanks.


Merging similar topics. Please refer to the solutions above.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2782
Followers: 206

Kudos [?]: 42 [0], given: 0

Premium Member
Re: If p is a positive odd integer, what is the remainder when p [#permalink] New post 28 Sep 2014, 06:29
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If p is a positive odd integer, what is the remainder when p   [#permalink] 28 Sep 2014, 06:29
    Similar topics Author Replies Last post
Similar
Topics:
1 If p is a positive odd integer, what is the remainder when p prince13 11 26 Oct 2008, 04:51
If p is a positive odd integer, what is the remainder when p Nerdboy 7 22 Sep 2008, 05:02
If p is a positive odd integer, what is the remainder when p AlbertNTN 8 17 Mar 2008, 06:51
If p is a positive odd integer, what is the remainder when p briks123 10 23 Jul 2007, 07:25
If p is a positive odd integer, what is the remainder when p kjmath 7 16 Jan 2007, 09:17
Display posts from previous: Sort by

If p is a positive odd integer, what is the remainder when p

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.