It is currently 23 Sep 2017, 16:49

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If positive integer p divided by 9 leaves a remainder of 1, which of

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124659 [1], given: 12079

If positive integer p divided by 9 leaves a remainder of 1, which of [#permalink]

Show Tags

New post 15 Jun 2017, 05:15
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

83% (00:38) correct 17% (00:40) wrong based on 62 sessions

HideShow timer Statistics

If positive integer p divided by 9 leaves a remainder of 1, which of the following must be true?

I. p is even.
II. p is odd.
III. p = 3z + 1 for some integer z.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124659 [1], given: 12079

Director
Director
User avatar
P
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 274 [0], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
If positive integer p divided by 9 leaves a remainder of 1, which of [#permalink]

Show Tags

New post 15 Jun 2017, 05:35
1
This post was
BOOKMARKED
Bunuel wrote:
If positive integer p divided by 9 leaves a remainder of 1, which of the following must be true?

I. p is even.
II. p is odd.
III. p = 3z + 1 for some integer z.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only


The number is in the form, \(p = 9x + 1\) --------- (x is the quotient )
Hence number when divided by 3 will leave remainder 1.
Therefore number must be in the form; \(p = 3z + 1\) ---------- (z is the quotient) (III)

Lets try even and odd numbers for p.
If p is 10, divided by 9 will leave remainder 1.
If p is 19 , divided by 9 will leave remainder 1.

Therefore p could be even or odd. Therefore I and II must not be true.

Only III. Answer C...

Kudos [?]: 274 [0], given: 261

Math Forum Moderator
User avatar
S
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 2991

Kudos [?]: 1054 [0], given: 325

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If positive integer p divided by 9 leaves a remainder of 1, which of [#permalink]

Show Tags

New post 15 Jun 2017, 08:03
Bunuel wrote:
If positive integer p divided by 9 leaves a remainder of 1, which of the following must be true?

I. p is even.
II. p is odd.
III. p = 3z + 1 for some integer z.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only


Values of p can be 1 , 10 , 19 , 28.........

I. p is even (Can be both even/odd)
II. p is odd (Can be both even/odd)
III. p = 3z + 1 for some integer z - True in all possible cases...

Thus, answer will (C)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1054 [0], given: 325

Director
Director
avatar
G
Joined: 22 May 2016
Posts: 655

Kudos [?]: 191 [0], given: 499

If positive integer p divided by 9 leaves a remainder of 1, which of [#permalink]

Show Tags

New post 15 Jun 2017, 08:34
Bunuel wrote:
If positive integer p divided by 9 leaves a remainder of 1, which of the following must be true?

I. p is even.
II. p is odd.
III. p = 3z + 1 for some integer z.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

Try to disprove each statement.

\(\frac{p}{9}\) = a + 1, so p = 9a + 1

p = 10, 19, 28, 37, 46, 55 ... (leaving out 1 on purpose)

From list, neither I nor II is true. 19, odd, and 10, even, disprove each respectively. At this point you could choose (C) and move on, because all other answers contain I and/or II

III. p = 3z + 1 for some integer z

10 = 3(3) + 1.
19 = 3(6) + 1.
55 = 3(18) + 1.
III is true. Answer C

Kudos [?]: 191 [0], given: 499

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1537

Kudos [?]: 778 [0], given: 2

Location: United States (CA)
Re: If positive integer p divided by 9 leaves a remainder of 1, which of [#permalink]

Show Tags

New post 17 Jun 2017, 05:09
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:
If positive integer p divided by 9 leaves a remainder of 1, which of the following must be true?

I. p is even.
II. p is odd.
III. p = 3z + 1 for some integer z.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only



Since positive integer p divided by 9 leaves a remainder of 1, we have:

p/9 = Q + 1/9

p = 9Q + 1

Thus, p can be values such as 1, 10, 19, 28, ….

Thus, p can be either even or odd.

Now we can look at Roman numeral III:

p = 3z + 1 for some integer z.

Recall that we have expressed that p = 9Q + 1, so p = 3(3Q) + 1. We see that if we let z = 3Q, we can express p as 3z + 1. So Roman numeral III is true.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 778 [0], given: 2

Manager
Manager
avatar
B
Joined: 06 Nov 2016
Posts: 91

Kudos [?]: 17 [0], given: 15

GMAT 1: 710 Q50 V36
Re: If positive integer p divided by 9 leaves a remainder of 1, which of [#permalink]

Show Tags

New post 21 Jun 2017, 02:07
P CAN BE 1,10,19....

hence I and II can be true or false

III is true for all cases

Option C

Kudos [?]: 17 [0], given: 15

Manager
Manager
avatar
B
Joined: 18 Jun 2017
Posts: 61

Kudos [?]: 2 [0], given: 166

Re: If positive integer p divided by 9 leaves a remainder of 1, which of [#permalink]

Show Tags

New post 16 Aug 2017, 08:57
p=3z+1 should be true where 1 is the remainder as per problem statement.
Since it is divisible by 9 z is quotient and the above expression cabe written as multiple of 3.
Option C.

Kudos [?]: 2 [0], given: 166

Re: If positive integer p divided by 9 leaves a remainder of 1, which of   [#permalink] 16 Aug 2017, 08:57
Display posts from previous: Sort by

If positive integer p divided by 9 leaves a remainder of 1, which of

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


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

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

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®.