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

It is currently 19 Jun 2018, 12:50

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

When positive integer p is divided by 7 the remainder is 2.

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

Hide Tags

Manager
Manager
avatar
Joined: 02 Aug 2007
Posts: 221
Schools: Life
When positive integer p is divided by 7 the remainder is 2. [#permalink]

Show Tags

New post Updated on: 05 Jun 2014, 01:17
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (01:08) correct 42% (01:13) wrong based on 289 sessions

HideShow timer Statistics

When positive integer p is divided by 7, the remainder is 2. Is p divisible by 8?

(1) p is divisible by 2 and 3

(2) p<100

M05-20

Originally posted by xALIx on 01 Feb 2009, 13:23.
Last edited by Bunuel on 05 Jun 2014, 01:17, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
1 KUDOS received
SVP
SVP
User avatar
Joined: 07 Nov 2007
Posts: 1738
Location: New York
Re: When integer p is divided by 7 [#permalink]

Show Tags

New post 01 Feb 2009, 13:57
1
1
x-ALI-x wrote:
When integer p is divided by 7, the remainder is 2. Is p divisible by 8?

1. p is divisible by 2 and 3
2. p < 100


* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient


p= 7k+2

p values when k=0,1,2,3,4,..

p=2,9,16,23,30,37,44,51,58,65,72,79,86,93,100

1)
p is divided by 2 and 3 = p is dived by 6
possible values are
30 -- remainder when divided by 8 --6
72-- remainder when divided by 8 --0.

not sufficient

2)
p<100

not sufficient.

commbined not sufficient see statement1

E
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Intern
Intern
User avatar
Joined: 15 Jan 2009
Posts: 45
Schools: Marshall '11
Re: When integer p is divided by 7 [#permalink]

Show Tags

New post 01 Feb 2009, 19:17
how did you get from this step:
p is divided by 2 and 3 = p is dived by 6
To this step:
possible values are
30 -- remainder when divided by 8 --6
72-- remainder when divided by 8 --0.

Could someone explain the logic behind it?
Senior Manager
Senior Manager
User avatar
Joined: 26 May 2008
Posts: 412
Schools: Kellogg Class of 2012
Re: When integer p is divided by 7 [#permalink]

Show Tags

New post 01 Feb 2009, 23:44
wcgmat,

of the sample values mentioned, there are only 2 numbers - 30, 72, that are divisible by both 2 and 3

Cheers,
Unplugged
Manager
Manager
avatar
Joined: 02 Aug 2007
Posts: 221
Schools: Life
Re: When integer p is divided by 7 [#permalink]

Show Tags

New post 02 Feb 2009, 17:38
x2suresh wrote:
x-ALI-x wrote:
When integer p is divided by 7, the remainder is 2. Is p divisible by 8?

1. p is divisible by 2 and 3
2. p < 100


* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient


p= 7k+2

p values when k=0,1,2,3,4,..

p=2,9,16,23,30,37,44,51,58,65,72,79,86,93,100

1)
p is divided by 2 and 3 = p is dived by 6
possible values are
30 -- remainder when divided by 8 --6
72-- remainder when divided by 8 --0.

not sufficient

2)
p<100

not sufficient.

commbined not sufficient see statement1

E


Great explanation Suresh!!! I've always considered it 7p+2, but you're correct in noting it as 7k+2.
Thanks!
Intern
Intern
User avatar
Joined: 15 Jan 2009
Posts: 45
Schools: Marshall '11
Re: When integer p is divided by 7 [#permalink]

Show Tags

New post 04 Feb 2009, 15:47
unplugged wrote:
wcgmat,

of the sample values mentioned, there are only 2 numbers - 30, 72, that are divisible by both 2 and 3

Cheers,
Unplugged


Ok, I see that in this example, 30 and 72 is obtained when we count out a bunch of numbers that fit the remainder equation that was provided. But when you encounter remainder type of problems like this, do you always just calculate out a bunch of sample numbers according to the equation provided? Is this the best strategy to use? Or are there mathematical ways to obtain numbers like 30 and 72?
Director
Director
avatar
Joined: 29 Aug 2005
Posts: 819
Re: When integer p is divided by 7 [#permalink]

Show Tags

New post 12 Feb 2009, 14:24
x2suresh wrote:
x-ALI-x wrote:
When integer p is divided by 7, the remainder is 2. Is p divisible by 8?

1. p is divisible by 2 and 3
2. p < 100


* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient


p= 7k+2

p values when k=0,1,2,3,4,..

p=2,9,16,23,30,37,44,51,58,65,72,79,86,93,100

1)
p is divided by 2 and 3 = p is dived by 6
possible values are
30 -- remainder when divided by 8 --6
72-- remainder when divided by 8 --0.

not sufficient

2)
p<100

not sufficient.

commbined not sufficient see statement1

E

As p is even, one can shorten the iteration by calculating p for even values of k.
Any more shortcuts?
Manager
Manager
avatar
Joined: 23 Jan 2013
Posts: 164
Concentration: Technology, Other
Schools: Haas
GMAT Date: 01-14-2015
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: When integer p is divided by 7 [#permalink]

Show Tags

New post 04 Jun 2014, 20:20
I got the answer by listing down multiples of 6 and ( multiples of 7 ) + 2 till i found a match for 2 numbers is there a faster way of doing this ?

Since in the gmat time matters the most !!!
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8100
Location: Pune, India
Re: When integer p is divided by 7 [#permalink]

Show Tags

New post 04 Jun 2014, 20:55
1
1
shelrod007 wrote:
I got the answer by listing down multiples of 6 and ( multiples of 7 ) + 2 till i found a match for 2 numbers is there a faster way of doing this ?

Since in the gmat time matters the most !!!


When you are given different remainders - 2 when divided by 7 and 0 when divided by 6 (using stmnt 1), you have to find the first such common number. Some tips and tricks of this method are discussed here:
http://www.veritasprep.com/blog/2011/05 ... s-part-ii/

It might help you reduce the time taken.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46167
Re: When positive integer p is divided by 7 the remainder is 2. [#permalink]

Show Tags

New post 05 Jun 2014, 01:18
When positive integer p is divided by 7, the remainder is 2. Is p divisible by 8?

When positive integer p is divided by 7 the remainder is 2: \(p=7q+2\), so p can be: 2, 9, 16, 23, 30, 37, 44, 51, 58, 65, 72, ...

(1) p is divisible by 2 and 3 --> p is a multiple of 6 --> p can be 30 (answer NO) or 72 (answer YES). Not sufficient.

(2) p < 100. Clearly insufficient.

(1)+(2) p can still be 30 (answer NO) or 72 (answer YES). Not sufficient.

Answer: E.
_________________

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

Intern
Intern
avatar
B
Joined: 07 Mar 2014
Posts: 16
Location: India
Concentration: Entrepreneurship, International Business
Re: When positive integer p is divided by 7 the remainder is 2. [#permalink]

Show Tags

New post 24 Feb 2016, 16:25
if P is divided by 7 then remainder is 2, then what will be the remainder if p is divided by 8

Statement 1:

p is divisible by 2 and 3
so we can say that p is divisible by all the multiples of 6

now we have to take the multiple of 6 which when divided by 7 gives remainder 2.
so the values are 30, 72 and so on

and when we divide 30 with 8 we get 6 as remainder but when we divide 72 with 8 we get o as remainder.

so this statement is clearly insufficient

Statement 2: p < 100

clearly insufficient as p can be any value and thus can give any remainder from 0 to 9 when divided by 8

Combining both the statements

Clearly insufficient as we already know that there are 2 possible values of p under 100 and both are giving different remainder( i.e 6 and 0 resp.)

therefore the answer is E
BSchool Forum Moderator
User avatar
D
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
Re: When positive integer p is divided by 7 the remainder is 2. [#permalink]

Show Tags

New post 22 Mar 2016, 03:43
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7004
Premium Member
Re: When positive integer p is divided by 7 the remainder is 2. [#permalink]

Show Tags

New post 22 Apr 2017, 06:58
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: When positive integer p is divided by 7 the remainder is 2.   [#permalink] 22 Apr 2017, 06:58
Display posts from previous: Sort by

When positive integer p is divided by 7 the remainder is 2.

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


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.