Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Aug 2007
Posts: 222
Schools: Life

When positive integer p is divided by 7 the remainder is 2. [#permalink]
Show Tags
01 Feb 2009, 12:23
2
This post was BOOKMARKED
Question Stats:
58% (01:12) correct 42% (01:16) wrong based on 274 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 M0520
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 05 Jun 2014, 00:17, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.



SVP
Joined: 07 Nov 2007
Posts: 1789
Location: New York

Re: When integer p is divided by 7 [#permalink]
Show Tags
01 Feb 2009, 12:57
1
This post received KUDOS
1
This post was BOOKMARKED
xALIx 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
Joined: 15 Jan 2009
Posts: 46
Schools: Marshall '11

Re: When integer p is divided by 7 [#permalink]
Show Tags
01 Feb 2009, 18:17
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
Joined: 26 May 2008
Posts: 426
Schools: Kellogg Class of 2012

Re: When integer p is divided by 7 [#permalink]
Show Tags
01 Feb 2009, 22:44
wcgmat,
of the sample values mentioned, there are only 2 numbers  30, 72, that are divisible by both 2 and 3
Cheers, Unplugged



Manager
Joined: 02 Aug 2007
Posts: 222
Schools: Life

Re: When integer p is divided by 7 [#permalink]
Show Tags
02 Feb 2009, 16:38
x2suresh wrote: xALIx 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
Joined: 15 Jan 2009
Posts: 46
Schools: Marshall '11

Re: When integer p is divided by 7 [#permalink]
Show Tags
04 Feb 2009, 14:47
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
Joined: 29 Aug 2005
Posts: 854

Re: When integer p is divided by 7 [#permalink]
Show Tags
12 Feb 2009, 13:24
x2suresh wrote: xALIx 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
Joined: 23 Jan 2013
Posts: 171
Concentration: Technology, Other
GMAT Date: 01142015
WE: Information Technology (Computer Software)

Re: When integer p is divided by 7 [#permalink]
Show Tags
04 Jun 2014, 19:20
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 !!!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7955
Location: Pune, India

Re: When integer p is divided by 7 [#permalink]
Show Tags
04 Jun 2014, 19:55
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
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 ... spartii/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



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: When positive integer p is divided by 7 the remainder is 2. [#permalink]
Show Tags
05 Jun 2014, 00:18
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? Extrahard Quant Tests with Brilliant Analytics



NonHuman User
Joined: 09 Sep 2013
Posts: 13777

Re: When positive integer p is divided by 7 the remainder is 2. [#permalink]
Show Tags
16 Feb 2016, 14:10
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



Intern
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
24 Feb 2016, 15:25
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



Retired Moderator
Joined: 12 Aug 2015
Posts: 2428
GRE 1: 323 Q169 V154

Re: When positive integer p is divided by 7 the remainder is 2. [#permalink]
Show Tags
22 Mar 2016, 02:43
Choose 72 and 30 as the two numbers and we can discard both the statements Hence E
_________________
Getting into HOLLYWOOD with an MBA Stone Cold's Mock Tests for GMATQuant(700+)



NonHuman User
Joined: 09 Sep 2013
Posts: 13777

Re: When positive integer p is divided by 7 the remainder is 2. [#permalink]
Show Tags
22 Apr 2017, 05:58
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, 05:58






