February 17, 2019 February 17, 2019 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. February 18, 2019 February 18, 2019 10:00 PM PST 11:00 PM PST We don’t care what your relationship status this year  we love you just the way you are. AND we want you to crush the GMAT!
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Sep 2014
Posts: 62

What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
08 Mar 2015, 03:59
Question Stats:
52% (02:35) correct 48% (02:27) wrong based on 162 sessions
HideShow timer Statistics
What is the remainder when the positive integer n is divided by 2? (1) When n is divided by 13, the remainder is 3 (2) n + 2 is a multiple of 7
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Press KUDOs if you find my explanation helpful




Math Expert
Joined: 02 Sep 2009
Posts: 52906

Re: What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
08 Mar 2015, 06:43
What is the remainder when the positive integer n is divided by 2?The remainder upon division n by 2 can be 0 (when n is even) or 1 (when n is odd). So, the question basically asks whether n is even or odd. (1) When n is divided by 13, the remainder is 3 > n = 13q + 3 > n can be: 3, 16, 29, 42, 55, 68, ... So, n can be even as well as odd. Not sufficient. (2) n + 2 is a multiple of 7 > n is 2 less than a multiple of 7, or, which is the same, n is 5 more than a multiple of 7 > n = 7p + 5: 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, ... So, n can be even as well as odd. Not sufficient. (1)+(2) From n = 13q + 3 and n = 7p + 5, we can get that n = 91k + 68 (check HERE to know to to derive general formula from these two), so n can be 68, 159, ... So, again, n can be even as well as odd. Not sufficient. Answer: E. Hope it's clear.
_________________
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




Manager
Joined: 10 Sep 2014
Posts: 62

Re: What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
09 Mar 2015, 13:05
Thanks Bunuel. Basically, i was confused about finding n = 91k + 68. Now, its clear.
_________________
Press KUDOs if you find my explanation helpful



Current Student
Joined: 25 Jul 2015
Posts: 110
Location: Thailand
Concentration: Entrepreneurship, Marketing
GMAT 1: 550 Q37 V28 GMAT 2: 660 Q47 V34 GMAT 3: 650 Q44 V35 GMAT 4: 680 Q49 V32 GMAT 5: 740 Q49 V42
GPA: 3.33

Re: What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
16 Nov 2016, 00:11
Could someone explain how n = 7p + 5 was derived?
_________________
My GMAT Journey From 550  740
My application debrief to Kellogg '19
My MBA Blog



Math Expert
Joined: 02 Sep 2009
Posts: 52906

Re: What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
16 Nov 2016, 00:41



Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 373

Re: What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
17 Nov 2016, 21:33
(1) n = 13q+3 (3,16,29,...)
if we try to divide each possible value of n by 2, we find R is not consistent (i.e. R = 1, R=0, R=1...)
NOT SUFFICIENT
(2) n+2 =7#
say n+2=7 > n=5 > 5/2 > R = 1 say n+2=14 > n=12 > 12/2 > R = 0
inconsistent remainders, thus NOT SUFFICIENT
(1) + (2) 13q+5=7#
13 is a prime number. There is no way we would be able to obtain 13 by subtracting 5 from a multiple of 7.
Thus, insufficient.
E



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827

Re: What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
29 Nov 2016, 15:45
TARGET730 wrote: What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 13, the remainder is 3 (2) n + 2 is a multiple of 7 We need to determine the remainder when the positive integer n is divided by 2. Keep in mind that when a positive integer is divided by 2, the remainder is either 0 (if the number is even) or 1 (if the number is odd). Statement One Alone:When n is divided by 13, the remainder is 3. There are many possible values for n. For example, n could be 16 or n could be 29. If n = 16, the remainder is 0 when n is divided by 2. However, if n = 29, the remainder is 1 when n is divided by 2. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D. Statement Two Alone:n + 2 is a multiple of 7. There are many possible values for n. For example, n could be 5 or n could be 12. If n = 5, the remainder is 1 when n is divided by 2. However, if n = 12, the remainder is 0 when n is divided by 2. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B. Statements One and Two Together:Even with the two statements, there are still many possible values for n. For example, n could be 68 or n could be 159. If n = 68, the remainder is 0 when n is divided by 2. However, if n = 159, the remainder is 1 when n is divided by 2. The two statements together are still not sufficient to answer the question. Answer: E
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 05 Dec 2016
Posts: 242
Concentration: Strategy, Finance

Re: What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
14 Feb 2017, 06:01
Bunuel wrote: What is the remainder when the positive integer n is divided by 2?The remainder upon division n by 2 can be 0 (when n is even) or 1 (when n is odd). So, the question basically asks whether n is even or odd. (1) When n is divided by 13, the remainder is 3 > n = 13q + 3 > n can be: 3, 16, 29, 42, 55, 68, ... So, n can be even as well as odd. Not sufficient. (2) n + 2 is a multiple of 7 > n is 2 less than a multiple of 7, or, which is the same, n is 5 more than a multiple of 7 > n = 7p + 5: 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, ... So, n can be even as well as odd. Not sufficient. (1)+(2) From n = 13q + 3 and n = 7p + 5, we can get that n = 91k + 68 (check HERE to know to to derive general formula from these two), so n can be 68, 159, ... So, again, n can be even as well as odd. Not sufficient. Answer: E. Hope it's clear. Hi Bunuel, Could you please advise if we can just add one equation to another? In that case we would have n=20k+1. By picking the numbers we see that it can either be even OR odd, so we get E as the answer. This approach is presented by MGM for tackling extra remainders problems. Thanks.



Math Expert
Joined: 02 Sep 2009
Posts: 52906

Re: What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
14 Feb 2017, 06:06
Alexey1989x wrote: Bunuel wrote: What is the remainder when the positive integer n is divided by 2?The remainder upon division n by 2 can be 0 (when n is even) or 1 (when n is odd). So, the question basically asks whether n is even or odd. (1) When n is divided by 13, the remainder is 3 > n = 13q + 3 > n can be: 3, 16, 29, 42, 55, 68, ... So, n can be even as well as odd. Not sufficient. (2) n + 2 is a multiple of 7 > n is 2 less than a multiple of 7, or, which is the same, n is 5 more than a multiple of 7 > n = 7p + 5: 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, ... So, n can be even as well as odd. Not sufficient. (1)+(2) From n = 13q + 3 and n = 7p + 5, we can get that n = 91k + 68 (check HERE to know to to derive general formula from these two), so n can be 68, 159, ... So, again, n can be even as well as odd. Not sufficient. Answer: E. Hope it's clear. Hi Bunuel, Could you please advise if we can just add one equation to another? In that case we would have n=20k+1. By picking the numbers we see that it can either be even OR odd, so we get E as the answer. This approach is presented by MGM for tackling extra remainders problems. Thanks. No, this would be incorrect. You cannot add n = 13 q + 3 and n = 7 p + 5 to get n = 20k + 1. Notice that the quotients there are different: q and p. The way you can get the general formula is given in the solution.
_________________
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



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827

Re: What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
15 Feb 2017, 15:19
TARGET730 wrote: What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 13, the remainder is 3 (2) n + 2 is a multiple of 7 We need to determine the remainder when n is divided by 2. Statement One Alone:When n is divided by 13, the remainder is 3. Statement one alone is not sufficient to answer the question. For example, when n = 3, the remainder when n is divided by 2 is 1. However, when n = 16, the remainder when n is divided by 2 is 0. Statement Two Alone:n + 2 is a multiple of 7. Statement two alone is not sufficient to answer the question. For instance, when n = 5, the remainder when n is divided by 2 is 1. However, when n = 12, the remainder when n is divided by 2 is 0. Statements One and Two Together:Let’s list out possible values of n from statement one: From statement one: n = 3, 16, 29, 42, 55, 68 We see that from the above list, 68 (since 68 + 2 = 70 is a multiple of 7) fulfills both statements one and two and provides a remainder of 0 when divided by 2. To determine the next value in the list, we can use the least common multiple of 13 and 7, which is 13 x 7 = 91. Thus, the next number that could be n is 68 + (7 x 13) = 159. Since 159 has a remainder of 1 when divided by 2, the two statements together are still not sufficient to answer the question. Answer: E
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 9838

Re: What is the remainder when the positive integer n is divided by 2?
[#permalink]
Show Tags
07 Feb 2019, 20:30
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: What is the remainder when the positive integer n is divided by 2?
[#permalink]
07 Feb 2019, 20:30






