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

It is currently 03 May 2016, 11:33
GMAT Club Tests

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 M and N are integers, is ((10^M)) + N)/3 an integer?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 17 Jul 2009
Posts: 299
Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
Followers: 1

Kudos [?]: 41 [1] , given: 9

If M and N are integers, is (10^M + N)/3 an integer? [#permalink]

Show Tags

New post 06 Aug 2009, 20:56
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

43% (01:59) correct 57% (00:47) wrong based on 109 sessions

HideShow timer Statictics

If M and N are integers, is (10^M + N)/3 an integer?

(1) N = 5
(2) MN is even
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jul 2015, 14:45, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
1 KUDOS received
Manager
Manager
User avatar
Joined: 18 Jul 2009
Posts: 169
Location: India
Schools: South Asian B-schools
Followers: 2

Kudos [?]: 82 [1] , given: 37

Re: If M and N are integers, is (10^M + N)/3 an integer? [#permalink]

Show Tags

New post 06 Aug 2009, 22:59
1
This post received
KUDOS
A

Statement 1: if u take N=5 and any value for M it will always hold true that is (10^M + N)/3 an integer; becoz 10^M ( let M = any value) will always leave a reminder of 1....and 1+5 = 6 which is divisable by 3 ....sufficient

Statement 2 : if MN is even ...this means (M,N) can be both even or odd (except both being odd at a time)....if taken an example....

(M,N) => (1,2) => 10+2 =12/3 => integer
(M,N) => (1,4) => 10+4 =14/3 => non-integer

hence insufficient

if u like my post....consider it for Kudos :wink:
_________________

Bhushan S.
If you like my post....Consider it for Kudos :-D

Expert Post
1 KUDOS received
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3580
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 474

Kudos [?]: 2708 [1] , given: 359

GMAT ToolKit User Premium Member
Re: If M and N are integers, is (10^M + N)/3 an integer? [#permalink]

Show Tags

New post 06 Aug 2009, 23:13
1
This post received
KUDOS
Expert's post
Let's consider \(10^M\)

at M>=0: \(10^M = {1, 10, 100, 1000....}\) or \(3k+1\)
at M<0: 10^M is a fraction and our expression is not an integer.

Now, let's see our statements:

1) N=5
at M>=0: (3k+1 + 5) /3 = k+2 - an integer
at M<0: a fraction.
insufficient

2) MN is even
a) at M=2, N=5 our expression is an integer
b) at M=-2, N=-5 our expression in a fraction
insufficient

1)&2) N=5 & MN is even --> N=5, M is even
For all even M>=0 we will get an integer.
Now we have interesting question: Could negative numbers be even or odd?
if yes, we can choose M=-2, N=5 and get a fraction.
if no, M cannot be negative and two statements are sufficient.

Judging by http://en.wikipedia.org/wiki/Even_and_odd_numbers negative integers can be classified as odd/even. So, our answer is insufficient.

E
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Intern
Intern
avatar
Joined: 07 Dec 2009
Posts: 14
Followers: 0

Kudos [?]: 17 [0], given: 4

Re: If M and N are integers, is (10^M + N)/3 an integer? [#permalink]

Show Tags

New post 17 Dec 2009, 20:25
how did you get 3k + 1? can someone please explain? thanks.
Manager
Manager
avatar
Joined: 12 Oct 2008
Posts: 58
Followers: 1

Kudos [?]: 2 [0], given: 3

Re: If M and N are integers, is (10^M + N)/3 an integer? [#permalink]

Show Tags

New post 18 Dec 2009, 21:18
10^K = 3k+1: for any K>=0
It means any number which is 10^K i.e. 1,10,100,1000 ..., when divide by 3, gives remainder 1.
Manager
Manager
avatar
Joined: 26 Nov 2009
Posts: 176
Followers: 3

Kudos [?]: 55 [0], given: 5

GMAT ToolKit User
Re: If M and N are integers, is (10^M + N)/3 an integer? [#permalink]

Show Tags

New post 23 Jan 2010, 10:56
Thanks I committed 2 careless mistakes

Initially I chose A ignoring the fact M and are just integers not positive integers

and then I chose C since MN is even I just assumed it is positive.

but the correct ans is E since both statements would be insufficient to ans the question
Intern
Intern
avatar
Joined: 12 Aug 2010
Posts: 14
Followers: 0

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

If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 24 Nov 2010, 01:44
1
This post was
BOOKMARKED
If M and N are integers, is ((10^M)) + N)/3 an integer?

(1) N = 5
(2) MN is even

Answer to question is
[Reveal] Spoiler:
E
.

From statement 1 and 2, M has to be Even Positive as N = 5 and MN is even.

Now when 5 is added to 10^M where M is even positive and then divided by 3 it always results into an integer.

M25-07
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32599
Followers: 5646

Kudos [?]: 68538 [2] , given: 9814

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 24 Nov 2010, 02:44
2
This post received
KUDOS
Expert's post
chiragatara wrote:
If M and N are integers, is ((10^M)) + N) / 3 an integer?

1. N = 5
2. MN is even

Answer to question is E.

From statement 1 and 2, M has to be Even Positive as N = 5 and MN is even.

Now when 5 is added to 10^M where M is even positive and then divided by 3 it always results into an integer.


Basically the the question ask whether \(10^m+n\) is divisible by 3. Now, in order \(10^m+n\) to be divisible by 3:
A. It must be an integer, and B. the sum of its digits must be multiple of 3.

(1) N = 5 --> if \(m<0\) (-1, -2, ...) then \(10^m+n\) won't be an integer at all (for example if \(m=-1\) --> \(10^m+n=\frac{1}{10}+5=\frac{51}{10}\neq{integer}\)), thus won't be divisible by 3, but if \(m\geq{0}\) (0, 1, 2, ...) then \(10^m+n\) will be an integer and also the sum of its digits will be divisible by 3 (for example for \(m=1\) --> \(10^m+n=10+5=15\) --> 15 is divisible by 3). Not sufficient.

(2) MN is even --> clearly insufficient, as again \(m\) can be -2 and \(n\) any integer and the answer to the question will be NO or \(m\) can be 0 and \(n\) can be 2 and the answer to the question will be YES. Not sufficient.

(1)+(2) From \(mn=even\) and \(n=5\) it's still possible for \(m\) to be negative even integer (-2, -4, ...), so \(10^m+n\) may or may not be divisible by 3. Not sufficient.

Answer: E.
_________________

New to the Math Forum?
Please read this: 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

Manager
Manager
User avatar
Joined: 26 Apr 2010
Posts: 121
Concentration: Strategy, Entrepreneurship
Schools: Fuqua '14 (M)
Followers: 2

Kudos [?]: 78 [0], given: 54

GMAT ToolKit User
Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 24 Nov 2010, 08:53
Thanks for the question...I missed the negative case in this question as well.

Bunuel, thanks for solving.
_________________

I appreciate the kudos if you find this post helpful! +1

Intern
Intern
avatar
Joined: 28 Jun 2013
Posts: 3
Followers: 0

Kudos [?]: 1 [0], given: 14

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 19 Sep 2013, 22:22
Hi,

"I read in a forum that negative numbers cannot be tagged as odd or even. So, if I get a DS question stating that X is a even integer, then it also implies that X>=0."

However, in the question given below, the logic is not holding true. I was considering the right answer to be C), because if MN = even and N =5 , then it implies that M must be odd integer (and hence M is > 0). Can you clarify if the argument above is false?

If M and N are integers, is 10M+N3 an integer?
(1) N=5

(2) MN is even

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.Mark as a guessHide Answer
The question does not mention whether M and N are positive. Hence, the statements taken together are not sufficient because the answer is YES if M=2, N=5 and NO if M=−2; N=5.


The correct answer is E
Director
Director
avatar
Joined: 24 Aug 2009
Posts: 505
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 12

Kudos [?]: 579 [0], given: 241

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 19 Sep 2013, 23:44
SurabhiStar wrote:
Hi,

"I read in a forum that negative numbers cannot be tagged as odd or even. So, if I get a DS question stating that X is a even integer, then it also implies that X>=0."

However, in the question given below, the logic is not holding true. I was considering the right answer to be C), because if MN = even and N =5 , then it implies that M must be odd integer (and hence M is > 0). Can you clarify if the argument above is false?

If M and N are integers, is 10M+N3 an integer?
(1) N=5
(2) MN is even



First, every number except zero "0" can be categorized either Even or odd.
Secondly, "X is a even integer" does not necessarily mean X>=0. X can be smaller than 0 as well.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32599
Followers: 5646

Kudos [?]: 68538 [0], given: 9814

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 20 Sep 2013, 00:57
Expert's post
fameatop wrote:
SurabhiStar wrote:
Hi,

"I read in a forum that negative numbers cannot be tagged as odd or even. So, if I get a DS question stating that X is a even integer, then it also implies that X>=0."

However, in the question given below, the logic is not holding true. I was considering the right answer to be C), because if MN = even and N =5 , then it implies that M must be odd integer (and hence M is > 0). Can you clarify if the argument above is false?

If M and N are integers, is 10M+N3 an integer?
(1) N=5
(2) MN is even



First, every number except zero "0" can be categorized either Even or odd.
Secondly, "X is a even integer" does not necessarily mean X>=0. X can be smaller than 0 as well.


1. EVEN/ODD

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

An odd number is an integer that is not evenly divisible by 2.

According to the above both negative and positive integers can be even or odd.

2. ZERO

Zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Hope it helps.
_________________

New to the Math Forum?
Please read this: 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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9270
Followers: 455

Kudos [?]: 115 [0], given: 0

Premium Member
Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 18 Jan 2015, 11:26
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

Expert Post
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 6234
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 262

Kudos [?]: 1841 [0], given: 160

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 18 Jan 2015, 13:06
Expert's post
Hi All,

This DS question can be solved by TESTing VALUES, but you have to thorough with your TESTs and thinking.

We're told that M and N are INTEGERS. We're asked if (10^M + N)/3 is an integer. This is a YES/NO question.

Fact 1: N = 5

IF....
M = 0
N = 5
6/3 IS an integer and the answer to the question is YES.

IF...
M = 1
N = 5
15/3 IS an integer and the answer to the question is YES.

At this point, it might be tempting to say that Fact 1 is sufficient, but we have NOT yet considered ALL TYPES of integers....

IF...
M = -1
N = 5
5.1/3 is NOT an integer and the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: MN is EVEN

IF...
M = 0
N = 5
6/3 is an integer and the answer to the question is YES.

IF....
M = 0
N = 1
2/3 is NOT an integer and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know....
N = 5,
MN is EVEN

IF....
M = 0
N = 5
6/3 is an integer and the answer to the question is YES.

IF....
M = -2
N = 5
5.01/3 is NOT an integer and the answer to the question is NO.
Combined, INSUFFICIENT

Final Answer:
[Reveal] Spoiler:
E


GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Intern
avatar
Joined: 26 Mar 2013
Posts: 23
Location: India
Concentration: Finance, Strategy
Schools: Booth PT '18 (S)
Followers: 0

Kudos [?]: 8 [0], given: 2

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 19 Jan 2015, 00:42
Nice question....

Initially didnt observe that M can be negative....then it looked too easy....well had it come in the early part of real test....i wud have thought im still in easy qtns zone....and put it as A

Thanks for posting the question
Intern
Intern
avatar
Joined: 26 Mar 2013
Posts: 23
Location: India
Concentration: Finance, Strategy
Schools: Booth PT '18 (S)
Followers: 0

Kudos [?]: 8 [0], given: 2

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 19 Jan 2015, 00:44
Ans is E here....good to see variations in such problems....(say adding an inequality/..)
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6480
Location: Pune, India
Followers: 1760

Kudos [?]: 10496 [0], given: 206

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

New post 19 Jan 2015, 01:03
Expert's post
chiragatara wrote:
If M and N are integers, is ((10^M)) + N)/3 an integer?

(1) N = 5
(2) MN is even

Answer to question is
[Reveal] Spoiler:
E
.

From statement 1 and 2, M has to be Even Positive as N = 5 and MN is even.

Now when 5 is added to 10^M where M is even positive and then divided by 3 it always results into an integer.

M25-07


Question: Is ((10^M)) + N)/3 an integer?
Re-worded: Is (10^M + N) a multiple of 3?

Note that 10^M will be something like 1000... if M is non-negative. Then, 10^M will be of the form (3a+1) because it will leave remainder 1 when divided by 3. If M is negative, 10^M will not be an integer.

Assuming M is non-negative, for 10^M + N to be a multiple of 3, N should be of them form 3n+2.

(1) N = 5
We don't know whether M is non-negative. Not sufficient.

(2) MN is even
again, we don't know whether M is non-negative. Not sufficient.

Using both, we know that M is even since N = 5 (odd) but we don't know whether it is non-negative.

Answer (E)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9270
Followers: 455

Kudos [?]: 115 [0], given: 0

Premium Member
Re: If M and N are integers, is (10^M + N)/3 an integer? [#permalink]

Show Tags

New post 05 Nov 2015, 04:44
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 M and N are integers, is (10^M + N)/3 an integer?   [#permalink] 05 Nov 2015, 04:44
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If n and m are integers, is n/3 an integer? Bunuel 3 25 Apr 2016, 03:55
Experts publish their posts in the topic If n is an integer, is n^3 divisible by 54? Bunuel 4 09 Mar 2016, 12:48
2 Experts publish their posts in the topic If n = 3k, is k an integer? Bunuel 3 28 Jul 2015, 00:44
If M and N are integers, is (10^M + N)/3 an integer? sprtng 0 05 Nov 2015, 04:44
3 Experts publish their posts in the topic If n is a positive integer, is n3 n divisible by 4? 1. n = sondenso 6 24 Feb 2008, 18:59
Display posts from previous: Sort by

If M and N are integers, is ((10^M)) + N)/3 an integer?

  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 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®.