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

It is currently 24 Oct 2014, 16:40

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 positive integers, is the remainder of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Manager
Manager
avatar
Joined: 16 Feb 2010
Posts: 225
Followers: 2

Kudos [?]: 77 [3] , given: 16

If m and n are positive integers, is the remainder of [#permalink] New post 24 Sep 2010, 14:11
3
This post received
KUDOS
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

38% (02:12) correct 62% (01:32) wrong based on 301 sessions
If m and n are positive integers, is the remainder of \frac{10^m + n}{3} larger than the remainder of \frac{10^n + m}{3} ?

(1) m \gt n
(2) The remainder of \frac{n}{3} is 2

[Reveal] Spoiler:
i disagree with the OA answer: -

"Statement (2) by itself is sufficient. If the remainder of \frac{n}{3} is 2, as S2 states, then n is 2, 5, or 8 and the sum of the digits of \frac{10^m + n}{3} is divisible by 3. Therefore, the remainder of \frac{10^m + n}{3} is 0, which cannot be larger that the remainder of \frac{10^n + m}{3} no matter what m is."but if m=n, then the remainder of both expresions will be 0!
even more weird is if m=2, n=5, therefore remainder 0 for both....


please advice
[Reveal] Spoiler: OA
Manager
Manager
avatar
Joined: 04 Aug 2010
Posts: 158
Followers: 2

Kudos [?]: 24 [0], given: 15

Re: GMAT Club > Tests > Number Properties - I Question 8 [#permalink] New post 24 Sep 2010, 14:42
The question asks if the reminder can be larger though. So even if the m = n and the reminders of both terms are 0, it's still not larger.

I agree with answer B.
5 KUDOS received
Manager
Manager
avatar
Joined: 30 May 2010
Posts: 191
Followers: 3

Kudos [?]: 47 [5] , given: 32

Re: GMAT Club > Tests > Number Properties - I Question 8 [#permalink] New post 24 Sep 2010, 14:52
5
This post received
KUDOS
To determine if a number is divisible by 3, add the digits and if they are divisible by 3, then the entire number is also.

We are given m and n are positive integers. The sum of the digits of 10 to any positive power will always be 1.

From statement 2, we are told the remainder of n/3 will be 2.

For (10^m + n)/3, the 10^m part will always give you 1 in the sum of the digits, and the n part will always give you 2 in the digits of the numerator. Therefore, this will always be divisible by 3 (have a remainder of 0).

The question asked if (10^m + n)/3 will ever have a larger remainder than (10^n + m)/3. Remainders can't be negative, therefore we know it will never be larger. There is no need to evaluate possible remainders of (10^n + m)/3.
Manager
Manager
avatar
Joined: 30 May 2008
Posts: 76
Followers: 0

Kudos [?]: 14 [0], given: 26

Re: If m and n are positive integers, is the remainder of [#permalink] New post 10 Apr 2012, 07:02
For (10^m + n) /3, the 10^m part will always give you 1 in the sum of the digits, and the n part will always give you 2 in the digits of the numerator. Therefore, this will always be divisible by 3 (have a remainder of 0).

I'm not sure i understand the bold face part, why will it give you 2? how did you come to this conclusion?
Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28920 [4] , given: 2871

Re: If m and n are positive integers, is the remainder of [#permalink] New post 10 Apr 2012, 07:08
4
This post received
KUDOS
Expert's post
catty2004 wrote:
For (10^m + n) /3, the 10^m part will always give you 1 in the sum of the digits, and the n part will always give you 2 in the digits of the numerator. Therefore, this will always be divisible by 3 (have a remainder of 0).

I'm not sure i understand the bold face part, why will it give you 2? how did you come to this conclusion?


m and n are positive integers. Is the remainder of \frac{10^m + n}{3} bigger than the remainder of \frac{10^n + m}{3} ?

First of all any positive integer can yield only three remainders upon division by 3: 0, 1, or 2.

Since, the sum of the digits of 10^m and 10^n is always 1 then the remainders of \frac{10^m + n}{3} and \frac{10^n + m}{3} are only dependant on the value of the number added to 10^m and 10^n. There are 3 cases:
If the number added to them is: 0, 3, 6, 9, ... then the remainder will be 1 (as the sum of the digits of 10^m and 10^n will be 1 more than a multiple of 3);
If the number added to them is: 1, 4, 7, 10, ... then the remainder will be 2 (as the sum of the digits of 10^m and 10^n will be 2 more than a multiple of 3);
If the number added to them is: 2, 5, 8, 11, ... then the remainder will be 0 (as the sum of the digits of 10^m and 10^n will be a multiple of 3).

(1) m \gt n. Not sufficient.

(2) The remainder of \frac{n}{3} is 2 --> n is: 2, 5, 8, 11, ... so we have the third case. Which means that the remainder of \frac{10^m + n}{3} is 0. Now, the question asks whether the remainder of \frac{10^m + n}{3}, which is 0, greater than the reminder of \frac{10^n + m}{3}, which is 0, 1, or 2. Obviously it cannot be greater, it can be less than or equal to. So, the answer to the question is NO. Sufficient.

Answer: B.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 30 May 2008
Posts: 76
Followers: 0

Kudos [?]: 14 [0], given: 26

Re: If m and n are positive integers, is the remainder of [#permalink] New post 10 Apr 2012, 07:28
crystal clear! Just hope that my brain will remember this on the test day!
Expert Post
4 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4877
Location: Pune, India
Followers: 1157

Kudos [?]: 5379 [4] , given: 165

Re: If m and n are positive integers, is the remainder of [#permalink] New post 12 Apr 2012, 10:28
4
This post received
KUDOS
Expert's post
zisis wrote:
If m and n are positive integers, is the remainder of \frac{10^m + n}{3} larger than the remainder of \frac{10^n + m}{3} ?

1. m \gt n
2. The remainder of \frac{n}{3} is 2



You can also use binomial theorem here. Again, let me reiterate that there are many concepts which are not essential for GMAT but knowing them helps you get to the answer quickly.

The moment I see \frac{10^m + n}{3} here, my mind sees \frac{(9+1)^m + n}{3}
So I say that \frac{10^m}{3} and \frac{10^n}{3} give remainder 1 in any case (m and n are positive integers). I just need to worry about n/3 and m/3.

1. m \gt n
Doesn't tell me about the remainder when m and n are divided by 3.

2. The remainder of \frac{n}{3} is 2
If n/2 gives a remainder of 2, total remainder of \frac{10^m + n}{3} is 1+2 = 3 which is equal to 0. So no matter what the remainder of \frac{m}{3}, the remainder of \frac{10^n + m}{3} will never be less than 0. Hence sufficient.

Answer B
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 22 Jan 2012
Posts: 35
Followers: 0

Kudos [?]: 12 [0], given: 0

Re: If m and n are positive integers, is the remainder of [#permalink] New post 29 Apr 2012, 09:32
I have a doubt why B is sufficient to answer the question.
I understood the solution but if we take only the statement B then there is nothing to prove that m is not equal to n.
As in the given statement m and n are positive integers but what is the relation between them is not provided whether m >n , m<n or m=n .

Also ,by B we are only able to prove that remainder will not be lesser but what if equal or greater.
Current Student
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 13

Kudos [?]: 146 [0], given: 73

GMAT ToolKit User
Re: remainder [#permalink] New post 29 Apr 2012, 10:26
m17-73674.html
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4877
Location: Pune, India
Followers: 1157

Kudos [?]: 5379 [0], given: 165

Re: If m and n are positive integers, is the remainder of [#permalink] New post 30 Apr 2012, 05:04
Expert's post
raingary wrote:
I have a doubt why B is sufficient to answer the question.
I understood the solution but if we take only the statement B then there is nothing to prove that m is not equal to n.
As in the given statement m and n are positive integers but what is the relation between them is not provided whether m >n , m<n or m=n .

Also ,by B we are only able to prove that remainder will not be lesser but what if equal or greater.


The question is:
is the remainder of 'a' larger than the remainder of 'b'?

We found that the remainder of 'a' is 0 which is the smallest possible remainder. No matter what the remainder of 'b' is, it will never be less than 0. So remainder of 'a' can never be larger than the remainder of 'b'. We can answer the question with 'No'. Therefore, statement 2 is sufficient.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 11 May 2011
Posts: 1
Concentration: Finance, Entrepreneurship
Schools: CBS '17 (S)
GMAT Date: 01-02-2014
GPA: 3.97
WE: Sales (Real Estate)
Followers: 0

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

CAT Tests
Re: If m and n are positive integers, is the remainder of [#permalink] New post 23 Jul 2012, 20:18
to rephrase the question is x greater than y ( here x and y are the remainders).
If x is greater than y, answer is yes but if x is not greater than y the answer is no.

If x is 0 and y is 0 ----No
If x is 1 or 2 and y is 0 , the Yes

Why is the answer not E?

If the question is reversed -- is the remainder of 10^n +m/3 larger than the remainder of 10^m+n/3 ? then the answer would be B as
0 can never be greater than 0, 1 or 2.
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4877
Location: Pune, India
Followers: 1157

Kudos [?]: 5379 [0], given: 165

Re: If m and n are positive integers, is the remainder of [#permalink] New post 24 Jul 2012, 04:17
Expert's post
nomis wrote:
to rephrase the question is x greater than y ( here x and y are the remainders).
If x is greater than y, answer is yes but if x is not greater than y the answer is no.

If x is 0 and y is 0 ----No
If x is 1 or 2 and y is 0 , the Yes

Why is the answer not E?

If the question is reversed -- is the remainder of 10^n +m/3 larger than the remainder of 10^m+n/3 ? then the answer would be B as
0 can never be greater than 0, 1 or 2.


Because you find that a = 0 (the remainder of the first expression is 0). Hence under no condition can 'a' be greater than 'b'. Hence, it is sufficient to answer with an emphatic 'No'.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28920 [0], given: 2871

Re: If m and n are positive integers, is the remainder of [#permalink] New post 22 Jul 2013, 23:07
Expert's post
Senior Manager
Senior Manager
User avatar
Joined: 03 Dec 2012
Posts: 367
Followers: 0

Kudos [?]: 41 [0], given: 291

Re: If m and n are positive integers, is the remainder of [#permalink] New post 20 Oct 2013, 23:42
karishma I did not understand this statement the total remainder 1+2=3 which is equal to zero
Intern
Intern
avatar
Joined: 05 Oct 2013
Posts: 15
Followers: 0

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

Re: If m and n are positive integers, is the remainder of [#permalink] New post 21 Oct 2013, 09:19
The remainder of 10/3 is 1. So 1^n =1 = 1^m is the remainder of 10^n / 3 as well as 10^m/3. Therefore, the remainder of (10^n + m)/3 is the remainder of (1+m)/3 and the remainder of (10^m +n)/3 is equal to the remainder of (1 +n)/3.
(1) m >n which does not give us any extra information about the remainder of m,n/3.
(2) 2 is the remainder of n/3, so 0 is the remainder of (1+n)/3. That means the remainder of \frac{10^m + n}{3} is not larger than the remainder of \frac{10^n + m}{3}
The answer is B
Re: If m and n are positive integers, is the remainder of   [#permalink] 21 Oct 2013, 09:19
    Similar topics Author Replies Last post
Similar
Topics:
If n and m are positive integers, what is the remainder when tl372 6 26 May 2006, 09:25
If n and m are positive integers, what is the remainder when ffgmat 4 30 Jan 2006, 22:39
If n and m are positive integers, what is the remainder when eskay05 6 10 Jan 2006, 13:13
If M and N are positive integers that have remainders of 1 shahnandan 3 24 Nov 2005, 07:34
If n and m are positive integers, what is the remainder when themagiccarpet 8 16 Nov 2005, 01:52
Display posts from previous: Sort by

If m and n are positive integers, is the remainder of

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.