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

It is currently 24 Jul 2016, 18:23
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 a and b are positive integers, what is the remainder when

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

Hide Tags

1 KUDOS received
Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 538
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 67

Kudos [?]: 2370 [1] , given: 217

If a and b are positive integers, what is the remainder when [#permalink]

Show Tags

New post 26 Feb 2012, 16:30
1
This post received
KUDOS
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (01:00) correct 32% (01:05) wrong based on 407 sessions

HideShow timer Statistics

If a and b are positive integers, what is the remainder when \(4^{2a+1+b}\) is divided by 10?

(1) a = 1
(2) b = 2

[Reveal] Spoiler:
Ok - this is how I am trying to solve this.

Statement 1

a = 1. Does not tell anything about b --therefore is insufficient on its own to answer the question.

Statement 2

b = 2

2a + 1 + b becomes

2a (even) + 1 (odd) + b (even) = ODD. So the exponent to 4 is ODD. So I understand that if we put 3, 5 etc I get the remainder 4, but why can't I put exponent as 1 as 1 is ODD too. Can you please help?
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

5 KUDOS received
Manager
Manager
avatar
Joined: 15 Dec 2011
Posts: 185
Schools: LBS '14 (A)
GMAT 1: 730 Q50 V39
GMAT 2: Q V
GPA: 3.9
Followers: 1

Kudos [?]: 42 [5] , given: 13

Re: Remainder when divided by 10 [#permalink]

Show Tags

New post 26 Feb 2012, 16:39
5
This post received
KUDOS
1
This post was
BOOKMARKED
powers of 4 go like this:

The unit place is:
1 = 4
2 = 6
3 = 4
4 = 6

So all even exponents have 6 in unit place, and all off exponents have 4 in unit place. To solve the problem we need to find whether the 2a + 1 + b is even or odd

As a is +ve integer, 2a is always even. 2a + 1 will be odd. Now to determine whether (2a + 1 + b) is even or odd, we need to know only b.

Therefore, the answer is B
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34029
Followers: 6081

Kudos [?]: 76347 [3] , given: 9973

Re: Remainder when divided by 10 [#permalink]

Show Tags

New post 26 Feb 2012, 16:58
3
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
If a and b are positive integers, what is the remainder when \(4^{2a+1+b}\) is divided by 10?

This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

Back to the question: 4 in positive integer power can have only 2 last digits: 4, when the power is odd or 6 when the power is even. Hence, to get the remainder of 4^x/10 we should know whether the power is odd or even: if it's odd the remainder will be 4 and if it's even the remainder will be 6.

(1) a = 1 --> \(4^{2a+1+b}=4^{3+b}\) depending on b the power can be even or odd. Not sufficient.

(2) b = 2 --> \(4^{2a+1+b}=4^{2a+3}=4^{even+odd}=4^{odd}\) --> the remainder upon division of \(4^{odd}\) by 10 is 4. Sufficient.

Answer: B.


enigma123 wrote:
2a (even) + 1 (odd) + b (even) = ODD. So the exponent to 4 is ODD. So I understand that if we put 3, 5 etc I get the remainder 4, but why can't I put exponent as 1 as 1 is ODD too. Can you please help?


The power of 4 is \(2a+3\) and since \(a\) is a positive integer then the lowest value of \(2a+3\) is 5, for \(a=1\). Next, even if the power were 1 then 4^1=4 and the remainder upon division of 4 by 10 would still be 4.

Hope it's clear.
_________________

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

Current Student
avatar
Joined: 03 Aug 2012
Posts: 915
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 20

Kudos [?]: 572 [0], given: 322

Premium Member
Re: If a and b are positive integers, what is the remainder when [#permalink]

Show Tags

New post 11 Aug 2013, 09:20
REM(4^(2a+1+b))/10

Means we have to find last digit of the expression.So rephrasing the question

What is the last digit of 4^(2a+1+b)

(1).
a=1

Break the expression as 4^2a * 4^1 * 4^b.

b is unknown hence INSUFFICIENT

(2).

b=2

4^2a * 4^1 * 4^b.

If you can observe the expression 4^2a, you will see that this will always give last digit as '6' you can try out numbers if you want.

So knowing the expression and value of b last digit can be calculated and hence the remainder can also be calculated.

Hence (B) it is !!
_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10581
Followers: 495

Kudos [?]: 129 [0], given: 0

Premium Member
Re: If a and b are positive integers, what is the remainder when [#permalink]

Show Tags

New post 30 Aug 2014, 05:22
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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10581
Followers: 495

Kudos [?]: 129 [0], given: 0

Premium Member
Re: If a and b are positive integers, what is the remainder when [#permalink]

Show Tags

New post 02 Sep 2015, 10:11
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
Math Revolution GMAT Instructor
User avatar
Joined: 16 Aug 2015
Posts: 1541
GPA: 3.82
Followers: 103

Kudos [?]: 817 [0], given: 0

If a and b are positive integers, what is the remainder when [#permalink]

Show Tags

New post 03 Sep 2015, 04:48
Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.


If a and b are positive integers, what is the remainder when 4 2a+1+b is divided by 10?

(1) a = 1
(2) b = 2


Transforming the original condition and the question, 4^(2a+1+b)=(4^2a)(4^(1+b))=(16^a)(4^(1+b))=(.......6)(4^(1+b)), because the first digit is always 6 when it's multiplied by 6. Since b is all we need to know, the answer is B.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

If a and b are positive integers, what is the remainder when   [#permalink] 03 Sep 2015, 04:48
    Similar topics Author Replies Last post
Similar
Topics:
33 Experts publish their posts in the topic If a and b are positive integers, what is the remainder when kingflo 8 20 Jul 2013, 09:26
10 Experts publish their posts in the topic What is the remainder when the positive integer x is divided albany09 9 07 Oct 2008, 06:25
7 Experts publish their posts in the topic If x and y are positive integers, what is the remainder when xALIx 6 01 Jul 2008, 15:57
12 Experts publish their posts in the topic What is the remainder when the positive integer x is divided ricokevin 12 15 Apr 2007, 05:57
1 n is a positive integer. What is the remainder when n is andrehaui 7 09 Apr 2007, 11:59
Display posts from previous: Sort by

If a and b are positive integers, what is the remainder when

  new topic post reply 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®.