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

It is currently 30 Aug 2014, 08:40

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 (243)^x(463)^y = n, where x and y are positive integers,

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 07 Nov 2009
Posts: 313
Followers: 4

Kudos [?]: 70 [0], given: 20

If (243)^x(463)^y = n, where x and y are positive integers, [#permalink] New post 07 Apr 2010, 22:37
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

33% (00:00) correct 67% (00:58) wrong based on 5 sessions
If (243)^x(463)^y = n, where x and y are positive integers, what is the units digit of n?

(1) x + y = 7
(2) x = 4

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-243-x-463-y-n-where-x-and-y-are-positive-integers-102054.html
[Reveal] Spoiler: OA
Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Manager
Manager
avatar
Joined: 10 Aug 2009
Posts: 123
Followers: 3

Kudos [?]: 13 [0], given: 13

Re: Units digit [#permalink] New post 07 Apr 2010, 22:43
I'd go with A

The units digit of 3^n follows the following patterns: 3,9,7,1,3,9,7,1,.....

Thus if we know what both x and y are, we can solve it (statement 1).
Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1318
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 56

Kudos [?]: 477 [0], given: 157

GMAT ToolKit User GMAT Tests User
Re: Units digit [#permalink] New post 07 Apr 2010, 23:23
nickk wrote:
I'd go with A

The units digit of 3^n follows the following patterns: 3,9,7,1,3,9,7,1,.....

Thus if we know what both x and y are, we can solve it (statement 1).


So how did you find the values of x & y from Stmt 1??
_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 10 Aug 2009
Posts: 123
Followers: 3

Kudos [?]: 13 [0], given: 13

Re: Units digit [#permalink] New post 07 Apr 2010, 23:59
Hussain15 wrote:
nickk wrote:
I'd go with A

The units digit of 3^n follows the following patterns: 3,9,7,1,3,9,7,1,.....

Thus if we know what both x and y are, we can solve it (statement 1).


So how did you find the values of x & y from Stmt 1??



Well we don't know the values of X and Y individually, but all we need to know is how many times a number with 3 in the units digit is multiplied by itself. Since X and Y are both exponents of such numbers, knowing x+y is sufficient.

Of course I might be wrong so the OA would be appreciated.
1 KUDOS received
Intern
Intern
avatar
Joined: 04 Apr 2010
Posts: 9
Followers: 0

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

Re: Units digit [#permalink] New post 08 Apr 2010, 01:02
1
This post received
KUDOS
In this case, since the base number is different i.e 243 & 463, it makes sense to use the various combinations of x & y:
1. 1&6 or 6&1
2. 2&5 or 5&2
3. 3&4 or 4&3

The units digit of 3^n follows the following patterns: 3,9,7,1,3,9,7,1,.....

Substituting n in the above combinations and multiplying the ending unit digits of each of these numbers, we get the same unit digit i.e., 7.

Choice (B), keeps the n open for y, so the unit digit of the resultant number may vary.

Hence correct answer is (A).
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25207
Followers: 3419

Kudos [?]: 25083 [3] , given: 2702

Re: Units digit [#permalink] New post 08 Apr 2010, 01:52
3
This post received
KUDOS
Expert's post
rohitgoel15 wrote:
If (243)^x(463)^y = n, where x and y are positive integers, what is the units digit of n?

(1) x + y = 7
(2) x = 4


Units digit of 243^x equals to units digit of 3^x and units digit of 463^y equals to units digit of 3^y (general rule). Hence units digit of 243^x*463^y equals to units digit of 3^x*3^y=3^{x+y}. So knowing the value of x+y is sufficient to determine units digit of n.

(1) x+y=7. Sufficient. (As cyclicity of 3 is 4, units digit of 3^7 would be the same as of units digit of 3^3 which is 7)

(2) x=4. No info about y. Not sufficient.

Answer: A.
_________________

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: 10 Aug 2009
Posts: 123
Followers: 3

Kudos [?]: 13 [0], given: 13

Re: Units digit [#permalink] New post 08 Apr 2010, 01:54
Bunuel can you please take a look at probability-question-84062.html
Intern
Intern
avatar
Joined: 04 Apr 2010
Posts: 9
Followers: 0

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

Re: Units digit [#permalink] New post 08 Apr 2010, 02:57
Thanks Bunuel for providing more info on this one.
Kudos
Senior Manager
Senior Manager
avatar
Joined: 07 Jan 2010
Posts: 250
Followers: 1

Kudos [?]: 6 [0], given: 16

GMAT Tests User
Re: Units digit [#permalink] New post 09 Apr 2010, 22:22
great question ....
I made the mistake of choosing C.
Re: Units digit   [#permalink] 09 Apr 2010, 22:22
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If 243^x*463^y = n, where x and y are positive integers, wha mattapraveen 4 05 Nov 2010, 03:05
6 Experts publish their posts in the topic If 243^x*463^y = n, where x and y are positive integers anilnandyala 8 02 Oct 2010, 03:44
If (243)x(463)y = n, where x and y are positive integers, ldpedroso 11 27 May 2008, 18:45
If 243^x*463^y = n, where x and y are positive integers, wha suntaurian 8 29 Mar 2008, 20:11
If (243)^x * (463)^y = n, where x and y are positive jimjohn 5 30 Oct 2007, 10:54
Display posts from previous: Sort by

If (243)^x(463)^y = n, where x and y are positive integers,

  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®.