It is currently 21 Nov 2018, 05:41
My 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.

13^x + 12^x = n, where x is a positive integer

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Senior Manager
Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 14

Kudos [?]: 49 [1] , given: 220

CAT Tests
13^x + 12^x = n, where x is a positive integer [#permalink] New post 24 Oct 2017, 01:22
1
This post received
KUDOS
00:00

Question Stats:

52% (01:14) correct 47% (01:12) wrong based on 21 sessions
\(13^x + 12^x = n\), where x is a positive integer

Quantity A
Quantity B
The number of distinct numbers that can be the units digit of n
4


A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given


Kudos for correct solution.
[Reveal] Spoiler: OA
Manager
Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 77 [0], given: 99

Re: 13^x + 12^x = n, where x is a positive integer [#permalink] New post 18 May 2018, 01:17
I think option A should be the answer since we raise 13 to different first few positive powers I got different units therefore same when we are adding 13^x +12^x then we are ought to get more than 4 types of unit digit.

Please clarify?
1 KUDOS received
Director
Director
User avatar
Joined: 07 Jan 2018
Posts: 540
Followers: 4

Kudos [?]: 467 [1] , given: 83

CAT Tests
Re: 13^x + 12^x = n, where x is a positive integer [#permalink] New post 18 May 2018, 03:25
1
This post received
KUDOS
No need to raise 13 and 12 to any digits. Since we are interested in finding the unit digits only we can work with 3 and 2.
We should also keep in mind that the unit digits of any number will reveal a pattern when raised to certain numbers.
For eg.

\(3^1 =3\)
\(3^2 = 9\)
\(3^3 = 27\)
\(3^4 = 81\)

\(3^5 = 243\)
\(3^6 = 729\)

You can notice that the units digit of \(3^5\) is same as \(3^1\) and units digit of \(3^2\) is same as \(3^6\)
Hence the units digits repeat in an interval of 4
Similar is the case for the powers of 2

\(2^1 =2\)
\(2^2 = 4\)
\(2^3 = 8\)
\(2^4 = 16\)
From here on the units digit of powers of 2 will repeat.

Now we just need to add the respective units digit of 2 and 3 for a given digit of power
For x = 1; 3+2 = 5
for x = 2; 9+4 = 13 or, 3
for x = 3; 7+8 = 15 or, 5
for x = 4; 1+6 = 7

since 5 is repeated we count it as 1.
Therefore there are in total 3 distinct unit digits
option B
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Intern
Intern
Joined: 15 May 2018
Posts: 39
Followers: 0

Kudos [?]: 5 [0], given: 1

Re: 13^x + 12^x = n, where x is a positive integer [#permalink] New post 22 May 2018, 05:19
IshanGre wrote:
I think option A should be the answer since we raise 13 to different first few positive powers I got different units therefore same when we are adding 13^x +12^x then we are ought to get more than 4 types of unit digit.

Please clarify?

Answer is B
Intern
Intern
Joined: 15 May 2018
Posts: 39
Followers: 0

Kudos [?]: 5 [0], given: 1

Re: 13^x + 12^x = n, where x is a positive integer [#permalink] New post 09 Jul 2018, 18:38
Bunuel wrote:
\(13^x + 12^x = n\), where x is a positive integer

Quantity A
Quantity B
The number of distinct numbers that can be the units digit of n
4


A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given


Kudos for correct solution.

My Answer is B
Intern
Intern
Joined: 15 May 2018
Posts: 39
Followers: 0

Kudos [?]: 5 [0], given: 1

Re: 13^x + 12^x = n, where x is a positive integer [#permalink] New post 09 Jul 2018, 18:39
Bunuel wrote:
\(13^x + 12^x = n\), where x is a positive integer

Quantity A
Quantity B
The number of distinct numbers that can be the units digit of n
4


A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given


Kudos for correct solution.

My Answer is B
Re: 13^x + 12^x = n, where x is a positive integer   [#permalink] 09 Jul 2018, 18:39
Display posts from previous: Sort by

13^x + 12^x = n, where x is a positive integer

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.