It is currently 23 Nov 2017, 13:49

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

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

Hide Tags

2 KUDOS received
Manager
Manager
avatar
Joined: 07 Feb 2010
Posts: 155

Kudos [?]: 769 [2], given: 101

If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 02 Oct 2010, 04:44
2
This post received
KUDOS
14
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (01:08) correct 42% (01:15) wrong based on 498 sessions

HideShow timer Statistics

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
[Reveal] Spoiler: OA

Kudos [?]: 769 [2], given: 101

Expert Post
6 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133143 [6], given: 12415

Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 02 Oct 2010, 04:56
6
This post received
KUDOS
Expert's post
8
This post was
BOOKMARKED
If \(243^x*463^y =n\), where x and y are positive integers, what is the units digit of n?

The units digit of \(243^x\) is the same as the units digit of \(3^x\) and similarly the units digit of \(463^y\) is the same as the units digit of \(3^y\), so the units digit of \(243^x*463^y\) equals to the units digit of \(3^x*3^y=3^{x+y}\). So, knowing the value of \(x+y\) is sufficient to determine the units digit of \(n\).

(1) \(x + y = 7\). Sufficient. (As cyclicity of units digit of \(3\) in integer power 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.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 133143 [6], given: 12415

Intern
Intern
User avatar
Joined: 10 Jul 2010
Posts: 44

Kudos [?]: 4 [0], given: 34

Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 03 Oct 2010, 09:50
Yup!! A it is....equation can be treated like 3^x*3^y hence (x+y)'s value can provide us the last digit...

Kudos [?]: 4 [0], given: 34

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15508

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 11 Sep 2013, 00:57
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

Kudos [?]: 283 [0], given: 0

Intern
Intern
avatar
Joined: 24 Feb 2014
Posts: 4

Kudos [?]: [0], given: 7

Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 03 Mar 2014, 05:18
I have a doubt. Cyclicity of unit digit of 3 is 4. Hence we know that every fourth power of 3 (3^4, 3^8, 3^12) will have the same unit digit, 1. Hence when option B says x = 4, knowing that x and y are positive integers, we know that xy will be a multiple of 4. Unit digit of 3^4k is always 1 isn't it? Shouldn't this be sufficient information?

Shouldn't the answer be D?

Kudos [?]: [0], given: 7

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133143 [0], given: 12415

Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 03 Mar 2014, 05:21
siriusblack1106 wrote:
I have a doubt. Cyclicity of unit digit of 3 is 4. Hence we know that every fourth power of 3 (3^4, 3^8, 3^12) will have the same unit digit, 1. Hence when option B says x = 4, knowing that x and y are positive integers, we know that xy will be a multiple of 4. Unit digit of 3^4k is always 1 isn't it? Shouldn't this be sufficient information?

Shouldn't the answer be D?


I think you are missing that \(3^x*3^y=3^{x+y}\), so the exponent is x+y not xy.

Does this make sense?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 133143 [0], given: 12415

Intern
Intern
avatar
Joined: 24 Feb 2014
Posts: 4

Kudos [?]: [0], given: 7

Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 03 Mar 2014, 05:26
Yes! Can't believe I just made that mistake. Such mistakes are gonna cost me. :/

Kudos [?]: [0], given: 7

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133143 [0], given: 12415

Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 03 Mar 2014, 05:28
siriusblack1106 wrote:
Yes! Can't believe I just made that mistake. Such mistakes are gonna cost me. :/


Yes, careless errors are the #1 cause of score drops on the GMAT! They cause you to miss easier questions, hurting your score a lot more than not know how to solve the harder ones. So, be more careful, before you submit your answer, double-check that it’s the answer to the proper question.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 133143 [0], given: 12415

1 KUDOS received
Manager
Manager
avatar
Joined: 18 May 2014
Posts: 62

Kudos [?]: 20 [1], given: 6

Location: United States
Concentration: General Management, Other
GMAT Date: 07-31-2014
GPA: 3.99
WE: Analyst (Consulting)
Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 18 May 2014, 09:53
1
This post received
KUDOS
243 = 3^5

463 ends with a 3. So we have to know how many times we will multiply 3's at the end of each numbers.

1) 7 times - SUF
2) we dont know Y - INSUF

Choose (a)

Kudos [?]: 20 [1], given: 6

Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 301

Kudos [?]: 83 [0], given: 23

Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 02 Nov 2014, 18:48
Bunuel wrote:
If \(243^x*463^y =n\), where x and y are positive integers, what is the units digit of n?

The units digit of \(243^x\) is the same as the units digit of \(3^x\) and similarly the units digit of \(463^y\) is the same as the units digit of \(3^y\), so the units digit of \(243^x*463^y\) equals to the units digit of \(3^x*3^y=3^{x+y}\). So, knowing the value of \(x+y\) is sufficient to determine the units digit of \(n\).

(1) \(x + y = 7\). Sufficient. (As cyclicity of units digit of \(3\) in integer power 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.

Hope it helps.


Hi Bunuel,

But surely shouldn't it matter if 3 is raised to 1 and or 6? Meaning, if it's 3^3 + 3^4 = 7 + 1 = 8. But, if its 3^2+3^5 = 9 + 3 = 12, units of 2. Doesn't that yield insufficient?

Kudos [?]: 83 [0], given: 23

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133143 [0], given: 12415

Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 03 Nov 2014, 01:50
russ9 wrote:
Bunuel wrote:
If \(243^x*463^y =n\), where x and y are positive integers, what is the units digit of n?

The units digit of \(243^x\) is the same as the units digit of \(3^x\) and similarly the units digit of \(463^y\) is the same as the units digit of \(3^y\), so the units digit of \(243^x*463^y\) equals to the units digit of \(3^x*3^y=3^{x+y}\). So, knowing the value of \(x+y\) is sufficient to determine the units digit of \(n\).

(1) \(x + y = 7\). Sufficient. (As cyclicity of units digit of \(3\) in integer power 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.

Hope it helps.


Hi Bunuel,

But surely shouldn't it matter if 3 is raised to 1 and or 6? Meaning, if it's 3^3 + 3^4 = 7 + 1 = 8. But, if its 3^2+3^5 = 9 + 3 = 12, units of 2. Doesn't that yield insufficient?


Are you sure you are reading the question correctly? It's 243^x*463^y, 243^x multiplied by 463^y not 243^x + 463^y...
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 133143 [0], given: 12415

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15508

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 05 Jan 2016, 12:15
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

Kudos [?]: 283 [0], given: 0

Intern
Intern
avatar
B
Joined: 04 Nov 2015
Posts: 36

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

Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 28 Jul 2016, 15:01
Well I don't agree the answer should be indeed D.
Option 1 suggests x+y=7 this can have multiple x and y combinations like (1,6) (2,5) (4,3) and so on so the units digit of 243^x and 463^y will differ .

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

Intern
Intern
avatar
Joined: 17 Mar 2016
Posts: 18

Kudos [?]: 11 [0], given: 30

Location: Singapore
GPA: 3.5
WE: Business Development (Energy and Utilities)
GMAT ToolKit User
Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 28 Jul 2016, 18:37
sandeep211986 wrote:
Well I don't agree the answer should be indeed D.
Option 1 suggests x+y=7 this can have multiple x and y combinations like (1,6) (2,5) (4,3) and so on so the units digit of 243^x and 463^y will differ .


Hey Buddy,

All the combinations, for x+y=7, will yield the same units digit. Consider the following
x=1,y=6
243*463*463*463*463*463*463 ~~ To find units digit we just need 3^1 * 3^6 = 3^7, i.e 7 (units digit of 2187)

Same goes with other combinations. 3^7 ends up deciding the units digit.

Should the question would have been something like, 245^x * 463^y = n, the combinations of different values of x & y would have yielded different units digits.

Hope that clears

Kudos [?]: 11 [0], given: 30

Intern
Intern
avatar
B
Status: Fighting Again to bell the CAT
Joined: 28 Aug 2016
Posts: 37

Kudos [?]: 26 [0], given: 24

Location: India
GMAT 1: 640 Q49 V30
GMAT 2: 710 Q50 V35
GPA: 3.61
Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 20 Dec 2016, 15:06
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

Last edited by amandeep_k on 20 Dec 2016, 15:37, edited 1 time in total.

Kudos [?]: 26 [0], given: 24

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367

Kudos [?]: 402 [0], given: 40

GPA: 3.98
Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 20 Dec 2016, 15:25
amandeep_k 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


I can't get how the answer can be A.

Had it been \(243^x * 463^y\). In this case we'll get same base 3 and we can add the powers

\(3^0*3^7\)
\(3^1*3^6\)
\(3^2*3^5\)
...

In each case we'll get \(3^7\) which units digit we can identify. That that will be sufficient.

But we have 3*x*3*y = 9*x*y which can take any values. Not sufficient. I can't get the idea how answer can be A.

Please correct me if I'm wrong.

Kudos [?]: 402 [0], given: 40

Intern
Intern
avatar
B
Status: Fighting Again to bell the CAT
Joined: 28 Aug 2016
Posts: 37

Kudos [?]: 26 [0], given: 24

Location: India
GMAT 1: 640 Q49 V30
GMAT 2: 710 Q50 V35
GPA: 3.61
Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 20 Dec 2016, 15:39
vitaliyGMAT wrote:
amandeep_k 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


I can't get how the answer can be A.

Had it been \(243^x * 463^y\). In this case we'll get same base 3 and we can add the powers

\(3^0*3^7\)
\(3^1*3^6\)
\(3^2*3^5\)
...

In each case we'll get \(3^7\) which units digit we can identify. That that will be sufficient.

But we have 3*x*3*y = 9*x*y which can take any values. Not sufficient. I can't get the idea how answer can be A.

Please correct me if I'm wrong.


Hi, You are right. my question was wrong. Sorry for the inconvenience. :cry:

Kudos [?]: 26 [0], given: 24

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133143 [0], given: 12415

Re: If 243^x*463^y = n, where x and y are positive integers [#permalink]

Show Tags

New post 20 Dec 2016, 23:04

Kudos [?]: 133143 [0], given: 12415

Re: If 243^x*463^y = n, where x and y are positive integers   [#permalink] 20 Dec 2016, 23:04
Display posts from previous: Sort by

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

  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 | Emoji artwork provided by EmojiOne

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®.