Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Jul 2010
Posts: 140

If n is a nonnegative integer such that 12^n is a divisor [#permalink]
Show Tags
18 Sep 2010, 11:48
3
This post received KUDOS
34
This post was BOOKMARKED
Question Stats:
60% (00:46) correct 40% (01:03) wrong based on 790 sessions
HideShow timer Statistics
If n is a nonnegative integer such that 12^n is a divisor of 3,176,793, what is the value of n^1212^n? A. 11 B. 1 C. 0 D. 1 E. 11
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 29 Mar 2013, 01:41, edited 2 times in total.
Edited the question



Retired Moderator
Joined: 02 Sep 2010
Posts: 792
Location: London

Re: Divisor of 3,176,793 [#permalink]
Show Tags
18 Sep 2010, 12:00
3
This post received KUDOS
3176793 is odd 12n is even How can 12n be a divisor ? The only answer I can think is n=0 which means 1 But I don't think you can count 0 as a "divisor"
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 25 Jul 2010
Posts: 140

Re: Divisor of 3,176,793 [#permalink]
Show Tags
18 Sep 2010, 12:06
1
This post was BOOKMARKED
Precisely, for this reason, I have posted this question here. I am unclear is 0 should be considered as divisor.



Retired Moderator
Joined: 02 Sep 2010
Posts: 792
Location: London

Re: Divisor of 3,176,793 [#permalink]
Show Tags
18 Sep 2010, 12:10
Orange08 wrote: Precisely, for this reason, I have posted this question here. I am unclear is 0 should be considered as divisor. What's the source of the question ? I am sure the only possible answer is 1, just not sure about the validity of the question
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings
Last edited by shrouded1 on 18 Sep 2010, 15:50, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 43363

Re: Divisor of 3,176,793 [#permalink]
Show Tags
18 Sep 2010, 19:11
11
This post received KUDOS
Expert's post
8
This post was BOOKMARKED
Orange08 wrote: If n is a nonnegative integer such that 12n is a divisor of 3,176,793, what is the value of n^12 – 12^n ?
a. 11 b. 1 c. 0 d. 1 e. 11 If the answer is B then I think it should be \(12^n\) instead of \(12n\) So the question would be: If n is a nonnegative integer such that 12^n is a divisor of 3,176,793, what is the value of n^1212^n?3,176,793 is an odd number. The only way it to be a multiple of \(12^n\) (even number in integer power) is when \(n=0\), in this case \(12^n=12^0=1\) and 1 is a factor of every integer. Then \(n^{12}12^n=0^{12}12^0=1\). Answer: B. 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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 17 Feb 2011
Posts: 187
Concentration: Real Estate, Finance
Schools: MIT (Sloan)  Class of 2014

Re: Divisor of 3,176,793 [#permalink]
Show Tags
25 Feb 2011, 08:56
Nice question!
Bunuel's approach is very good.
Thanks!



Intern
Joined: 14 Feb 2011
Posts: 6

Re: Divisor of 3,176,793 [#permalink]
Show Tags
25 Feb 2011, 21:22
Thanks Bunnel's for this in depth explanation!!



Manager
Joined: 27 Oct 2011
Posts: 182
Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)

1
This post was BOOKMARKED
12^n will always be an even number because it will be a multiple of 12. however 3,176,793 is odd and there is no case when a positive number of n would be a factor of 3,176,793. Only number that would match is when n is zero.
_________________
DETERMINED TO BREAK 700!!!



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 624

Re: If n is a nonnegative integer such that 12n is a divisor of [#permalink]
Show Tags
28 Mar 2013, 21:12
nave81 wrote: If n is a nonnegative integer such that \(12^n\) is a divisor of 3,176,793, what is the value of n^12  12^n?
A. 11 B.  1 C. 0 D. 1 E. 11 n is any integer \(>=0\). Also, \(12^n\) is a divisor of the given number. \(12^0\) = 1 is a divisor of the given number. Replacing n = 0 in the given expression, we have 0^12  12^0 = 1. Note that for any other value of n, there will be a factor of 2 in \(12^n\). But the given number is odd and thus, has no factor of 2. Therefore, any other power of 12, can not be a divisor of the given number. B.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1121
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: If n is a nonnegative integer such that 12n is a divisor of [#permalink]
Show Tags
28 Mar 2013, 23:24
nave81 wrote: If n is a nonnegative integer such that \(12^n\) is a divisor of 3,176,793, what is the value of n^12  12^n?
A. 11 B.  1 C. 0 D. 1 E. 11 The only way that \(12^n\) can be a divisor of 3 is if \(n=0, 12^0=1\). So \(n=0\) 0^(12)  12^0=01=1 B
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Director
Joined: 29 Nov 2012
Posts: 860

Re: Divisor of 3,176,793 [#permalink]
Show Tags
05 Jul 2013, 08:08
3,176,793 is an odd number. The only way it to be a multiple of \(12^n\) (even number in integer power) is when \(n=0\), in this case \(12^n=12^0=1\) and 1 is a factor of every integer.
Can you elaborate on this.. The sum of the digits add up to 9 the only example I thought of 12^2 = 144 does sum of the digits have any relation to this question or it isn't related?
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Math Expert
Joined: 02 Sep 2009
Posts: 43363

Re: Divisor of 3,176,793 [#permalink]
Show Tags
05 Jul 2013, 08:17
fozzzy wrote: 3,176,793 is an odd number. The only way it to be a multiple of \(12^n\) (even number in integer power) is when \(n=0\), in this case \(12^n=12^0=1\) and 1 is a factor of every integer.
Can you elaborate on this.. The sum of the digits add up to 9 the only example I thought of 12^2 = 144
does sum of the digits have any relation to this question or it isn't related? No, the sum of the digits is not relevant for this question. 3,176,793 is an odd number. An odd number cannot be a multiple of any even number, and 12^n is even for any positive integer n. Therefore n cannot be positive which means that n can only be 0. Hope it's clear. Similar question to practice: newtoughandtrickyexponentsandrootsquestions12595640.html#p1029223
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 26 Jan 2015
Posts: 94

Re: If n is a nonnegative integer such that 12^n is a divisor [#permalink]
Show Tags
09 Mar 2016, 10:36
Bunuel wrote: fozzzy wrote: 3,176,793 is an odd number. The only way it to be a multiple of \(12^n\) (even number in integer power) is when \(n=0\), in this case \(12^n=12^0=1\) and 1 is a factor of every integer.
Can you elaborate on this.. The sum of the digits add up to 9 the only example I thought of 12^2 = 144
does sum of the digits have any relation to this question or it isn't related? No, the sum of the digits is not relevant for this question. 3,176,793 is an odd number. An odd number cannot be a multiple of any even number, and 12^n is even for any positive integer n. Therefore n cannot be positive which means that n can only be 0. Hope it's clear. Similar question to practice: newtoughandtrickyexponentsandrootsquestions12595640.html#p1029223Hi Bunuel, I did not notice that the number given is odd and do the thinking in mind. Rather I read the Q and understood that 12^n should be a divisor on the huge number. 1 is a divisor of the number. and 12^0=1 and hence n=0 satisfies the Q. So I realized that n&^1212^n = 1. if I follow this approach, Will I face a pit fall in any other question similar to this one?
_________________
Kudos is the best way to say Thank you! Please give me a kudos if you like my post



Manager
Joined: 20 Jun 2016
Posts: 53

Re: If n is a nonnegative integer such that 12^n is a divisor [#permalink]
Show Tags
20 Aug 2017, 21:46
2
This post received KUDOS
0^anything=0 anything^0=1 Therefore the only value for n=0. Answer : 01=1(B)
_________________
Life is a challenge face it.



SVP
Joined: 11 Sep 2015
Posts: 1999
Location: Canada

Re: If n is a nonnegative integer such that 12^n is a divisor [#permalink]
Show Tags
17 Jan 2018, 15:53
Orange08 wrote: If n is a nonnegative integer such that 12^n is a divisor of 3,176,793, what is the value of n^1212^n?
A. 11 B. 1 C. 0 D. 1 E. 11 First notice the big hint right from the start: n is a nonnegative integerYour first reaction should be " Why not just tell us that n is positive?" The reason is that the testmaker wants to include zero as a possible value for n (and zero is neither positive nor negative). Since the testmaker went to the trouble to keep zero as a possible value for n, let's check to see whether n = 0 works. Well, 12^ 0 = 1, and 1 is a divisor of 3,176,793. So n must equal 0. Now that we know the value of n, we can evaluate n^12  12^n n^12  12^n = 0^12  12^ 0 = 0  1 = 1 Answer: B Cheers, Brent
_________________
Brent Hanneson – Founder of gmatprepnow.com




Re: If n is a nonnegative integer such that 12^n is a divisor
[#permalink]
17 Jan 2018, 15:53






