Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 May 2017, 20:32

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The function p(n) on non-negative integer n is defined in

Author Message
TAGS:

Hide Tags

Manager
Joined: 25 Feb 2012
Posts: 62
Followers: 1

Kudos [?]: 24 [0], given: 8

The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

28 Apr 2012, 06:05
10
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

32% (03:16) correct 68% (02:18) wrong based on 245 sessions

HideShow timer Statistics

The function p(n) on non-negative integer n is defined in the following way: the units digit of n is the exponent of 2 in the prime factorization of p(n), the tens digit is the exponent of 3, and in general, for positive integer k, the digit in the 10^(k–1) th place of n is the exponent on the kth smallest prime (compared to the set of all primes) in the prime factorization of p(n). For instance, p(102) = 20, since 20 = (5^1)(3^0)(2^2). What is the smallest positive integer that is not equal to p(n) for any permissible n?

(A) 1
(B) 29
(C) 31
(D) 1,024
(E) 2,310

OA after some discussion.
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Apr 2012, 06:21, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 38798
Followers: 7714

Kudos [?]: 105798 [2] , given: 11581

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

28 Apr 2012, 06:18
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
qtrip wrote:
The function p(n) on non-negative integer n is defined in the following way: the units digit of n is the exponent of 2 in the prime factorization of p(n), the tens digit is the exponent of 3, and in general, for positive integer k, the digit in the 10^(k–1) th place of n is the exponent on the kth smallest prime (compared to the set of all primes) in the prime factorization of p(n). For instance, p(102) = 20, since 20 = (5^1)(3^0)(2^2). What is the smallest positive integer that is not equal to p(n) for any permissible n?

(A) 1
(B) 29
(C) 31
(D) 1,024
(E) 2,310

OA after some discussion.

The function basically transforms the digits of integer n into the power of primes: 2, 3, 5, ...

For example:
$$p(9)=2^9$$;
$$p(49)=2^9*3^4$$;
$$p(349)=2^9*3^4*5^3$$;
$$p(6349)=2^9*3^4*5^3*7^4$$;
...

The question asks for the leas number that cannot be expressed by the function p(n).

So, the digits of n transform to the power and since single digit cannot be more than 10 then p(n) cannot have the power of 10 or higher.

So, the least number that cannot be expressed by the function p(n) is $$2^{10}=1,024$$ (n just cannot have 10 as its digit).

P.S. If you have the OA you have to indicate it under the spoiler.
_________________
Manager
Joined: 25 Feb 2012
Posts: 62
Followers: 1

Kudos [?]: 24 [0], given: 8

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

28 Apr 2012, 06:21
Thanks Bunuel..I was wondering how something like 11 can be represented. But now I understand why 1024 has to be the right answer.
Math Expert
Joined: 02 Sep 2009
Posts: 38798
Followers: 7714

Kudos [?]: 105798 [1] , given: 11581

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

28 Apr 2012, 06:27
1
KUDOS
Expert's post
qtrip wrote:
Thanks Bunuel..I was wondering how something like 11 can be represented. But now I understand why 1024 has to be the right answer.

11 can be expressed as $$p(10,000)=2^0*3^0*5^0*7^0*11^1$$.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38798
Followers: 7714

Kudos [?]: 105798 [0], given: 11581

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

25 Jun 2013, 05:56
Expert's post
1
This post was
BOOKMARKED
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

_________________
Manager
Joined: 14 Dec 2012
Posts: 82
Location: United States
Followers: 1

Kudos [?]: 16 [0], given: 186

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

01 Aug 2013, 20:24
Bunuel wrote:
qtrip wrote:
The function p(n) on non-negative integer n is defined in the following way: the units digit of n is the exponent of 2 in the prime factorization of p(n), the tens digit is the exponent of 3, and in general, for positive integer k, the digit in the 10^(k–1) th place of n is the exponent on the kth smallest prime (compared to the set of all primes) in the prime factorization of p(n). For instance, p(102) = 20, since 20 = (5^1)(3^0)(2^2). What is the smallest positive integer that is not equal to p(n) for any permissible n?

(A) 1
(B) 29
(C) 31
(D) 1,024
(E) 2,310

OA after some discussion.

The function basically transforms the digits of integer n into the power of primes: 2, 3, 5, ...

For example:
$$p(9)=2^9$$;
$$p(49)=2^9*3^4$$;
$$p(349)=2^9*3^4*5^3$$;
$$p(6349)=2^9*3^4*5^3*7^4$$;
...

The question asks for the leas number that cannot be expressed by the function p(n).

So, the digits of n transform to the power and since single digit cannot be more than 10 then p(n) cannot have the power of 10 or higher.

So, the least number that cannot be expressed by the function p(n) is $$2^{10}=1,024$$ (n just cannot have 10 as its digit).

P.S. If you have the OA you have to indicate it under the spoiler.

Hi Bunuel,
I am a bit confused here.Cant p(1024) be 2^4 *3^2*5^0*7^1..
kindly elaborate...i get what you mean but am unable to implement it here...
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629
Followers: 83

Kudos [?]: 1191 [2] , given: 136

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

02 Aug 2013, 01:22
2
KUDOS
1
This post was
BOOKMARKED
up4gmat wrote:
Bunuel wrote:
qtrip wrote:
The function p(n) on non-negative integer n is defined in the following way: the units digit of n is the exponent of 2 in the prime factorization of p(n), the tens digit is the exponent of 3, and in general, for positive integer k, the digit in the 10^(k–1) th place of n is the exponent on the kth smallest prime (compared to the set of all primes) in the prime factorization of p(n). For instance, p(102) = 20, since 20 = (5^1)(3^0)(2^2). What is the smallest positive integer that is not equal to p(n) for any permissible n?

(A) 1
(B) 29
(C) 31
(D) 1,024
(E) 2,310

OA after some discussion.

The function basically transforms the digits of integer n into the power of primes: 2, 3, 5, ...

For example:
$$p(9)=2^9$$;
$$p(49)=2^9*3^4$$;
$$p(349)=2^9*3^4*5^3$$;
$$p(6349)=2^9*3^4*5^3*7^4$$;
...

The question asks for the leas number that cannot be expressed by the function p(n).

So, the digits of n transform to the power and since single digit cannot be more than 10 then p(n) cannot have the power of 10 or higher.

So, the least number that cannot be expressed by the function p(n) is $$2^{10}=1,024$$ (n just cannot have 10 as its digit).

P.S. If you have the OA you have to indicate it under the spoiler.

Hi Bunuel,
I am a bit confused here.Cant p(1024) be 2^4 *3^2*5^0*7^1..
kindly elaborate...i get what you mean but am unable to implement it here...

We don't have to find p(1024). In-fact, the question asks to find the value of the smallest integer which can never be assumed by the function p(n), for any non-negative integer,n.
For eg, for p(n) =5, the initial integer n = 100, for p(n) = 7, n = 1000 and so on. Now, if p(n) were to be $$1024 = 2^{10}$$, that would mean that the units digit of n was 10, which is not possible.

Hope this helps.
_________________
Manager
Joined: 07 Apr 2014
Posts: 141
Followers: 1

Kudos [?]: 24 [0], given: 81

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

24 Aug 2014, 13:01
Hi, Could you use some options in the answer choice & explain the reasoning so that i could understand the concept clearly.

Math Expert
Joined: 02 Sep 2009
Posts: 38798
Followers: 7714

Kudos [?]: 105798 [0], given: 11581

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

24 Aug 2014, 13:10
luckyme17187 wrote:
Hi, Could you use some options in the answer choice & explain the reasoning so that i could understand the concept clearly.

Solution is given here: the-function-p-n-on-non-negative-integer-n-is-defined-in-131459.html#p1079514 Please read it and also the discussion below it. If something will remain unclear please ask but try to be a little bit more specific. Thank you.
_________________
Intern
Joined: 20 Oct 2014
Posts: 1
Followers: 0

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

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

26 Oct 2014, 15:50
The case of 1. p(what)=1?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7368
Location: Pune, India
Followers: 2281

Kudos [?]: 15076 [0], given: 224

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

26 Oct 2014, 21:35
zaolupa wrote:
The case of 1. p(what)=1?

If n = 0,
p(0) = 2^0 = 1
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7368 Location: Pune, India Followers: 2281 Kudos [?]: 15076 [0], given: 224 Re: The function p(n) on non-negative integer n is defined in [#permalink] Show Tags 26 Oct 2014, 21:42 qtrip wrote: The function p(n) on non-negative integer n is defined in the following way: the units digit of n is the exponent of 2 in the prime factorization of p(n), the tens digit is the exponent of 3, and in general, for positive integer k, the digit in the 10^(k–1) th place of n is the exponent on the kth smallest prime (compared to the set of all primes) in the prime factorization of p(n). For instance, p(102) = 20, since 20 = (5^1)(3^0)(2^2). What is the smallest positive integer that is not equal to p(n) for any permissible n? (A) 1 (B) 29 (C) 31 (D) 1,024 (E) 2,310 OA after some discussion. The question asks for the value that p(n) cannot take. p(n) is of the form $$2^a * 3^b * 5^c * 7^d$$... etc We know that this is prime factorization and that every positive integer can be prime factorized. Then what is the constraint on the value of p(n)? a, b, c, d etc are single digits. So if the prime factorization of a number is $$2^{10}$$ or $$3^{24}$$, it cannot be p(n). The smallest value that p(n) cannot take is $$2^{10} = 1024$$. Answer (D) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15386
Followers: 648

Kudos [?]: 204 [0], given: 0

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

12 Nov 2015, 23:42
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 Club Legend
Joined: 09 Sep 2013
Posts: 15386
Followers: 648

Kudos [?]: 204 [0], given: 0

Re: The function p(n) on non-negative integer n is defined in [#permalink]

Show Tags

09 Feb 2017, 00:02
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.
_________________
Re: The function p(n) on non-negative integer n is defined in   [#permalink] 09 Feb 2017, 00:02
Similar topics Replies Last post
Similar
Topics:
4 For all nonnegative integers a, b, and c, the function G is defined by 3 18 Mar 2017, 15:11
25 For each positive integer n, p(n) is defined to be the product of.. 9 21 Oct 2016, 11:22
13 If, for all positive integer values of n, P(n) is defined as 7 11 Nov 2016, 05:08
19 The function f is defined for all the positive integers n by 8 10 Mar 2017, 11:49
14 The function F is defined for all positive integers n by the 6 28 Jul 2016, 23:39
Display posts from previous: Sort by