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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

28 Apr 2012, 06:05

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

32% (03:29) correct
68% (02:19) wrong based on 192 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?

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

Show Tags

28 Apr 2012, 06:18

2

This post received 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).

Answer: D.

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

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).

Answer: D.

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...

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

Show Tags

02 Aug 2013, 01:22

1

This post received KUDOS

Expert's post

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).

Answer: D.

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.

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

Show Tags

26 Oct 2014, 21:42

Expert's post

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 \(2^{10} = 1024\).

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. _________________

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...