GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Nov 2018, 10:42

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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

For each positive integer n, p(n) is defined to be the product of..

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

Hide Tags

Intern
Intern
avatar
Joined: 17 Jan 2016
Posts: 10
For each positive integer n, p(n) is defined to be the product of..  [#permalink]

Show Tags

New post Updated on: 05 May 2016, 09:39
4
30
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:53) correct 38% (01:57) wrong based on 682 sessions

HideShow timer Statistics

For each positive integer \(n\), \(p(n)\) is defined to be the product of the digits of \(n\). For example, \(p(724) = 56\) since \(7 * 2 * 4 =56\).

Which of the following statements must be true?

I. \(p(10n) = p(n)\)

II. \(p(n+1) > p(n)\)

III. \(p(2n) = 2p(n)\)

--

A. None
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

Originally posted by broilerc on 05 May 2016, 09:16.
Last edited by Vyshak on 05 May 2016, 09:39, edited 1 time in total.
Formatted the question
Most Helpful Expert Reply
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: For each positive integer n, p(n) is defined to be the product of..  [#permalink]

Show Tags

New post 30 Aug 2016, 15:40
9
7
broilerc wrote:
For each positive integer \(n\), \(p(n)\) is defined to be the product of the digits of \(n\). For example, \(p(724) = 56\) since \(7 * 2 * 4 =56\).

Which of the following statements must be true?

I. \(p(10n) = p(n)\)

II. \(p(n+1) > p(n)\)

III. \(p(2n) = 2p(n)\)

--

A. None
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


Let’s go through each statement given in the Roman numerals.

I. p(10n) = p(n)

This is not true. For example, if n = 12, p(12) = 2 since 1 x 2 = 2. However, 10n = 10(12) = 120 and p(120) = 0 since 1 x 2 x 0 = 0. Since p(120) ≠ p(12), p(10n) = p(n) is not a true statement.

II. p(n +1) > p(n)

This is not true. For example, if n = 19, then p(19) = 9 since 1 x 9 = 9. However, n + 1 = 19 + 1 = 20 and p(20) = 0 since 2 x 0 = 0. Since p(20) < p (19), p(n +1) > p(n) is not a true statement.

Since neither I nor II is true, it can’t be choices B, C, D or E. So the correct choice must be A. However, let’s show III is also not true.

III. p(2n) = 2p(n)

For example, if n = 15, then p(15) = 5 since 1 x 5 = 5 and 2p(15) = 2 x 5 = 10. However, 2n = 2 x 15 = 30 and p(30) = 0 since 3 x 0 = 0. Since p(30) ≠ 2p(15), p(2n) = 2p(n) is not a true statement.

Answer: A
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Most Helpful Community Reply
SC Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1689
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
GMAT ToolKit User Premium Member
Re: For each positive integer n, p(n) is defined to be the product of..  [#permalink]

Show Tags

New post 05 May 2016, 09:37
9
6
I) p(10n) = p(n)
p(10n) will always have units digit as 0 --> p(10n) = 0
p(n) can be any integer.
Not a must be true statement

II) p(n + 1) > p(n)
If n = 2; p(n +1) = 3 and p(n) = 2 --> p(n + 1) > p(n)
If n = 9; p(n + 1) = 0 and p(n) = 9 --> p(n + 1) < p(n)
Not a must be true statement

III) p(2n) = 2*p(n)
If n = 12; p(2n) = p(24) = 8 and 2*p(n) = 4
Not a must be true statement

Answer: A
General Discussion
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4488
Re: For each positive integer n, p(n) is defined to be the product of the  [#permalink]

Show Tags

New post 17 Jun 2016, 15:47
1
tanad wrote:
For each positive integer n, p(n) is defined to be the product of the digits of n. For example, p(724) = 56, since 7 x 2 x 4 = 56. Which of the following statements must be true?

I. p(10n) = p(n)
II. p(n + 1) > p(n)
III. p(2n) = 2p(n)

A: None
B: I and II only
C: I and III only
D: II and III only
E: I, II and III

Dear tanad,
I'm happy to respond. :-)

My friend, I gather that you are relatively new to GMAT Club. I will share with you an important piece of GC etiquette. Please do NOT start a brand new thread for a question that has already been posted. This particular question has already be posted here:
for-each-positive-integer-n-p-n-is-defined-to-be-the-product-of-217887.html
Always search before you start a separate post. You may find your question answered in that post, and if you don't, you can add your own question to that existing thread. Bunuel will merge this post into that thread.

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Current Student
avatar
Joined: 21 Apr 2016
Posts: 29
Location: United States
GMAT ToolKit User Reviews Badge
Re: For each positive integer n, p(n) is defined to be the product of..  [#permalink]

Show Tags

New post 29 Aug 2016, 13:08
Bunuel wrote:
tanad wrote:
For each positive integer n, p(n) is defined to be the product of the digits of n. For example, p(724) = 56, since 7 x 2 x 4 = 56. Which of the following statements must be true?

I. p(10n) = p(n)
II. p(n + 1) > p(n)
III. p(2n) = 2p(n)

A: None
B: I and II only
C: I and III only
D: II and III only
E: I, II and III

___________________________
Merging topics.


Hi Bunuel, can you please help to answer?
Read the response by Vyshak and still confused. Didn't see other responses so reaching out.

Thanks!
Current Student
avatar
Joined: 21 Apr 2016
Posts: 29
Location: United States
GMAT ToolKit User Reviews Badge
Re: For each positive integer n, p(n) is defined to be the product of..  [#permalink]

Show Tags

New post 31 Aug 2016, 03:48
JeffTargetTestPrep wrote:
broilerc wrote:
For each positive integer \(n\), \(p(n)\) is defined to be the product of the digits of \(n\). For example, \(p(724) = 56\) since \(7 * 2 * 4 =56\).

Which of the following statements must be true?

I. \(p(10n) = p(n)\)

II. \(p(n+1) > p(n)\)

III. \(p(2n) = 2p(n)\)

--

A. None
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


Let’s go through each statement given in the Roman numerals.

I. p(10n) = p(n)

This is not true. For example, if n = 12, p(12) = 2 since 1 x 2 = 2. However, 10n = 10(12) = 120 and p(120) = 0 since 1 x 2 x 0 = 0. Since p(120) ≠ p(12), p(10n) = p(n) is not a true statement.

II. p(n +1) > p(n)

This is not true. For example, if n = 19, then p(19) = 9 since 1 x 9 = 9. However, n + 1 = 19 + 1 = 20 and p(20) = 0 since 2 x 0 = 0. Since p(20) < p (19), p(n +1) > p(n) is not a true statement.

Since neither I nor II is true, it can’t be choices B, C, D or E. So the correct choice must be A. However, let’s show III is also not true.

III. p(2n) = 2p(n)

For example, if n = 15, then p(15) = 5 since 1 x 5 = 5 and 2p(15) = 2 x 5 = 10. However, 2n = 2 x 15 = 30 and p(30) = 0 since 3 x 0 = 0. Since p(30) ≠ 2p(15), p(2n) = 2p(n) is not a true statement.

Answer: A



Thanks Jeff! Clear now.
Btw, did you think to pick specifically those numbers to test? I see you tried to pick ones were you would end up with a 0 as a multiplier.
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
For each positive integer n, p(n) is defined to be the product of..  [#permalink]

Show Tags

New post 31 Aug 2016, 03:54
18967mba wrote:
JeffTargetTestPrep wrote:
broilerc wrote:
For each positive integer \(n\), \(p(n)\) is defined to be the product of the digits of \(n\). For example, \(p(724) = 56\) since \(7 * 2 * 4 =56\).

Which of the following statements must be true?

I. \(p(10n) = p(n)\)

II. \(p(n+1) > p(n)\)

III. \(p(2n) = 2p(n)\)

--

A. None
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


Let’s go through each statement given in the Roman numerals.

I. p(10n) = p(n)

This is not true. For example, if n = 12, p(12) = 2 since 1 x 2 = 2. However, 10n = 10(12) = 120 and p(120) = 0 since 1 x 2 x 0 = 0. Since p(120) ≠ p(12), p(10n) = p(n) is not a true statement.

II. p(n +1) > p(n)

This is not true. For example, if n = 19, then p(19) = 9 since 1 x 9 = 9. However, n + 1 = 19 + 1 = 20 and p(20) = 0 since 2 x 0 = 0. Since p(20) < p (19), p(n +1) > p(n) is not a true statement.

Since neither I nor II is true, it can’t be choices B, C, D or E. So the correct choice must be A. However, let’s show III is also not true.

III. p(2n) = 2p(n)

For example, if n = 15, then p(15) = 5 since 1 x 5 = 5 and 2p(15) = 2 x 5 = 10. However, 2n = 2 x 15 = 30 and p(30) = 0 since 3 x 0 = 0. Since p(30) ≠ 2p(15), p(2n) = 2p(n) is not a true statement.

Answer: A



Thanks Jeff! Clear now.
Btw, did you think to pick specifically those numbers to test? I see you tried to pick ones were you would end up with a 0 as a multiplier.


Yeah, so I thought it would be easiest to select numbers that had a zero as one of the digits. Glad I could help!
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Retired Moderator
User avatar
S
Joined: 18 Sep 2014
Posts: 1127
Location: India
GMAT ToolKit User Premium Member Reviews Badge
Re: For each positive integer n, p(n) is defined to be the product of..  [#permalink]

Show Tags

New post 21 Oct 2016, 10:22
broilerc wrote:
For each positive integer \(n\), \(p(n)\) is defined to be the product of the digits of \(n\). For example, \(p(724) = 56\) since \(7 * 2 * 4 =56\).

Which of the following statements must be true?

I. \(p(10n) = p(n)\)

II. \(p(n+1) > p(n)\)

III. \(p(2n) = 2p(n)\)

--

A. None
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


let n=23
Consider III
P(2n)=p(46)=4*6=24
p(n)=2*3=6
24 is not equal to two times of 6.........so III is not must be true ruling out C, D and E options.

Come to I, any number multiplied by ten will have 0 as one of its integers and product will be zero. Ruling out B as well leaving only A as correct choice.
Intern
Intern
avatar
Joined: 08 Mar 2017
Posts: 1
Re: For each positive integer n, p(n) is defined to be the product of..  [#permalink]

Show Tags

New post 22 Jan 2018, 09:22
Hello,

They mentionned for any positive number n the multiplication works. so p(10n)=1*n without multiplying it by 0 because 0 is not considered positive.
What is the part I don't get?

Best,
G
Intern
Intern
avatar
B
Joined: 30 Nov 2017
Posts: 41
Re: For each positive integer n, p(n) is defined to be the product of..  [#permalink]

Show Tags

New post 15 Feb 2018, 06:27
It was easy to eliminate I and III, but I initially thought that II was correct.

Thankfully "II only" was not in the answer choices, which made me think again. Then I realized that if the last digit was 9, then II will be violated.
GMAT Club Bot
Re: For each positive integer n, p(n) is defined to be the product of.. &nbs [#permalink] 15 Feb 2018, 06:27
Display posts from previous: Sort by

For each positive integer n, p(n) is defined to be the product of..

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.