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

 It is currently 22 Jan 2019, 00:25

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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
• Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

For any integer P greater than 1, P! denotes the product of all the in

Author Message
Current Student
Joined: 27 May 2014
Posts: 524
GMAT 1: 730 Q49 V41
For any integer P greater than 1, P! denotes the product of all the in  [#permalink]

Show Tags

07 Mar 2018, 09:44
00:00

Difficulty:

65% (hard)

Question Stats:

57% (01:10) correct 43% (01:35) wrong based on 14 sessions

HideShow timer Statistics

For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45^m is a factor of 48!?

A) 1
B) 2
C) 5
D) 10
E) 11

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
For any integer P greater than 1, P! denotes the product of all the in  [#permalink]

Show Tags

07 Mar 2018, 10:12
1
saswata4s wrote:
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45^m is a factor of 48!?

A) 1
B) 2
C) 5
D) 10
E) 11

$$45^m=(3^2*5)^m=3^{2m}*5^m$$

so to know the value of $$m$$ we need to know how many powers of $$5$$ are possible in $$48!$$, this can be done as

$$\frac{48}{5}+\frac{48}{5^2}=9+1=10$$. Hence $$m=10$$

Option D
Manager
Joined: 26 Apr 2011
Posts: 60
Location: India
GPA: 3.5
WE: Information Technology (Computer Software)
Re: For any integer P greater than 1, P! denotes the product of all the in  [#permalink]

Show Tags

08 Mar 2018, 03:20
niks18 wrote:
saswata4s wrote:
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. What is the greatest integer m for which 45^m is a factor of 48!?

A) 1
B) 2
C) 5
D) 10
E) 11

$$45^m=(3^2*5)^m=3^{2m}*5^m$$

so to know the value of $$m$$ we need to know how many powers of $$5$$ are possible in $$48!$$, this can be done as

$$\frac{48}{5}+\frac{48}{5^2}=9+1=10$$. Hence $$m=10$$

Option D

Why you did not consider powers of 3?
_________________

Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3626
For any integer P greater than 1, P! denotes the product of all the in  [#permalink]

Show Tags

08 Mar 2018, 03:39
1
MrCleantek wrote:
Why you did not consider powers of 3?

Hey MrCleantek ,

3 is not considered because out of 3 and 5, we will always have atleast as many number of 3s as 5s whereas the converse is not true.

Consider an example here: Let's say we have 20! and we need to find out number of 10s. Now every 10 will be composed of one 2 and one 5.

If you find the number of 2's, you will get 18

Number of 5's = 4. Hence, you can see we cannot have more than four 10s because we have only four 4s. Thus finding the number of 5s would do.

Does that make sense?

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.

For any integer P greater than 1, P! denotes the product of all the in &nbs [#permalink] 08 Mar 2018, 03:39
Display posts from previous: Sort by