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

 It is currently 20 Jan 2019, 21:44

### 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
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.

# 3^q is a factor of (300!/100!) where q is a positive integer. What is

Author Message
TAGS:

### Hide Tags

Manager
Joined: 30 Dec 2016
Posts: 230
GMAT 1: 650 Q42 V37
GPA: 4
3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

### Show Tags

31 Mar 2018, 03:30
1
1
00:00

Difficulty:

65% (hard)

Question Stats:

54% (02:19) correct 46% (02:33) wrong based on 51 sessions

### HideShow timer Statistics

3^q is a factor of (300!/100!) where q is a positive integer. What is the highest possible value of q?

A) 67
B) 89
C) 100
D) 114
E) 148

_________________

Regards
SandySilva

____________
Please appreciate the efforts by pressing +1 KUDOS (:

Manager
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

### Show Tags

Updated on: 01 Apr 2018, 03:31
1
sandysilva wrote:
3^q is a factor of (300!/100!) where q is a positive integer. What is the highest possible value of q?

A) 67
B) 89
C) 100
D) 114
E) 148

Total number of factors of 3 in 300!=148
Total number of factors of 3 in 100!=48

3^q=(3^148)/(3^48)=3^100

option c

Originally posted by kunalcvrce on 31 Mar 2018, 03:36.
Last edited by kunalcvrce on 01 Apr 2018, 03:31, edited 1 time in total.
Manager
Joined: 16 May 2017
Posts: 58
Location: India
WE: General Management (Retail Banking)
Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

### Show Tags

31 Mar 2018, 04:07
kunalcvrce wrote:
sandysilva wrote:
3^q is a factor of (300!/100!) where q is a positive integer. What is the highest possible value of q?

A) 67
B) 89
C) 100
D) 114
E) 148

Total number of factors of 3 in 300!=157
Total number of factors of 3 in 100!=57

3^q=(3^157)/(3^57)=3^100

option c
How did you calculate it?

Sent from my Redmi 4 using GMAT Club Forum mobile app
_________________

"The harder you work the luckier you get"

Manager
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

### Show Tags

31 Mar 2018, 04:17
aghosh54 wrote:
kunalcvrce wrote:
sandysilva wrote:
3^q is a factor of (300!/100!) where q is a positive integer. What is the highest possible value of q?

A) 67
B) 89
C) 100
D) 114
E) 148

Total number of factors of 3 in 300!=157
Total number of factors of 3 in 100!=57

3^q=(3^157)/(3^57)=3^100

option c
How did you calculate it?

Sent from my Redmi 4 using GMAT Club Forum mobile app

the number of factors for 3 in 300!
[300/3]+[300/3^2]+[300/3^3]+[300/3^4]+[300/3^5]+[300/3^6]=157

formula is summation of [number/factor(increase the factor)]
you can do similarly for 100!

Hope u get it..
Intern
Joined: 12 Mar 2018
Posts: 3
Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

### Show Tags

01 Apr 2018, 02:00
1
Further explanations for the rule can be found here:
The principle of calculation done by kunalcvrce is correct, however, the divident and divisor should be 148/48, as 100/3 + 100/3^2 ... etc is 48
Intern
Joined: 27 Jun 2017
Posts: 17
GMAT 1: 680 Q43 V40
GMAT 2: 710 Q47 V41
Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

### Show Tags

01 Apr 2018, 03:20
kunalcvrce wrote:

Total number of factors of 3 in 300!=157
Total number of factors of 3 in 100!=57

[300/3]+[300/3^2]+[300/3^3]+[300/3^4]+[300/3^5]+[300/3^6]=157

formula is summation of [number/factor(increase the factor)]
you can do similarly for 100!

Hope u get it..

Still not sure how you calculated 157... If I calculate it, the number of factor 3 in 300! is 148 and in 100! it's 48 (still the same result though.

I think you went one step too far, 3^6 is already 729, and you "can't divide" 300 by 729.

Best,
T
Manager
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

### Show Tags

01 Apr 2018, 03:30
Tommy87HG wrote:
kunalcvrce wrote:

Total number of factors of 3 in 300!=157
Total number of factors of 3 in 100!=57

[300/3]+[300/3^2]+[300/3^3]+[300/3^4]+[300/3^5]+[300/3^6]=157

formula is summation of [number/factor(increase the factor)]
you can do similarly for 100!

Hope u get it..

Still not sure how you calculated 157... If I calculate it, the number of factor 3 in 300! is 148 and in 100! it's 48 (still the same result though.

I think you went one step too far, 3^6 is already 729, and you "can't divide" 300 by 729.

Best,
T

Hi Tommy,

Thanks for correcting it 148 and 48 only..
Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is &nbs [#permalink] 01 Apr 2018, 03:30
Display posts from previous: Sort by