Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 19 Jul 2019, 20:23 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # q is the smallest positive integer for which 3^q is a factor of 8124.

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56300
q is the smallest positive integer for which 3^q is a factor of 8124.  [#permalink]

### Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 67% (01:17) correct 33% (01:49) wrong based on 49 sessions

### HideShow timer Statistics q is the smallest positive integer for which $$3^q$$ is a factor of 8124. What is the value of $$3^q− ­ q^3$$ ?

A. 0
B. 1
C. 2
D. 3
E. More than 3

_________________
VP  D
Joined: 31 Oct 2013
Posts: 1392
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
q is the smallest positive integer for which 3^q is a factor of 8124.  [#permalink]

### Show Tags

Bunuel wrote:
q is the smallest positive integer for which $$3^q$$ is a factor of 8124. What is the value of $$3^q− ­ q^3$$ ?

A. 0
B. 1
C. 2
D. 3
E. More than 3

q is the smallest positive integer.

Let q be 1

8 + 1 + 2 + 4 =15

15 is divisible by $$3^q$$or $$3^1$$ or 3.

Required Value :

$$3^q - q^3$$ = 3 - 1 = 2.

Senior Manager  G
Joined: 22 Nov 2018
Posts: 483
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Re: q is the smallest positive integer for which 3^q is a factor of 8124.  [#permalink]

### Show Tags

Bunuel wrote:
q is the smallest positive integer for which $$3^q$$ is a factor of 8124. What is the value of $$3^q− ­ q^3$$ ?

A. 0
B. 1
C. 2
D. 3
E. More than 3

8124 is divisible by 3. So Smallest positive integer for q=1; 3-1=2 IMO C
_________________
Give +1 kudos if this answer helps..!!
Director  G
Joined: 20 Jul 2017
Posts: 550
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: q is the smallest positive integer for which 3^q is a factor of 8124.  [#permalink]

### Show Tags

Bunuel wrote:
q is the smallest positive integer for which $$3^q$$ is a factor of 8124. What is the value of $$3^q− ­ q^3$$ ?

A. 0
B. 1
C. 2
D. 3
E. More than 3

8124 = 3*2708 [2708 is not a multiple of 3]
--> 3^1 is the factor
--> q = 1

$$3^q− ­ q^3$$ = 3^1 - 1^3 = 3 - 1 = 2

IMO Option C

Pls Hit Kudos if you like the solution Re: q is the smallest positive integer for which 3^q is a factor of 8124.   [#permalink] 18 Jun 2019, 02:43
Display posts from previous: Sort by

# q is the smallest positive integer for which 3^q is a factor of 8124.  