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

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

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17 Jun 2019, 23:40
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Difficulty:

35% (medium)

Question Stats:

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

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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

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

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17 Jun 2019, 23:55
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.

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Re: q is the smallest positive integer for which 3^q is a factor of 8124.  [#permalink]

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18 Jun 2019, 00:26
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
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Re: q is the smallest positive integer for which 3^q is a factor of 8124.  [#permalink]

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18 Jun 2019, 02:43
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

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Re: q is the smallest positive integer for which 3^q is a factor of 8124.   [#permalink] 18 Jun 2019, 02:43
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