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# q is the smallest positive integer for which

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Manager
Joined: 07 Jun 2017
Posts: 174
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
q is the smallest positive integer for which  [#permalink]

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06 Nov 2017, 21:21
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:22) correct 24% (01:19) wrong based on 54 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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Re: q is the smallest positive integer for which  [#permalink]

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06 Nov 2017, 23:08
Sum of digits of 8124 = 8+1+2+4 = 15, so its definitely divisible by 3. Thus smallest positive integer value of q is 1 (3^1 = 3 is divisible by 8124).

Put q =1 in given: 3^q - q^3 = 3^1 - 1^3 = 3-1 = 2

Re: q is the smallest positive integer for which &nbs [#permalink] 06 Nov 2017, 23:08
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