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# q is the smallest positive integer for which

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Manager
Joined: 07 Jun 2017
Posts: 176

Kudos [?]: 90 [0], given: 59

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, 22:21
00:00

Difficulty:

15% (low)

Question Stats:

69% (01:12) correct 31% (01:16) wrong based on 29 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
[Reveal] Spoiler: OA

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Naveen
email: nkmungila@gmail.com
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Kudos [?]: 90 [0], given: 59

Senior Manager
Joined: 22 Aug 2013
Posts: 488

Kudos [?]: 161 [0], given: 271

Location: India
Re: q is the smallest positive integer for which [#permalink]

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07 Nov 2017, 00:08
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

Kudos [?]: 161 [0], given: 271

Re: q is the smallest positive integer for which   [#permalink] 07 Nov 2017, 00:08
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