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Is 3^n > 1,000? (1) 3^(n−2) < 500 (2) 3^n = 3^(n+1) − 486

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Manager
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Joined: 06 Jul 2013
Posts: 61
Location: United States
GMAT 1: 720 Q49 V38
Is 3^n > 1,000? (1) 3^(n−2) < 500 (2) 3^n = 3^(n+1) − 486  [#permalink]

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New post 08 Jul 2018, 18:43
1
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (02:35) correct 24% (02:08) wrong based on 39 sessions

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Is 3^n > 1,000?

(1) 3^(n−2) < 500
(2) 3^n = 3^(n+1) − 486
Manager
Manager
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Joined: 22 Jun 2017
Posts: 71
Location: Brazil
GMAT 1: 600 Q48 V25
GPA: 3.5
WE: Engineering (Energy and Utilities)
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Re: Is 3^n > 1,000? (1) 3^(n−2) < 500 (2) 3^n = 3^(n+1) − 486  [#permalink]

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New post 08 Jul 2018, 19:28
1
Option B

\(3^1 = 3\)
\(3^2 = 9\)
\(3^3 = 27\)
\(3^4 = 81\)
\(3^5 = 243\)
\(3^6 = 729\)
\(3^7 = 2187\)

(1) \(3^{n−2} < 500\) >> Not Sufficient

- If n=3:

\(3^{3−2} = 3\) < 500
\(3^3 = 27\) < 1000

- If n = 7:

\(3^{7−2} = 243\) < 500
\(3^7 = 2187\) > 1000



(2) \(3^{n} = 3^{n+1} − 486\) >> Sufficient

\(3^5 = 243\)
\(3^6 = 729\)

729 - 243 = 486

Hence, n = 5
VP
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Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: Is 3^n > 1,000? (1) 3^(n−2) < 500 (2) 3^n = 3^(n+1) − 486  [#permalink]

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New post 08 Jul 2018, 22:38
1
TippingPoint93 wrote:
Is 3^n > 1,000?

(1) 3^(n−2) < 500
(2) 3^n = 3^(n+1) − 486


Question stem , Is \(3^n > 1,000\)? (Y/N)

St1:
\(3^{n−2} < 500\)
Or,\(\frac{3^n}{3^2}\)<\(500\)
Or, \(3^n<4500\)
Clearly insufficient since \(3^n\) could be \(<1000\) and \(>1000\) too.

St2:-
\(3^n = 3^{n+1} − 486\)
Or,\(3^{n+1}-3^{n}=486\)
Or, \(3^n*(3-1)=486\)
Or, \(3^n=\frac{486}{2}=243<1000\)
Sufficient.
Ans. (B)
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PKN

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Re: Is 3^n > 1,000? (1) 3^(n−2) < 500 (2) 3^n = 3^(n+1) − 486   [#permalink] 08 Jul 2018, 22:38
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