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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
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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08 Jul 2018, 18:43
1
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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
Joined: 22 Jun 2017
Posts: 71
Location: Brazil
GMAT 1: 600 Q48 V25
GPA: 3.5
WE: Engineering (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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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
Status: Learning stage
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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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)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
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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# Is 3^n > 1,000? (1) 3^(n−2) < 500 (2) 3^n = 3^(n+1) − 486

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