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# If 3^x - 3^(x-1) = 162, then x(x-1)= a. 12 b. 16 c. 20 d. 30

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Manager
Joined: 08 Feb 2006
Posts: 124

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If 3^x - 3^(x-1) = 162, then x(x-1)= a. 12 b. 16 c. 20 d. 30 [#permalink]

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19 Apr 2006, 21:47
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If 3^x - 3^(x-1) = 162, then x(x-1)=

a. 12

b. 16

c. 20

d. 30

e. 81

Kudos [?]: 12 [0], given: 0

Director
Joined: 04 Jan 2006
Posts: 922

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19 Apr 2006, 21:51
C...
LHS>.
3^x - 3^(x-1)

==> 3^x - 3^(x) /3
==> 3^x(1-1/3) ==> 3^x * 2/3 ==> 2*3^(x-1)

RHS.. 162 = 3^4*2
lhs = rhs
x = 5
so 20..

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VP
Joined: 07 Nov 2005
Posts: 1115

Kudos [?]: 52 [0], given: 1

Location: India

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20 Apr 2006, 00:28
3^x - 3^(x-1) = 162
Now,
3^x - 3^x / 3 = 162

3^x ( 1 - 1/3) = 162

3^x = 162*3/2 = 243

=> x = 5;

So x(x-1) = 5 (5 -1) = 20

Hence C

Last edited by buzzgaurav on 20 Apr 2006, 20:46, edited 1 time in total.

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Manager
Joined: 08 Feb 2006
Posts: 124

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20 Apr 2006, 00:38
now, i understand. Thanks! OA is C

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VP
Joined: 29 Apr 2003
Posts: 1403

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20 Apr 2006, 06:32
Nope I think it shud be C... U mite what to recheck the workings!

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VP
Joined: 07 Nov 2005
Posts: 1115

Kudos [?]: 52 [0], given: 1

Location: India

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20 Apr 2006, 20:44
gmatacer wrote:
x = 5

so, x(x-1) = 40

Buddy, if x=5 then shouldn't

5 ( 5-1 ) be 20 and not 40.

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Senior Manager
Joined: 08 Sep 2004
Posts: 257

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Location: New York City, USA

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20 Apr 2006, 21:44
Late, but agree with C.

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GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5034

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Location: Singapore

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20 Apr 2006, 23:16
3^x - (3^x)(1/3) = 162
3^x (1-1/3) = 162
3^x = 243
x = 5

x(x-1) = 5*4 = 20

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Senior Manager
Joined: 05 Jan 2006
Posts: 381

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21 Apr 2006, 08:03
gmatacer wrote:
x = 5

so, x(x-1) = 40

buddy, this silly mistakes will kill you.

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21 Apr 2006, 08:03
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