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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: 128
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Kudos [?]: 6 [0], given: 0

If 3^x - 3^(x-1) = 162, then x(x-1)= a. 12 b. 16 c. 20 d. 30 [#permalink]  19 Apr 2006, 20:47
If 3^x - 3^(x-1) = 162, then x(x-1)=

a. 12

b. 16

c. 20

d. 30

e. 81
Director
Joined: 04 Jan 2006
Posts: 926
Followers: 1

Kudos [?]: 16 [0], given: 0

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..
VP
Joined: 07 Nov 2005
Posts: 1132
Location: India
Followers: 3

Kudos [?]: 28 [0], given: 1

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, 19:46, edited 1 time in total.
Manager
Joined: 08 Feb 2006
Posts: 128
Followers: 1

Kudos [?]: 6 [0], given: 0

now, i understand. Thanks! OA is C
VP
Joined: 29 Apr 2003
Posts: 1405
Followers: 2

Kudos [?]: 18 [0], given: 0

Nope I think it shud be C... U mite what to recheck the workings!
VP
Joined: 07 Nov 2005
Posts: 1132
Location: India
Followers: 3

Kudos [?]: 28 [0], given: 1

gmatacer wrote:
x = 5

so, x(x-1) = 40

Buddy, if x=5 then shouldn't

5 ( 5-1 ) be 20 and not 40.
Senior Manager
Joined: 08 Sep 2004
Posts: 258
Location: New York City, USA
Followers: 1

Kudos [?]: 9 [0], given: 0

Late, but agree with C.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

3^x - (3^x)(1/3) = 162
3^x (1-1/3) = 162
3^x = 243
x = 5

x(x-1) = 5*4 = 20
Senior Manager
Joined: 05 Jan 2006
Posts: 383
Followers: 1

Kudos [?]: 29 [0], given: 0

gmatacer wrote:
x = 5

so, x(x-1) = 40

buddy, this silly mistakes will kill you.
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