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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
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If 3^x - 3^(x-1) = 162, then x(x-1)= a. 12 b. 16 c. 20 d. 30 [#permalink] New post 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
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 [#permalink] New post 19 Apr 2006, 20:51
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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 [#permalink] New post 19 Apr 2006, 23:28
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, 19:46, edited 1 time in total.
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 [#permalink] New post 19 Apr 2006, 23:38
now, i understand. :beat Thanks! OA is C
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 [#permalink] New post 20 Apr 2006, 05:32
Nope I think it shud be C... U mite what to recheck the workings!
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 [#permalink] New post 20 Apr 2006, 19:44
gmatacer wrote:
x = 5

so, x(x-1) = 40


Buddy, if x=5 then shouldn't

5 ( 5-1 ) be 20 and not 40. :idea:
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 [#permalink] New post 20 Apr 2006, 20:44
Late, but agree with C.
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 [#permalink] New post 20 Apr 2006, 22:16
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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 [#permalink] New post 21 Apr 2006, 07:03
gmatacer wrote:
x = 5

so, x(x-1) = 40


buddy, this silly mistakes will kill you.
  [#permalink] 21 Apr 2006, 07:03
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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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