3^x - 3^x-1 = 162, what is x(x-1)? Ans: 20 : Quant Question Archive [LOCKED]
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# 3^x - 3^x-1 = 162, what is x(x-1)? Ans: 20

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3^x - 3^x-1 = 162, what is x(x-1)? Ans: 20 [#permalink]

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15 Jul 2006, 17:45
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

3^x - 3^x-1 = 162, what is x(x-1)?

Ans: 20
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15 Jul 2006, 18:29
shehreenquayyum wrote:
3^x - 3^x-1 = 162, what is x(x-1)?

Ans: 20

tricky question...
follow the link below. apparently this has been discussed before... they have the solutions aswell.

http://www.gmatclub.com/phpbb/viewtopic ... light=x+x1
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15 Jul 2006, 19:29
shehreenquayyum wrote:
3^x - 3^x-1 = 162, what is x(x-1)?

Ans: 20

This is not bad as it seems. Just think for a second.

SUPPOSE, x=5, then
3^x - 3^(x-1) is same as 3^5 - 3^4.
This, in turn, is same as [(3*3^4) - 3^4], which is [3^4 * 2].

Similarly, 3^x - 3^(x-1) is same as:

[3^(x-1)] * 2, which is 162
thus
[3^(x-1)] = 81

thus
3^(x-1) = 3^4

thus, (x-1) = 4, which means x = 5.

If x = 5, then x(x-1) = 5*4 = 20
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15 Jul 2006, 19:50
Shorter approach:

3^x - 3^(x-1) = 162
3^x - (3^x)/3 = 162
(3^x)(1-1/3) = 162
(3^x)(2/3) = 162
(3^x)/3 = 81
3^(x-1) = 3^4
x-1 = 4
x= 5
Now
x(x-1) = 5*4 = 20
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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16 Jul 2006, 06:01
Ahhh....I get it! Thank you both for the detailed response!
16 Jul 2006, 06:01
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