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djsir007: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sun Apr 15, 2007 2:48 pm

by djsir007 » Wed Apr 18, 2007 3:58 pm

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

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81

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Source: Beat The GMAT — Problem Solving | Wed Apr 18, 2007 3:58 pm

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

Re: GMATPrep

by jayhawk2001 » Wed Apr 18, 2007 8:14 pm

djsir007 wrote:3^x-3^x-1=162, then x(x-1)=

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81

I think this was posted in a recent thread.

3^(x-1) [ 3 - 1] = 162
3^(x-1) = 81 = 3^4
x-1 = 4

x(x-1) = 20

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Thu Apr 19, 2007 1:50 am

Discussed in an earlier post!

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scoutkb: Senior | Next Rank: 100 Posts; Posts: 53; Joined: Mon Feb 05, 2007 4:26 am

by scoutkb » Thu Apr 19, 2007 2:39 am

Can you please explain how 3^X becomes [ 3 - 1] ? Thanks

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djsir007: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sun Apr 15, 2007 2:48 pm

by djsir007 » Thu Apr 19, 2007 3:00 am

Without going through every post, how are we supposed to find them without reposting?

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8135; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Nov 12, 2018 7:29 am

djsir007 wrote:3^x-3^x-1=162, then x(x-1)=

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81

We can simplify the left side of the equation by factoring out a common 3^x from both terms, and then factor 162 as 3^4 * 2^1. Then we have:

3^x - 3^x * 3^-1 = 3^4 * 2^1

3^x(1 - 3^-1) = 3^4 * 2^1

On the left side, note that the expression 1 - 3^-1 = 1 - â…“ = â…”. We now have:

3^x(2/3) = 3^4 * 2^1

3^x = (3^4 * 2)(3/2)

3^x = 3^4 *3

3^x = 3^5

x = 5

So, x(x-1) = 5(4) = 20.

Alternate Solution:

Note that 3^x = 3 * 3^(x - 1). Then the left hand side of the equation becomes:

3^x - 3^(x - 1) = 3 * 3^(x - 1) - 3^(x - 1)

Let's factor the common 3^(x - 1):

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

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

3^(x - 1)(2) = 162

3^(x - 1) = 81

3^(x - 1) = 3^4

x - 1 = 4

x = 5

Then, x(x - 1) = 20.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Nov 13, 2018 10:28 am

Hi All,

We're told that 3^(X) - 3^(X-1) = 162. We're asked for the value of then (X)(X-1). This question can be solved rather easily with a bit of 'brute force' arithmetic.

Since we're dealing with 'powers of 3', let's map out the first several values:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243

We're subtracting two consecutive powers of 3 and ending up with 162. Looking at the list so far, we have an obvious 'pair' of values that fits what we're looking for:

3^5 and 3^4
243 - 81 = 162

Thus, X = 5 and the answer to the question is (5)(5-1) = 20

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Tue Nov 13, 2018 12:52 pm

djsir007 wrote:3^x-3^(x-1)=162, then x(x-1)=

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81

\[? = x\left( {x - 1} \right)\]
\[\left. \begin{gathered}
{3^x} - {3^{x - 1}} = {3^{x - 1}}\left( {3 - 1} \right)\,\,\, \hfill \\
162 = 2 \cdot 81 = 2 \cdot {3^4} \hfill \\
\end{gathered} \right\}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{stem}}} \,\,\,\,\,\,\,{3^{x - 1}} = {3^4}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{3}}\,\, \notin \,\,\left\{ {0,1, - 1} \right\}} \,\,\,\,\,\,\,x - 1 = 4\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 20\,\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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