Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 02:49

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 09 Apr 2006
Posts: 1
Location: Russia
Followers: 0

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

If 3 x - 3 x-1 = 162 , then x(x-1)= [#permalink]

### Show Tags

23 Apr 2008, 05:11
If 3x - 3x-1 = 162, then x(x-1)=?
CEO
Joined: 29 Mar 2007
Posts: 2562
Followers: 21

Kudos [?]: 453 [1] , given: 0

Re: Math question \ powers and equations [#permalink]

### Show Tags

23 Apr 2008, 05:29
1
KUDOS
stinger wrote:
If 3x - 3x-1 = 162, then x(x-1)=?

This one was kinda nasty. IM not the best with exponent problems

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

Factor out the 162.

3^x-3^(x-1)=3^4*2 ---> Divide by 3^4 --> 3^x/3^4 - 3^(x-1)/3^4 ---> 3^x-4 - 3^x-5 =2

Now from here I just plugged in a few numbers for X. You can see this wont be very tough b/c -3^x-5 in most cases is going to cancel out 3^x-4 and create a negative number.

Only when x=5 does 3^x-4- 3^x-5 =2. ---> 3^1 - 3^0 = 2.

so now 5(5-1) = 20.
Manager
Joined: 02 Mar 2008
Posts: 209
Concentration: Finance, Strategy
Followers: 1

Kudos [?]: 48 [0], given: 1

Re: Math question \ powers and equations [#permalink]

### Show Tags

23 Apr 2008, 06:24
3^x-3^(x-1)=3^(x-1)*(3-1) -> 3^(x-1) = 162/2 =81
->x=5
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 51

Kudos [?]: 2171 [0], given: 193

Re: If 3 x - 3 x-1 = 162 , then x(x-1)= [#permalink]

### Show Tags

15 Jan 2015, 22:04
$$3^x - 3^{(x-1)} = 162$$

$$3^x (1 - \frac{1}{3}) = 162$$

$$3^x * \frac{2}{3} = 162$$

$$3^x = 3^5$$

x = 5; x-1 = 4

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

Kindly press "+1 Kudos" to appreciate

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9120
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 445

Kudos [?]: 2873 [0], given: 169

Re: If 3 x - 3 x-1 = 162 , then x(x-1)= [#permalink]

### Show Tags

16 Jan 2015, 00:17
Hi All,

If you're not an expert at tougher exponent rule questions such as this, you can sometimes get to the answer with a bit of "brute force", even without knowing the exact exponent rules involved in the prompt. Here's how:

This question involves 3 raised to different "powers"; you can calculate them rather easily...

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243

3^X and 3^(X-1) are consecutive powers of 3.
We're told that 3^X - 3^(X-1) = 162, so we just need to find 2 consecutive multiples of 3 that differ by 162.

Notice how...
3^5 - 3^4 =
243 - 81 =
162

This is EXACTLY what we're looking for.

X = 5
(X-1) = 4

So....(X)(X-1) = (5)(4) = 20

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If 3 x - 3 x-1 = 162 , then x(x-1)=   [#permalink] 16 Jan 2015, 00:17
Similar topics Replies Last post
Similar
Topics:
3 For all numbers x, the function f is defined by f(x) = 3x + 1 and the 1 31 Aug 2015, 13:41
If x^2 - 5x + 1 = 0, the value of x^3 + 1/x^3 is... ? 9 28 Sep 2014, 19:20
|x+1| + |x+2| + | x-1|= 20 3 01 Aug 2013, 08:02
solution for X^3+Y^3+Z^3 2 14 Oct 2010, 17:35
1) Is x = 3? a) x = 1 OR x = 3 b) x = 2 OR x = 3 2 23 Aug 2010, 13:03
Display posts from previous: Sort by