It is currently 18 Nov 2017, 01:41

### 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

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

Location: Russia
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)=?

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

CEO
Joined: 29 Mar 2007
Posts: 2553

Kudos [?]: 527 [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.

Kudos [?]: 527 [1], given: 0

Manager
Joined: 02 Mar 2008
Posts: 205

Kudos [?]: 53 [0], given: 1

Concentration: Finance, Strategy
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

Kudos [?]: 53 [0], given: 1

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1852

Kudos [?]: 2707 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
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

Kudos [?]: 2707 [0], given: 193

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10111

Kudos [?]: 3505 [0], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
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 Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

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

Kudos [?]: 3505 [0], given: 173

Re: If 3 x - 3 x-1 = 162 , then x(x-1)=   [#permalink] 16 Jan 2015, 00:17
Display posts from previous: Sort by