GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Jun 2018, 08:31

### 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+2) – 3^x = (6^3)(3^7), what is the value of x?

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 423
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
If 3^(x+2) – 3^x = (6^3)(3^7), what is the value of x? [#permalink]

### Show Tags

25 Feb 2015, 06:33
2
6
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:14) correct 17% (01:59) wrong based on 121 sessions

### HideShow timer Statistics

If $$3^{(x+2)} –3^x=(6^3)(3^7)$$, what is the value of x?

A. 10

B. 11

C. 12

D. 13

E. 14
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 423
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: If 3^(x+2) – 3^x = (6^3)(3^7), what is the value of x? [#permalink]

### Show Tags

Updated on: 25 Feb 2015, 06:38
One step at a time...:

3^(x+2) –3^x = 6^3 (3^7)
3^(x+2) –3^x = 2^3 *3^3 *3^7
3^x (3^2-1) = 2^3* 3^3 *3^7
3^x* 2^3 = 2^3* 3^3* 3^7
3^x = (2^3*3^3*3^7) / 2^3
3^x = 3^10
x = 10

So, ANS A

Originally posted by pacifist85 on 25 Feb 2015, 06:37.
Last edited by pacifist85 on 25 Feb 2015, 06:38, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 46303
Re: If 3^(x+2) – 3^x = (6^3)(3^7), what is the value of x? [#permalink]

### Show Tags

25 Feb 2015, 06:37
3
1
pacifist85 wrote:
If 3^(x+2) –3^x=6^3(3^7) , what is the value of x?

A. 10

B. 11

C. 12

D. 13

E. 14

$$3^{(x+2)} - 3^x=6^3(3^7)$$

$$3^x*3^2 - 3^x=2^3*3^3*(3^7)$$

$$3^x(3^2 - 1)=8(3^{10})$$

$$3^x*8=8(3^{10})$$

$$3^x=3^{10}$$

x=10

_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11834
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If 3^(x+2) – 3^x = (6^3)(3^7), what is the value of x? [#permalink]

### Show Tags

25 Feb 2015, 22:58
Hi All,

This question involves Exponent rules and some Arithmetic. As pacifist85 and Bunuel have approached it, the "steps" are really just about re-organizing the values until you isolate the value of X. I'd likely approach it the same way under normal circumstances.

Here though, the answer choices ARE numbers, so one of them MUST be the value of X. If you're not comfortable with all of the necessary Exponent rules (in the abstract) just yet, then you can still get to the correct answer by TESTing THE ANSWERS.

I'm going to start with the "right side" of the equation, since it's all numbers:

(6^3)(3^7)

6^3 = (2^3)(3^3)

substituting that value in, we have....

(2^3)(3^3)(3^7) =
(8)(3^10)

So the "left side" must equal (8)(3^10)

Since we're dealing with (3^10), chances are that X isn't much bigger than maybe 10 or 11.

Let's TEST X = 11....

Plugging that into the "left-side", we get...

3^13 - 3^11

We can factor out 3^11, which gives us...

3^11(3^2 - 1) =
(3^11)(9-1) =
(3^11)(8)

This is close to what we're looking for, but is a little too BIG (we need (8)(3^10)), so X MUST be smaller. There's only one answer left...

Here's the proof:

IF...X = 10

3^12 - 3^10 =
3^10(3^2 - 1)
(3^10)(9 - 1)
(3^10)(8)

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!*********************** SVP Joined: 06 Nov 2014 Posts: 1888 Re: If 3^(x+2) – 3^x = (6^3)(3^7), what is the value of x? [#permalink] ### Show Tags 28 Feb 2015, 05:30 pacifist85 wrote: If 3^(x+2) –3^x=6^3(3^7) , what is the value of x? A. 10 B. 11 C. 12 D. 13 E. 14 Given that 3^(x+2) –3^x=6^3(3^7) So, 3^x[3^2 - 1] = 6^3 * 3^7 So, 3^x(8) = (2*3)^3 * 3^7 So, 3^x(8) = (2^3) * (3^3) (3^7) So, 3^x(8) = 8 * 3^10 So, x = 10 Hence option A. -- Optimus Prep's GMAT On Demand course for only$299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 553
GPA: 2.81
Re: If 3^(x+2) – 3^x = (6^3)(3^7), what is the value of x? [#permalink]

### Show Tags

03 Sep 2015, 00:37
1
3^(x+2) -3^x=6^3(3^7)

or,3^x(3^2) -3^x =6^3(3^7)
or,3^x(3^2 -1)=6^3(3^7)
or,3^x=$$\frac{(6^3 3^7)}{8}$$
or,3^x=$$\frac{(2^3 3^3 3^7)}{2^3}$$
or,3^x=3^3 3^7
or,3^x =3^10
0r,x=10

So the Correct Answer is A
_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Director
Joined: 21 May 2013
Posts: 649
Re: If 3^(x+2) – 3^x = (6^3)(3^7), what is the value of x? [#permalink]

### Show Tags

03 Sep 2015, 00:48
Bunuel wrote:
If $$3^{(x+2)}-3^{x}=6^{3}(3^{7})$$, what is the value of x?

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

Kudos for a correct solution.

3^x(3^2-1)=3^7*3^3*2^3
3^x(2^3)=3^10*2^3
x=10
Non-Human User
Joined: 09 Sep 2013
Posts: 7063
Re: If 3^(x+2) – 3^x = (6^3)(3^7), what is the value of x? [#permalink]

### Show Tags

13 May 2018, 23:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If 3^(x+2) – 3^x = (6^3)(3^7), what is the value of x?   [#permalink] 13 May 2018, 23:28
Display posts from previous: Sort by