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# If 3^(x+2) –3^x=6^3(3^7)

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Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 432
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)

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25 Feb 2015, 05:33
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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
[Reveal] Spoiler: OA
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
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Location: Netherlands
GMAT Date: 02-11-2015
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25 Feb 2015, 05:37
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

Last edited by pacifist85 on 25 Feb 2015, 05:38, edited 1 time in total.
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25 Feb 2015, 05:37
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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

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25 Feb 2015, 21:58
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...

[Reveal] Spoiler:
A

Here's the proof:

IF...X = 10

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

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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: 1904 Re: If 3^(x+2) –3^x=6^3(3^7) [#permalink] ### Show Tags 28 Feb 2015, 04:30 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
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Re: If 3^{(x+2)}-3^{x}=6^{3}(3^{7}), what is the value of x? [#permalink]

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02 Sep 2015, 23:37
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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
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Re: If 3^{(x+2)}-3^{x}=6^{3}(3^{7}), what is the value of x? [#permalink]

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02 Sep 2015, 23:48
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
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15 Apr 2017, 03:32
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Re: If 3^(x+2) –3^x=6^3(3^7)   [#permalink] 15 Apr 2017, 03:32
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