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

 It is currently 21 Jun 2018, 10:48

### 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
Your Progress

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 (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46264
If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ? [#permalink]

### Show Tags

31 Jul 2017, 23:16
00:00

Difficulty:

25% (medium)

Question Stats:

77% (00:45) correct 23% (01:02) wrong based on 121 sessions

### HideShow timer Statistics

If $$\frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2} = \frac{1}{36}$$, what is the value of n ?

A. -1
B. 0
C. 1
D. 2
E. 3

_________________
Director
Joined: 18 Aug 2016
Posts: 634
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ? [#permalink]

### Show Tags

31 Jul 2017, 23:36
Bunuel wrote:
If $$\frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2} = \frac{1}{36}$$ ?

A. -1
B. 0
C. 1
D. 2
E. 3

$$2^{(-n-1)} * 3^{(-n-1)} = 2^{-2} * 3^{-2}$$

$$-n-1 =-2$$
$$-n=-1$$
$$n=1$$

C
_________________

We must try to achieve the best within us

Thanks
Luckisnoexcuse

Director
Joined: 04 Dec 2015
Posts: 700
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ? [#permalink]

### Show Tags

31 Jul 2017, 23:38
Bunuel wrote:
If $$\frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2} = \frac{1}{36}$$, what is the value of n ?

A. -1
B. 0
C. 1
D. 2
E. 3

$$\frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2} = \frac{1}{36}$$

$$\frac{1}{3*2^n}*\frac{1}{2*3^n} = \frac{1}{2^2*3^2}$$

$$\frac{1}{3*2^n*2*3^n} = \frac{1}{2^2*3^2}$$

$$\frac{1}{2^{(n+1)}*3^{(n+1)}} = \frac{1}{2^2*3^2}$$

$$\frac{1}{2^{(n+1)}*3^{(n+1)}} = \frac{1}{2^2*3^2}$$

$$2^{(n+1)} = 2^2$$

$$n + 1 = 2$$ $$=> n = 2-1 = 1$$

$$3^{(n+1)} = 3^2$$

$$n + 1 = 2$$ $$=> n = 2-1 = 1$$

Therefore $$n = 1$$

Answer (C)...
Manager
Joined: 03 May 2017
Posts: 108
If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ? [#permalink]

### Show Tags

01 Aug 2017, 15:40
By just dropping the numerators down. We see that we get the 1/ (36)^(n)^2 = 1/36, n=1. C
Senior Manager
Joined: 19 Oct 2012
Posts: 342
Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35
GMAT 2: 710 Q50 V38
GPA: 3.81
WE: Information Technology (Computer Software)
Re: If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ? [#permalink]

### Show Tags

01 Aug 2017, 21:31
We need 36 in denominator of LHS such that it equals the RHS. It can be only gotten when the value of n = 1. Hence C.
_________________

Citius, Altius, Fortius

SC Moderator
Joined: 22 May 2016
Posts: 1757
If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ? [#permalink]

### Show Tags

02 Aug 2017, 08:56
Bunuel wrote:
If $$\frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2} = \frac{1}{36}$$, what is the value of n ?

A. -1
B. 0
C. 1
D. 2
E. 3

$$\frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2} = \frac{1}{36}$$

$$\frac{1}{2^{n}3^{1}}*\frac{1}{3^{n}2^{1}} = \frac{1}{6^{2}}$$

Different base, same exponent rule: $$a^{n}*b^{n} = (ab)^{n}$$. Combine $$2^{n}$$ * $$3^{n}$$ (=$$6^{n}$$), as well as $$2^1$$ * $$3^1$$ (=$$6^1$$)

$$\frac{1}{6^{n}6^{1}} = \frac{1}{6^{2}}$$

$$\frac{6^{(-n)}}{6^{1}} = 6^{(-2)}$$

$$6^{(-n-1)} = 6^{(-2)}$$

$$-n - 1 = -2$$
$$n = 1$$

Answer C
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

CEO
Joined: 12 Sep 2015
Posts: 2567
Location: Canada
Re: If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ? [#permalink]

### Show Tags

05 Oct 2017, 12:26
Top Contributor
Bunuel wrote:
If $$\frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2} = \frac{1}{36}$$, what is the value of n ?

A. -1
B. 0
C. 1
D. 2
E. 3

Given: $$\frac{2^{(-n)}}{3}*\frac{3^{(-n)}}{2}=\frac{1}{36}$$

On the left side of this equation, let's multiply the numerators together, and then we'll multiply the denominators.

NUMERATORS:
$$2^{-n}$$ x $$3^{-n}$$ = $$6^{-n}$$

DENOMINATORS:
3 x 2 = 6

So, when we simplify the left side of the equation, we get: $$\frac{6^{(-n)}}{6} = \frac{1}{36}$$

From here, we can multiply both sides by 6 to get: $$6^{(-n)} = \frac{1}{6}$$

Next, recognize that $$\frac{1}{6} = 6^{(-1)}$$

So, we can write: $$6^{(-n)} = 6^{(-1)}$$

From this, we can conclude that -n = -1, which means n = 1

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Re: If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ?   [#permalink] 05 Oct 2017, 12:26
Display posts from previous: Sort by

# If (2^(-n)/3)(3^(-n)/2) = 1/36, what is the value of n ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.