GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 27 Jan 2020, 23:32

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

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

Hide Tags

Find Similar Topics 
Director
Director
User avatar
P
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 717
Location: United States (CA)
Age: 40
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: Q168 V169
WE: Education (Education)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 05 Apr 2016, 22:31
Attached is a visual that should help.
Attachments

Screen Shot 2016-04-05 at 10.29.41 PM.png
Screen Shot 2016-04-05 at 10.29.41 PM.png [ 123.7 KiB | Viewed 2270 times ]

Intern
Intern
avatar
Joined: 14 May 2016
Posts: 4
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 24 May 2016, 18:53
Can someone please explain where the 1/2^36 is coming from?
Marshall & McDonough Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1683
Location: India
GMAT ToolKit User
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 24 May 2016, 20:53
sahmedmartinez wrote:
Can someone please explain where the 1/2^36 is coming from?


(1/5)^m * (1/4)^18 = 1 / (2 * (10)^35)

= (1/5)^m * (1/2^2)^18 = 1/( 2* (2 * 5)^35)

Two formulas are used here:
1. (a^m)^n = a^(mn)
2. a^m * a^n = a^(m + n)

=(1/5)^m * (1/2^36) = 1/(2^36 * 5^35)
Director
Director
User avatar
V
Joined: 05 Mar 2015
Posts: 964
Reviews Badge
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 16 Dec 2016, 04:02
Tessa8 wrote:
If \(([1][/5]^m [1][/4]^(18) = [1][/2(10)^(35)]\) , then m = ?

a) 17
b) 18
c) 34
d) 35
e) 36

screenshot of question attached


(1/4)^18==[(1/2)^2]^18==(1/2)^36
also (1/10)^35==[1/(2*5)]^35

putting above both values in equation we get

(1/5)^m(1/2)^36=1/2*[1/(2*5)]^35
(1/5)^m(1/2)^36=[1/2]^36*(1/5)^35
cancelling 1/2^36 both sides
(1/5)^m=(1/5)^35

thus equating powers we get m=35

Ans D
Manager
Manager
User avatar
G
Status: Not Applying
Joined: 27 Apr 2009
Posts: 178
Location: India
Schools: HBS '14 (A)
GMAT 1: 730 Q51 V36
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 11 May 2017, 05:55
(1/5)^m * (1/4)^18 = 1/(2*(10)^35)

(1/5)^m * (1/2)^36 = 1/(2*(2*5)^35)

(1/5)^m * (1/2)^36 = 1/(2^36) * (1/5^35)

For the two sides of the equation to be true, the powers of each base should be the same.

=> m = 35
_________________
http://www.wizius.in
Better Prep. Better Scores. Better Schools

Guaranteed Admission to Top-50 MBA Programs
You either get-in or get your money-back.
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 727
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 11 May 2017, 06:40
domu904 wrote:
If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

A. 17
B. 18
C. 34
D. 35
E. 36


(1/5)^m * (1/4)^18 = 1/(2*(10)^35)
-> \(\frac{(1)}{(5^m*2^3^6)}=\frac{(1)}{(2^3^6*5^3^5)}\)
m = 35

Answer D
Manager
Manager
avatar
B
Joined: 16 Jan 2017
Posts: 59
GMAT 1: 620 Q46 V29
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 12 May 2017, 15:26
Pretty straight forward. M=35. I fel like asking for what r is would be more challenging. As it would require to realise that 2 is to the power of 36, so r=18. Great question though! So this is a low 600 level question?
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 727
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 13 May 2017, 04:04
vmelgargalan wrote:
Pretty straight forward. M=35. I fel like asking for what r is would be more challenging. As it would require to realise that 2 is to the power of 36, so r=18. Great question though! So this is a low 600 level question?


Yes it is a pretty straight forward question and hence below 600 level question...

You can just solve the question in mind. Will not take more than 20 seconds.. :)
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2806
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 15 May 2017, 17:32
1
domu904 wrote:
If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

A. 17
B. 18
C. 34
D. 35
E. 36


The negative exponent rule states: (1/a)^b can be re-expressed as a^(-b). Let’s flip all of the fractions using the negative exponent rule:

5^-m x 4^-18 = 2^-1 x 10^-35

5^-m x 2^-36 = 2^-1 x 2^-35 x 5^-35

5^-m x 2^-36 = 2^-36 x 5^-35

5^-m = 5^-35

m = 35

Answer: D
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
B
Joined: 21 Mar 2015
Posts: 8
GMAT ToolKit User
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 21 Aug 2017, 09:14
I feel the question is pretty straight forward but ans was incorrect in many of the docs floating.

My take was

Left hand side denominator : 5^M
Right hand side denominator: 10^35 implies 5^35 * 2^35
So
M=35
Senior Manager
Senior Manager
User avatar
D
Joined: 18 Jun 2018
Posts: 250
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 21 Aug 2018, 10:16
domu904 wrote:
If \((\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*(10)^{35}}\), then m = ?

A. 17
B. 18
C. 34
D. 35
E. 36


OA:D

\((\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*(10)^{35}}\)

\((5)^{-m} * (2)^{-2*18} = 2^{-36}*(5)^{-35}\)

\(5^{-m} * 2^{-36}-2^{-36}*(5)^{-35}=0\)

\(2^{-36}(5^{-m}-5^{-35})=0\)

\(5^{-m}=5^{-35}\)

\(-m=-35\)

\(m=35\)
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4234
Location: Canada
If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

Show Tags

New post 09 Aug 2019, 09:49
Top Contributor
domu904 wrote:
If \((\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*(10)^{35}}\), then m = ?

A. 17
B. 18
C. 34
D. 35
E. 36


Exponent property #1: \((\frac{a}{b})^k=\frac{a^k}{b^k}\)

Exponent property #2: \((b^x)^y = b^{xy}\)

Exponent property #3: \((ab)^x = a^xb^x\)


------------------------------------------------------
Given: \((\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*(10)^{35}}\)

Applying exponent property#1, we get: Given: \((\frac{1^m}{5^m})(\frac{1^{18}}{4^{18}}) = \frac{1}{2*(10)^{35}}\)

Simplify to get: Given: \((\frac{1}{5^m})(\frac{1}{4^{18}}) = \frac{1}{2*(10)^{35}}\)

ASIDE: To determine the value of m, we must rewrite both sides of the equation with similar base.
So, for the left side, we'll rewrite \(4\) as \(2^2\)
For the right side, we'll rewrite \(10\) as \(2 \times 5\)

We get: \((\frac{1}{5^m})(\frac{1}{(2^2)^{18}}) = \frac{1}{2*(2 \times 5)^{35}}\)

Applying exponent property#2, we get: \((\frac{1}{5^m})(\frac{1}{(2^{36}}) = \frac{1}{2*(2 \times 5)^{35}}\)

Applying exponent property#3, we get: \((\frac{1}{5^m})(\frac{1}{(2^{36}}) = \frac{1}{2*(2^{35})(5^{35})}\)

Since \(2*(2^{35} = 2^{36}\), we can write: \((\frac{1}{5^m})(\frac{1}{(2^{36}}) = \frac{1}{(2^{36})(5^{35})}\)

NOTE: Notice that I really didn't need to spend so much time working on the powers of 2, since the variable m was the exponent of 5.
Had I focused solely on the powers of 5, I could have answered the question MUCH faster.


That said, I wanted to show all of the exponent properties at work. :)

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Bot
If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?   [#permalink] 09 Aug 2019, 09:49

Go to page   Previous    1   2   [ 32 posts ] 

Display posts from previous: Sort by

If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne