Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Jul 2014, 23:27

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 14 Apr 2010
Posts: 5
Followers: 0

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

If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ? [#permalink] New post 16 Apr 2010, 17:41
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

94% (01:59) correct 6% (03:00) wrong based on 32 sessions
If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ?

A. 17
B. 18
C. 34
D. 35
E. 36
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18663
Followers: 3228

Kudos [?]: 22128 [0], given: 2595

Re: Please help with this question (number properties, exponents [#permalink] New post 17 Apr 2010, 07:17
Expert's post
shahany wrote:
I have a feeling I am missing something obvious, but I cannot figure out how to quickly calculate the answer to this:

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

a) 17
b) 18
c) 34
d) 35
3) 36

Thank you!


Long way:
(\frac{1}{5})^m*(\frac{1}{4})^{18}= \frac{1}{2*10^{35}} --> \frac{1}{5^m}*\frac{1}{2^{36}}= \frac{1}{2*2^{35}*5^{35}} --> \frac{1}{5^m}*\frac{1}{2^{36}}= \frac{1}{2^{36}*5^{35}} --> \frac{1}{5^m}= \frac{1}{5^{35}} --> m=35.

Answer: D.

Short way:
(\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*10^{35}} --> \frac{1}{5^m}* (\frac{1}{4})^{18} = \frac{1}{2*2^{35}*5^{35}} --> as there are only integers in the answer choices then we can concentrate only on the power of 5: they should be equal on both sides --> m=35.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 14 Apr 2010
Posts: 5
Followers: 0

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

Re: Please help with this question (number properties, exponents [#permalink] New post 17 Apr 2010, 18:50
Very helpful - thank you! I need to brush up on my properties...
Senior Manager
Senior Manager
avatar
Joined: 24 Jul 2009
Posts: 298
Followers: 2

Kudos [?]: 64 [0], given: 0

GMAT Tests User
Re: How do you solve this? [#permalink] New post 14 May 2010, 06:49
vannbj wrote:
If (\frac{1}{5})^m (\frac{1}{4})^1^8 = \frac{1}{(2(10)^3^5} then m =

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


IMHO D

(1/5^m) (1/2^36) = 1/(2 * 2^35 * 2^35)
(1/5^m) (1/2^36) = 1/(2^36 * 2^35)
m= 35
Manager
Manager
avatar
Joined: 16 Feb 2010
Posts: 175
Followers: 2

Kudos [?]: 10 [0], given: 10

GMAT Tests User
Re: How do you solve this? [#permalink] New post 14 May 2010, 10:38
indeed, m=35 , option D is the answer.
Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GMAT 1: 710 Q49 V38
GMAT 2: 660 Q V
GPA: 3.64
WE: Accounting (Accounting)
Followers: 0

Kudos [?]: 50 [0], given: 74943

Re: Exponents & Fractions [#permalink] New post 24 Jul 2010, 02:52
Ah, I got it.

rewrite for simplicity:
5^{-m} * 4^{-18} = 2^{-1} * 10^{-35}

Divide both sides by 2 (ie. multiply by 2^(-1)) and split up the term on the RHS:
2 * 5^{-m} * 2^{-18} * 2^{-18} = 2^{-35} * 5^{-35}

Group the term on the LHS:
2 * 5^{-m} * 2^{-36} = 2^{-35} * 5^{-35}

And divide both sides by 2^(-36):
2 * 5^{-m} = 2 * 5^{-35}

Divide both sides by 2, and you're left with:
5^{-m} = 5^{-35}

and so m = 35
Veritas Prep GMAT Instructor
User avatar
Joined: 26 Jul 2010
Posts: 201
Followers: 91

Kudos [?]: 204 [0], given: 20

Re: Please help with this question (number properties, exponents [#permalink] New post 09 Sep 2010, 15:31
Nice work, everyone - I posted this on another thread today, too, and thought it was fitting that the next question I clicked on would use the same ideology so here it is, also:

For exponents, your core competencies are:

Multiplication (so you should look to factor addition/subtraction to set up an opportunity to multiply)
Finding common bases for multiplication and equations (which is what you need to use here to get the 10 in terms of 2 and 5)
Looking for patterns and number properties (units digit, positive/negative, etc.)


When you see exponent-based problems, the above skills are those that you should be looking for, and keeping those at the forefront of your mind will help you to make quick, efficient decisions on how to proceed.
_________________

Brian

Save $100 on live Veritas Prep GMAT Courses and Admissions Consulting

Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior Manager
User avatar
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 411
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Followers: 7

Kudos [?]: 107 [0], given: 50

Re: GMATPrep problem [#permalink] New post 03 Oct 2010, 18:36
TehJay wrote:
This was the first problem I got on my practice exam today and it totally threw me off. I couldn't for the life of me figure it out. I'm sure I'm just forgetting basic exponent rules, but how do you do it?


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

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

(1/5^m)(1/4^{18}) = (1/({2^{36}}*{5^{35}}))

Equating the powers of 5=> m=35 (D).
_________________

:good Support GMAT Club by putting a GMAT Club badge on your blog :thanks

Ms. Big Fat Panda
Ms. Big Fat Panda
User avatar
Status: Biting Nails Into Oblivion
Joined: 09 Jun 2010
Posts: 1855
Followers: 329

Kudos [?]: 1336 [0], given: 194

GMAT ToolKit User GMAT Tests User
Re: GMATPrep problem [#permalink] New post 03 Oct 2010, 18:54
TehJay wrote:
This was the first problem I got on my practice exam today and it totally threw me off. I couldn't for the life of me figure it out. I'm sure I'm just forgetting basic exponent rules, but how do you do it?


So you are given that \frac{1}{5^m} * \frac{1}{4^1^8} = \frac{1}{2*10^3^5}

Breaking down the prime factors to the bare levels we get:

LHS = \frac{1}{5^m} * \frac{1}{4^1^8} = \frac{1}{5^m} * \frac{1}{2^3^6} = \frac{1}{5^m * 2^3^6}

RHS = \frac{1}{2*10^3^5} = \frac{1}{2* (5*2)^3^5} = \frac{1}{2^3^6 * 5^3^5}

Thus m = 35.
Manager
Manager
User avatar
Joined: 08 Sep 2010
Posts: 237
Location: India
WE 1: 6 Year, Telecom(GSM)
Followers: 4

Kudos [?]: 67 [0], given: 21

GMAT Tests User
Re: Quant 600 level question [#permalink] New post 24 Oct 2010, 12:35
(1/5)^m (1/4)^18 = 1/2(10)^35

or, (1/5)^m (1/2)^36 =(1/2) * 1/(10)^35

or, (1/5)^m= 2^35 * {1/(10)^35}
or, (1/5)^m = (2/10)^35
or, (1/5)^m = (1/5)^35
Hence m =35.

Consider KUDOS if it is helpful to u.
Intern
Intern
User avatar
Joined: 13 May 2010
Posts: 26
Followers: 0

Kudos [?]: 7 [0], given: 13

GMAT ToolKit User
Re: Quant 600 level question [#permalink] New post 24 Oct 2010, 12:41
Thank you for responding, so when you say "or" at the beginning of each line are you illustrating successive steps in solving the question or showing alternative ways to find the solution?
_________________

"Effort only fully releases its reward after a person refuses to quit." - Napoleon Hill

If my post helped you in any way please give KUDOS!

Manager
Manager
User avatar
Joined: 20 Jul 2010
Posts: 52
Followers: 2

Kudos [?]: 23 [0], given: 51

GMAT Tests User
Re: Quant 600 level question [#permalink] New post 24 Oct 2010, 12:45
Given:

(\frac{1}{5})^m * (\frac{1}{2})^(36) = (\frac{1}{2}) * (\frac{1}{10})^(35))

Since, 10 = 2 * 5 and a^n * b^n = (ab)^n

==> (\frac{1}{5})^m * (\frac{1}{2})^(36) = (\frac{1}{2}) * (\frac{1}{2})^(35) *(\frac{1}{5})^(35)

==> Cancelling (\frac{1}{2})^(36) on both sides gives m = 35
_________________

Cheers!
Ravi


If you like my post, consider giving me some KUDOS !!!

Intern
Intern
User avatar
Joined: 13 May 2010
Posts: 26
Followers: 0

Kudos [?]: 7 [0], given: 13

GMAT ToolKit User
Re: Quant 600 level question [#permalink] New post 24 Oct 2010, 12:55
Thank you! How do you cancel (1/2)^36 on both sides?
_________________

"Effort only fully releases its reward after a person refuses to quit." - Napoleon Hill

If my post helped you in any way please give KUDOS!

Manager
Manager
User avatar
Joined: 03 Sep 2010
Posts: 75
Location: Israel
GMAT 1: 660 Q47 V34
GMAT 2: 670 Q48 V34
GPA: 3.2
WE: Operations (Non-Profit and Government)
Followers: 3

Kudos [?]: 25 [0], given: 2

Re: Solving exponents [#permalink] New post 14 Nov 2010, 14:47
Pepe wrote:
Can you help me with following question?

If (\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2(10)^{35}, what value has m?

A 17
B 18
C 34
D 35
E 36


(1/4)^18 = 1/4^18 = 1/2^36

1/2*10^35 = 1/2*2^35*10^35 = 1/2^36*5^35

(1/5)^m = 1/5^m

Thus:

1/5^m*2^36 = 1/2^36*5^m

The correct answer is D m=35
SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1695
Followers: 161

Kudos [?]: 32 [0], given: 0

Premium Member
Re: If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ? [#permalink] New post 18 Jul 2014, 23:35
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ?   [#permalink] 18 Jul 2014, 23:35
    Similar topics Author Replies Last post
Similar
Topics:
If (1/5)^m (1/4)^18 = 1/(2(10)^35), then m= 17 18 34 35 36 bsjames2 5 05 Jan 2008, 13:08
1/5)^m (1/4)^18 = 1/2(10)^35 what is m g1m2a3t406 2 28 Nov 2006, 01:39
1) if (1/5)^m * )1/4)^18 = 1/2(10)^35, then m=? 2) for every ankurkanwar 12 10 Nov 2006, 20:22
If (1/5)^m times (1/4)^18 = 1/(2(10^35)), then m = A) 17 B) diegmat 5 09 Oct 2006, 07:42
If (1/5)^m * (1/4)^18 = 1/2(10)^35, then m= A.17 B.18 gvogelei 3 25 Apr 2006, 04:14
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.