Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 22:01

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 05 Dec 2011
Posts: 10
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 36 [1] , given: 11

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

### Show Tags

09 Feb 2012, 14:17
1
KUDOS
32
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

79% (01:46) correct 21% (00:59) wrong based on 1050 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7740

Kudos [?]: 106262 [22] , given: 11618

Re: If (1/5)^{m} (1/4)^{18} = \frac{1}{2(10)^{35} [#permalink]

### Show Tags

09 Feb 2012, 14:24
22
KUDOS
Expert's post
25
This post was
BOOKMARKED
If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ?

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

Step by step:
$$(\frac{1}{5})^m*(\frac{1}{4})^{18}= \frac{1}{2*10^{35}}$$ --> $$\frac{1}{5^m}*\frac{1}{2^{36}}= \frac{1}{2*2^{35}*5^{35}}$$ --> $$\frac{1}{5^m}*\frac{1}{2^{36}}= \frac{1}{2^{36}*5^{35}}$$ --> $$\frac{1}{5^m}= \frac{1}{5^{35}}$$ --> $$m=35$$.

Shortcut approach:
$$(\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*10^{35}}$$ --> $$\frac{1}{5^m}* (\frac{1}{4})^{18} = \frac{1}{2*2^{35}*5^{35}}$$ --> 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 --> $$m=35$$.

_________________
Intern
Joined: 05 Dec 2011
Posts: 10
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 36 [0], given: 11

Re: If (1/5)^{m} (1/4)^{18} = \frac{1}{2(10)^{35} [#permalink]

### Show Tags

09 Feb 2012, 14:31
Thanks Bunnuel for the quick reply. So does that mean 1^m will always equal to 1? Because I was assuming m could be negative integer.
Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7740

Kudos [?]: 106262 [1] , given: 11618

Re: If (1/5)^{m} (1/4)^{18} = \frac{1}{2(10)^{35} [#permalink]

### Show Tags

09 Feb 2012, 14:39
1
KUDOS
Expert's post
domu904 wrote:
Thanks Bunnuel for the quick reply. So does that mean 1^m will always equal to 1? Because I was assuming m could be negative integer.

Yes, 1^m=1, for any m.
_________________
Intern
Joined: 27 Mar 2013
Posts: 1
Followers: 0

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

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

### Show Tags

02 Apr 2013, 07:58
steliossb wrote:
hey guys

this is the first question i got from the prep program and i am having trouble figuring it out:

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

find M

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

any help will greatly be appreciated

4=2^2 => (1/2)^36*5^m=2*10^35

in order to get 10^35 you have to have 2^35*5^35. since we have 2^36, 2 will be left and the answer will be 2*10^35
Intern
Status: Yes. It was I who let the dogs out.
Joined: 03 Dec 2012
Posts: 42
H: B
GMAT Date: 08-31-2013
Followers: 1

Kudos [?]: 42 [1] , given: 27

Re: I got this question on a Mock GMAT and I hate it so much [#permalink]

### Show Tags

10 Aug 2013, 19:53
1
KUDOS
sokenyou wrote:
(1/5)^m * (1/4)^18 = 1/2(10)^35

What is the value of m?

1. 17
2. 18
3. 34
4. 35
5. 36

I just don't get how to solve it using backsolving or picking numbers or something that is quick....I just hate it...

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

$$(5^-1)^m * (2^-2)^18 = (2^-1 * 2^-35 * 5^-35)$$

$$5^(-m) * 2^(-36) = 2^(-36) * 5^(-35)$$

$$5^(-m) = * 5^(-35)$$

$$- m = -35$$

$$m = 35$$

Since you are asked to find the power of 5 i.e. m, you should be looking for 5 on the right hand side of the equation raised to some power. There is 10 on the denominator which is 2 * 5 raised to the power 35. The rest of the solution is rearranging to compare the powers of 5 on both sides.
_________________

Yogi Bhajan: If you want to learn a thing, read that; if you want to know a thing, write that; if you want to master a thing, teach that.
This message transmitted on 100% recycled electrons.

Last edited by hb on 10 Aug 2013, 20:07, edited 1 time in total.
Intern
Status: Preparation
Joined: 03 Apr 2012
Posts: 7
Location: India
GMAT 1: 700 Q50 V34
GPA: 2.9
Followers: 0

Kudos [?]: 6 [0], given: 10

Re: I got this question on a Mock GMAT and I hate it so much [#permalink]

### Show Tags

11 Aug 2013, 01:32
In these types of problems we can compare(qualize) the indices of the comparable variables.

a^m = a^n implies m=n

So the only term on the left hand side with five in it is 1/5 ^m
The only term on the right hand side with 5 in it is (1/10)^35

as 1/10 contains only one five so the resultant power on the right hand side is (1/5)^35

So equalizing comparable terms on both sides we get m = 35
Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7740

Kudos [?]: 106262 [0], given: 11618

### Show Tags

13 Mar 2014, 08:36
chrish06 wrote:
How can I approach this question? Why is the answer 'D'?

If (1/5)m(1/4)18 = 1/2(10)35, m?
a. 18
b. 17
c. 21
d. 35
e. 3

Merging similar topics. Please refer to the solutions above and ask if anything remains unclear.

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

_________________
Moderator
Joined: 01 Sep 2010
Posts: 3175
Followers: 858

Kudos [?]: 7316 [0], given: 1065

Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

### Show Tags

11 Jul 2014, 09:44
I came across with this question lately during the test prep in the latest stage and I think is not a sub 600 level ??

someone can confirm me this impression ??

thanks
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7740

Kudos [?]: 106262 [1] , given: 11618

Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

### Show Tags

11 Jul 2014, 11:21
1
KUDOS
Expert's post
carcass wrote:
I came across with this question lately during the test prep in the latest stage and I think is not a sub 600 level ??

someone can confirm me this impression ??

thanks

I think it's at most 620-630 level question.
_________________
Moderator
Joined: 01 Sep 2010
Posts: 3175
Followers: 858

Kudos [?]: 7316 [0], given: 1065

Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

### Show Tags

11 Jul 2014, 12:44
weird...final score 740......anyhow

Thanks guy for confirming
_________________
Affiliations: Oracle certified java programmer , adobe certified developer
Joined: 14 Jul 2013
Posts: 124
GMAT Date: 02-12-2015
GPA: 3.87
WE: Programming (Telecommunications)
Followers: 1

Kudos [?]: 23 [0], given: 37

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

### Show Tags

23 Aug 2014, 23:26
Just need to break the equations a bit:
1. (1/5)^m (1/4)^18 = (1/5)^m (1/2)^36 = so now we have 36 powers of 1/2 and need to find for 5 , what we need is the relation between this equation and other so we will try to sync them up.
2. 1/(2(10)^35) = 1/(2(2*5)^35 = so now we have 36 powers of 2 and 35 powers of 5
Finally what we need is how many powers of 5?? its 35 , OA:D.
Hope its clear
_________________

IF IT IS TO BE , IT IS UP TO ME

Manager
Joined: 20 Jul 2012
Posts: 166
Location: India
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 34 [0], given: 559

Re: If (1/5)^m(1/4)^18=1/2(10)^35, then m = [#permalink]

### Show Tags

31 Aug 2014, 05:33
GMATcrusher wrote:
Does anyone know how to solve this practice question from the free GMAT Pill practice set?

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

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

Firstly simplify the equation on the left and bring it in the form of Prime Numbers as

(1/5)^m * (1/2)^36 as (1/4)^18= (1/2^2)^18
Equation on right-
1/2 *( 1/10)^35
= 1/2 * (1/2)^35 * (1/5)^35
=(1/2)^36 * (1/5)^35

Comparing left and right side (1/2)^36 is same on both sides . For equation to be true (1/5)^35 should equal to (1/5)^m
which is possible when m=35
_________________

Preparing for another shot...

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 51

Kudos [?]: 2172 [11] , given: 193

Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

### Show Tags

08 Sep 2014, 00:41
11
KUDOS
4
This post was
BOOKMARKED
$$\frac{1}{5^m} * \frac{1}{4^{18}} = \frac{1}{2*10^{35}}$$

Reciprocal the complete equation; Get rid of the fraction

$$5^m * 2^{18*2} = 2 * 2^{35} * 5^{35}$$

$$5^m * 2^{36} = 2^{36} * 5^{35}$$

m = 35

_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 15 Oct 2014
Posts: 7
Followers: 0

Kudos [?]: 7 [0], given: 27

### Show Tags

02 Feb 2015, 14:31
Hey!

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

m= 35

This was a problem solving question but i do not understand how they got m=35!

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4041
Followers: 1418

Kudos [?]: 6785 [1] , given: 84

### Show Tags

02 Feb 2015, 15:16
1
KUDOS
Expert's post
annaleroy wrote:
Hey!

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

m= 35

This was a problem solving question but i do not understand how they got m=35!

Dear annaleroy,
My friend, perhaps you are new to the GC forum, but you have committed a classic no-no. You see, this very math question has been posted many times before, for example:
if-1-5-m-1-4-18-frac-127321.html
1-5-m-1-4-18-1-2-10-35-what-is-m-25136.html
if-1-5-m-1-4-18-1-2-10-35-then-m-121477.html
if-1-5-m-1-4-18-1-2-10-35-then-m-92796.html
Rather than starting a brand new thread, users are supposed to find the already existing threads that discuss the same question. It may be that you will find your answer already posted there, and if you don't, you can ask your question as part of that thread, thus enhancing that discussion, rather than starting a new and separate discussion.

In all likelihood, Bunuel will merge this thread into one of these pre-existing threads.

Does all this make sense?
Mike
_________________

Mike McGarry
Magoosh Test Prep

Intern
Joined: 15 Oct 2014
Posts: 7
Followers: 0

Kudos [?]: 7 [0], given: 27

### Show Tags

02 Feb 2015, 15:18
mikemcgarry wrote:
annaleroy wrote:
Hey!

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

m= 35

This was a problem solving question but i do not understand how they got m=35!

Dear annaleroy,
My friend, perhaps you are new to the GC forum, but you have committed a classic no-no. You see, this very math question has been posted many times before, for example:
if-1-5-m-1-4-18-frac-127321.html
1-5-m-1-4-18-1-2-10-35-what-is-m-25136.html
if-1-5-m-1-4-18-1-2-10-35-then-m-121477.html
if-1-5-m-1-4-18-1-2-10-35-then-m-92796.html
Rather than starting a brand new thread, users are supposed to find the already existing threads that discuss the same question. It may be that you will find your answer already posted there, and if you don't, you can ask your question as part of that thread, thus enhancing that discussion, rather than starting a new and separate discussion.

In all likelihood, Bunuel will merge this thread into one of these pre-existing threads.

Does all this make sense?
Mike

Hi Mike,

Yes! Thank you very much! Won't be doing this going forward!! Thank you!
Current Student
Joined: 24 Dec 2014
Posts: 128
Location: India
GMAT 1: 700 Q47 V39
GMAT 2: 790 Q51 V50
GPA: 3.65
WE: Operations (Energy and Utilities)
Followers: 17

Kudos [?]: 120 [1] , given: 10

### Show Tags

02 Feb 2015, 15:23
1
KUDOS
annaleroy wrote:
Hey!

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

m= 35

This was a problem solving question but i do not understand how they got m=35!

Pretty Straight forward. forget about the LHS and re arrange the R.H.S to match the LHS fractions

RHS:

1/(2(2*5)^35)

1/(2^36*5^35)

1/(4^18 * 5^35) ...... [ 2^36 is same as saying (2^2)^18]

break the denominator as per the LHS

(1/4)^18 * (1/5)^35

and Whalaa you have Mr. m
Manager
Joined: 26 Feb 2015
Posts: 127
Followers: 0

Kudos [?]: 15 [0], given: 43

Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

### Show Tags

04 Mar 2015, 06:17
devilbart wrote:
annaleroy wrote:
Hey!

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

m= 35

This was a problem solving question but i do not understand how they got m=35!

Pretty Straight forward. forget about the LHS and re arrange the R.H.S to match the LHS fractions

RHS:

1/(2(2*5)^35)

1/(2^36*5^35)

1/(4^18 * 5^35) ...... [ 2^36 is same as saying (2^2)^18]

break the denominator as per the LHS

(1/4)^18 * (1/5)^35

and Whalaa you have Mr. m

I got a few stupid questions:

1) What is RHS / LHS?
2) How come you can go from 4^18 --> 2^36 but not from, say 5^4 --> 10^2? When does the "divide by 2 and multiply by 2 rule apply"?

3) 1/5^m - How do I get rid of the ^m in the numerator? I mean, isnt 1/5^m $$1^m/5^m?$$
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4515
Followers: 394

Kudos [?]: 4200 [0], given: 109

Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

### Show Tags

04 Mar 2015, 06:27
erikvm wrote:
devilbart wrote:
annaleroy wrote:
Hey!

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

m= 35

This was a problem solving question but i do not understand how they got m=35!

Pretty Straight forward. forget about the LHS and re arrange the R.H.S to match the LHS fractions

RHS:

1/(2(2*5)^35)

1/(2^36*5^35)

1/(4^18 * 5^35) ...... [ 2^36 is same as saying (2^2)^18]

break the denominator as per the LHS

(1/4)^18 * (1/5)^35

and Whalaa you have Mr. m

I got a few stupid questions: no doubts are stupid and its always better to clear your basic doubt then to remain with them

hi erik,

1) What is RHS / LHS?
RHS is right hand side of equality sign and LHS is left hand side ...
2) How come you can go from 4^18 --> 2^36 but not from, say 5^4 --> 10^2? When does the "divide by 2 and multiply by 2 rule apply"?
4^18=(2*2)^18=$$(2^2)$$^18=2^(2*18)=2^36.....
5^4=(5^2)^2=25^2

3) 1/5^m - How do I get rid of the ^m in the numerator? I mean, isnt 1/5^m $$1^m/5^m?$$..
1^m=1 for all values of 1.... if we divide or multiply 1 any number of times, the result will be 1 so m can be removed from power..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?   [#permalink] 04 Mar 2015, 06:27

Go to page    1   2    Next  [ 38 posts ]

Similar topics Replies Last post
Similar
Topics:
2 If m < 15 and m > –4, which of the following must be true? 3 30 Jan 2017, 11:42
4 If 15!/m^3 is a multiple of 5, which of the following cannot be the 1 25 Dec 2016, 04:02
3 In a 100m, A beats B by 15m and B beats C by 10m. If A beats C by 5 se 2 06 Jun 2016, 22:53
if (1/5)^m (1/4)^18= 1/{2(10)^35}. then m= 2 04 Oct 2011, 02:47
2 If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ? 14 19 Jul 2014, 00:35
Display posts from previous: Sort by