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

 It is currently 18 Feb 2019, 06:21

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!
• ### Get FREE Daily Quiz for 2 months

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

Buy "All-In-One Standard (\$149)", get free Daily quiz (2 mon). Coupon code : SPECIAL

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

### Show Tags

09 Feb 2012, 13:17
6
65
00:00

Difficulty:

5% (low)

Question Stats:

80% (01:24) correct 20% (02:05) wrong based on 1446 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 52935
If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

09 Feb 2012, 13:24
38
32
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:

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

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

Since 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: $$m=35$$.

_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1821
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

07 Sep 2014, 23:41
22
6
$$\frac{1}{5^m} * \frac{1}{4^{18}} = \frac{1}{2*10^{35}}$$

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

##### General Discussion
Intern
Joined: 05 Dec 2011
Posts: 10
WE: Information Technology (Computer Software)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

09 Feb 2012, 13:31
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: 52935
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

09 Feb 2012, 13:39
2
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
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

02 Apr 2013, 06:58
1
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: 38
H: B
GMAT Date: 08-31-2013
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

Updated on: 10 Aug 2013, 19:07
1
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.

Originally posted by hb on 10 Aug 2013, 18:53.
Last edited by hb on 10 Aug 2013, 19:07, edited 1 time in total.
Intern
Status: Preparation
Joined: 03 Apr 2012
Posts: 6
Location: India
GMAT 1: 700 Q50 V34
GPA: 2.9
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

11 Aug 2013, 00:32
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: 52935
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

13 Mar 2014, 07:36
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

_________________
Board of Directors
Joined: 01 Sep 2010
Posts: 3349
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

11 Jul 2014, 08:44
1
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: 52935
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

11 Jul 2014, 10:21
1
1
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.
_________________
Affiliations: Oracle certified java programmer , adobe certified developer
Joined: 14 Jul 2013
Posts: 59
GMAT Date: 02-12-2015
GPA: 3.87
WE: Programming (Telecommunications)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

23 Aug 2014, 22:26
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: 129
Location: India
WE: Information Technology (Computer Software)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

31 Aug 2014, 04:33
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...

Manager
Joined: 24 Dec 2014
Posts: 129
Location: India
GMAT 1: 700 Q47 V39
GMAT 2: 790 Q51 V50
GPA: 3.65
WE: Operations (Energy and Utilities)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

02 Feb 2015, 14:23
1
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: 114
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

04 Mar 2015, 05:17
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 $$1^m/5^m?$$
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

04 Mar 2015, 05:27
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..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Manager
Joined: 26 Feb 2015
Posts: 114
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

04 Mar 2015, 05:33
Thanks for the quick response. I actually know these rules but I forget to apply them, its really frustrating
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

04 Mar 2015, 05:36
erikvm wrote:
Thanks for the quick response. I actually know these rules but I forget to apply them, its really frustrating

doesnt matter erik... it happens with everyone if we don't refresh basics.... i am sure you will overcome all this by putting in some hardwork.. all the best..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

CEO
Joined: 20 Mar 2014
Posts: 2629
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

04 Oct 2015, 04:13
1
jst6059 wrote:
Question from the practice test that has me dumbfounded:

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

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

Format your question properly and search for a question before you post. The question has already been discussed. Look above for the solution.

Topics merged.

As for your question, for all such questions, you need to break the bigger numbers down to their respective prime factors by noting that $$4=2^2$$ and $$10=2*5$$, After you are doing breaking both sides of the equation down to the respective prime factors, equate the powers of similar 'bases' to get to your final answer.

Also $$1/x = x^{-1}$$ and $$x^a*x^b = x^{(a+b)}$$

Applying these relations to the question at hand you get:

$$5^{-m}*4^{-18} = 2^{-1}*10^{-35}$$ ---> $$5^{-m}*(2^2)^{-18} = 2^{-1}*(2*5)^{-35}$$ ---> $$5^{-m}*2^{-36} = 2^{-1}*(2^{-35}*5^{-35})$$

---> $$5^{-m}*2^{-36} = 2^{-1}*(2^{-35}*5^{-35})$$ ---> $$5^{-m}*2^{-36} = 2^{-36}*5^{-35}$$, equate both sides now to see that m=35. D is the correct answer.
SVP
Joined: 06 Nov 2014
Posts: 1877
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?  [#permalink]

### Show Tags

04 Oct 2015, 05:52
erikvm wrote:
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 $$1^m/5^m?$$

1) What is RHS / LHS?
LHS and RHS are the acronyms of Left hand side and RIgh hand side respectively.
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"?
We can go from 4^18 --> 2^36, because 4 is a power of two, (2^2 = 4)
Whereas 10 is not a power of 5. You cannot express 10 just by using 5.
Divide and multiply by 2 rules means to divide and multiply an expression by 2 to make it simpler.

For example: 18/5 = 18*2/5*2 = 36/10 = 3.6
By doing this, we can solve easily

3) 1/5^m - How do I get rid of the ^m in the numerator? I mean, isnt 1/5^m 1m/5m?..
Yes (1/5)^m = 1^m/5^m, but however many times you multiply 1, the result will always be 1.
Hence we can write 1^m simply as 1.
Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?   [#permalink] 04 Oct 2015, 05:52

Go to page    1   2    Next  [ 32 posts ]

Display posts from previous: Sort by