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

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

09 Feb 2012, 14:17

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Question Stats:

81% (01:40) correct

18% (02:16) wrong

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

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

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

09 Feb 2012, 14:24

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

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

Long way 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.

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

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.

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

09 Feb 2012, 14:39

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

09 Feb 2012, 21:25

Answer is m=35
expanding the equation we get 2*2^35*5^35 = 2^36*5^m

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Firts Quant question in GMAT Prep Software [#permalink]

01 May 2012, 03:20

Hi,

can someone help me with the first Quant question in GMAT Prep Software:

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

m=?

The answer is m=35, but I don't know how to get there without a calculator...

Thanks for your support!

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Re: Firts Quant question in GMAT Prep Software [#permalink]

01 May 2012, 03:28

palatimate wrote:

Welcome to GMAT Club. I merged your question with an earlier discussion of the same problem. Please ask if anything remains unclear.

P.S. Please always post answer choices for PS problems.
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

01 May 2012, 03:37

Thanks a lot for your prompt help!
This problem kept my thinking for more than one hour now!
Cheers

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

01 May 2012, 03:52

Quote:

--> 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.

@Bunuel: Can you give details on the short way? Why is it possible to concentrate only on the power of 5? :?:

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If (1/5)^m (1/4)^18=1/(2(10)^35) what is the value of m? [#permalink]

16 May 2012, 05:05

Will somebody please explain to me this concept in simple terms? I'm continually struggling with these types of problems and continuing to read the book definitions etc doesn't seem to be providing much light. Thanks in advance, Andrew.

If (1/5)^m (1/4)^18=1/(2(10)^35) what is the value of m?

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Re: If (1/5)^m (1/4)^18=1/(2(10)^35) what is the value of m? [#permalink]

16 May 2012, 05:13

wynnandrewj wrote:

Merging similar topics. Please ask if anything remains unclear.

P.S. Please post answer choices for PS questions.
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If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ? [#permalink]

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

If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ? [#permalink] 02 Apr 2013, 07:58

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

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

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

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