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

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16 Nov 2005, 22:00
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83% (01:56) correct 17% (01:33) wrong based on 124 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-1-5-m-1-4-18-frac-127321.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Aug 2014, 00:12, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

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17 Nov 2005, 07:07
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(1/5)^m (1/4)^18 = 1/{2(10)^35}
2(10)^35/4^18 = 5^m
[2(2^35)(5^35)]/[2^36] = 5^m
5^35 = 5^m
m=35
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

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17 Nov 2005, 09:26
wiseguy wrote:
1/5 ^m times 1/4 ^18 = 1/2(10) ^35

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

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

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17 Nov 2005, 09:27
D

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

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

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

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

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17 Nov 2005, 11:27
yup got m =35 as well.
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

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17 Nov 2005, 14:21
Guys I don't get it, could rexplain.

thx,

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

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17 Nov 2005, 14:25
wiseguy wrote:
Guys I don't get it, could rexplain.
thx,
wiseguy

[(1/5)^m]*[(1/4)^18] = 1/[2(10)^35] = 1/[2(5*2)^35] = 1/[2^36 * 5^35]
Cross multiply,
2^36 * 5^35 = 5^m * 4^18 = 5^m * (2^2)^16 = 5^m * 2^26
So, 5^35 = 5^m -> m=35
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

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06 Aug 2014, 17:12
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

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06 Aug 2014, 17:36
This question does not require any calculation as such. On comparing powers of primes between LHS and RHA, we find that RHS has 2^35 (10^35=(2*5)^35) so m has to be 35
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]

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12 Aug 2014, 00:14
wiseguy wrote:
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 --> $$m=35$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-1-5-m-1-4-18-frac-127321.html
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?   [#permalink] 12 Aug 2014, 00:14
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