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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, 23:00
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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: if15m1418frac127321.html
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Last edited by Bunuel on 12 Aug 2014, 01:12, 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, 08:07
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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, 10:26
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, 10:27
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, 12:27
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, 15:21
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, 15:25
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, 18:12
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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, 18:36
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, 01:14
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:\((\frac{1}{5})^m*(\frac{1}{4})^{18}= \frac{1}{2*10^{35}}\) > \(\frac{1}{5^m}*\frac{1}{2^{36}}= \frac{1}{2*2^{35}*5^{35}}\) > \(\frac{1}{5^m}*\frac{1}{2^{36}}= \frac{1}{2^{36}*5^{35}}\) > \(\frac{1}{5^m}= \frac{1}{5^{35}}\) > \(m=35\). Answer: D. 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 > \(m=35\). Answer: D. OPEN DISCUSSION OF THIS QUESTION IS HERE: if15m1418frac127321.html
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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ?
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