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What is the value of m in the equation below?

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What is the value of m in the equation below?  [#permalink]

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New post 12 Feb 2016, 18:57
2
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A
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E

Difficulty:

  15% (low)

Question Stats:

72% (00:51) correct 28% (00:56) wrong based on 188 sessions

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What is the value of m in the equation below? \((\frac{1}{5})^m * (\frac{1}{4})^{24} = (\frac {1}{2(10)^{47}})\)

A) 23

B) 24

C) 46

D) 47

E) 48

EDITED THE Q
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Re: What is the value of m in the equation below?  [#permalink]

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New post 08 Jul 2017, 14:22
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3
zxcvbnmas wrote:
What is the value of m in the equation below? \((\frac{1}{5})^m * (\frac{1}{4})^{24} = (\frac {1}{2(10)^{47}})\)

A) 23

B) 24

C) 46

D) 47

E) 48

EDITED THE Q



\((\frac{1}{5})^m * (\frac{1}{4})^{24} = (\frac {1}{2(10)^{47}})\)

\((\frac{1}{5})^m * (\frac{1}{4})^{24} = (\frac {1}{2(2)^{47}(5)^{47}})\)

\((\frac{1}{5})^m * (\frac{1}{4})^{24} = (\frac {1}{(2)^{48}(5)^{47}})\)

\((\frac{1}{5})^m * (\frac{1}{4})^{24} = (\frac {1}{(4)^{24}(5)^{47}})\)

\((\frac{1}{5})^m * (\frac{1}{4})^{24} = (\frac{1}{5})^{47} * (\frac{1}{4})^{24}\)

Hence, we see that \(m = 47\)

Hence, Answer is D
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Re: What is the value of m in the equation below?  [#permalink]

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New post 12 Feb 2016, 20:25
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zxcvbnmas wrote:
What is the value of m in the equation below? \((\frac{1}{5})^m * (\frac{1}{4})^{24} = (\frac {1}{2(10)})^{47}\)

A) 23

B) 24

C) 46

D) 47

E) 48


Hi,

firsly, the Q in its present state cannot be correct and cannot have any of these answers..
the Q should have been
\((\frac{1}{5})^m * (\frac{1}{4})^{24} = (\frac {1}{2(10)^{47}})\)


In such Qs, we should get all the values in its simplest form..
\((\frac{1}{5})^m * (\frac{1}{4})^{24} = (\frac {1}{2(10)^{47}})\)..
\((\frac{1}{5})^m * (\frac{1}{2})^{24*2} = (\frac {1}{2*2^{47}*5^{47}})\)..
\((\frac{1}{5})^m * (\frac{1}{2})^{48} = (\frac {1}{2^{48}*5^{47}})\)..
fromthe two sides of eq we can get the power of 5 has to be 47..
so m =47...
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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


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Re: What is the value of m in the equation below?  [#permalink]

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New post 10 Jul 2017, 20:39
1
The strategy is to convert each side of the equation into multiples of 2 and 5 and then finally equate.
\(10^{47}\) can be written as \((2.5)^{47}\)

Rewriting the equation as below:

\(\frac{(1)^m}{(5)^m}\) . \(\frac{(1)^{24}}{(4)^{24}}\) = \(\frac{1}{2.(2.5)^{47}}\)

\(4^{24}\) can be written as \((2^2)^{24}\), which is equal to \(2^{48}\)

\(\frac{1}{(5)^m}\) . \(\frac{1}{(2)^{48}}\) = \(\frac{1}{2.(2.5)^{47}}\)

Now, cross multiply the denominators on both the sides.

\(2.(2.5)^{47}\) = \(5^m\) . \(2^{48}\)

Separating the powers, we get:

\(2^{48}.5^{47}\) = \(5^m\) . \(2^{48}\)

Rewriting the equation above

\(2^{48}.5^{47}\) = \(2^{48}\).\(5^m\)

Finally, since the bases are equal on either side of the equation, we could equate the powers of each base.

Therefore,
m=47
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Re: What is the value of m in the equation below?  [#permalink]

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New post 14 Jul 2017, 23:37
Option D is correct
This is how I attempted
(1/5)^m*(1/4)^24=1/2(10)47
(1/5)^m=4^24/2(2*5)^47
(1/5)^m=2^48/2^48*5^47
left it with
(1/5)^m=1/5^47
so
m=47
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Re: What is the value of m in the equation below?  [#permalink]

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New post 23 Jul 2018, 03:47
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Re: What is the value of m in the equation below? &nbs [#permalink] 23 Jul 2018, 03:47
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