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# What is the value of m in the equation below?

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Manager
Joined: 06 Jun 2014
Posts: 90
Location: United States
Concentration: Finance, General Management
GMAT 1: 450 Q27 V21
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What is the value of m in the equation below?  [#permalink]

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12 Feb 2016, 17:57
2
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:17) correct 20% (01:52) wrong based on 196 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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08 Jul 2017, 13:22
4
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 $$m = 47$$

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##### General Discussion
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Joined: 02 Aug 2009
Posts: 7035
Re: What is the value of m in the equation below?  [#permalink]

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12 Feb 2016, 19:25
4
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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10 Jul 2017, 19:39
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
Intern
Joined: 13 Jul 2017
Posts: 29
Re: What is the value of m in the equation below?  [#permalink]

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14 Jul 2017, 22:37
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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23 Jul 2018, 02:47
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Re: What is the value of m in the equation below? &nbs [#permalink] 23 Jul 2018, 02:47
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