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# If (2^15)(25^S) = 5(10^m) what is the value of m ?

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Intern
Joined: 26 Jan 2015
Posts: 9
If (2^15)(25^S) = 5(10^m) what is the value of m ? [#permalink]

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08 Feb 2015, 09:13
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Difficulty:

15% (low)

Question Stats:

87% (00:51) correct 13% (02:21) wrong based on 54 sessions

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If (2^15)(25^S) = 5(10^m) what is the value of m ?

A) 7
B) 8
C) 15
D) 16
E) 23
[Reveal] Spoiler: OA
Intern
Joined: 09 Apr 2013
Posts: 32
Schools: Booth '16
Re: If (2^15)(25^S) = 5(10^m) what is the value of m ? [#permalink]

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08 Feb 2015, 10:21
given

2^15 * 25^s = 5 * 10^2

=> 2^15 * 5^(2s) = 2^m * 5^(m+1)

Ans C
on comparing the power of 2 => m=15
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Re: If (2^15)(25^S) = 5(10^m) what is the value of m ? [#permalink]

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08 Feb 2015, 19:32
1
KUDOS
Expert's post
Hi sauberheine1,

This question is all about how you "rewrite" exponents. Before I go through the explanation, I have to ask if this question was transcribed correctly - are we supposed to solve for the value of M or the value of S?

Here, we're given (2^15)(25^S) = 5(10^M). Here's how we can solve for the value of M.

On the "left side":
(2^15) we'll leave alone
(25^S) can be rewritten as (5^2)^S = 5^(2S)

On the "right side":
5 can be written as 5^1
(10^M) can be rewritten as [(2)(5)]^M = (2^M)(5^M)

So now the overall equation is...
(2^15)[5^(2S)] = (5^1)(5^M)(2^M)

Looking at the "base 2" part of each side, we have...(2^15) and (2^M), so M MUST = 15

If we're solving for M, then the answer is
[Reveal] Spoiler:
C

Using M = 15, we can now figure out the value of S.....

[5^(2S)] = (5^1)(5^15)
[5^(2S)] = (5^16)
2S = 16
S = 8

If we're solving for S, then the answer is
[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich
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Re: If (2^15)(25^S) = 5(10^m) what is the value of m ? [#permalink]

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08 Feb 2015, 20:23
1
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2
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$$2^{15} * 25^S = 5 * 10^m$$

$$2^{15} * 5^{2S} = 5 * (5*2)^m$$

$$2^{15} * 5^{2S} = 5^{m+1} * 2^m$$

Bases are same, so equating the powers

m = 15

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Director
Joined: 23 Jan 2013
Posts: 600
Schools: Cambridge'16
Re: If (2^15)(25^S) = 5(10^m) what is the value of m ? [#permalink]

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08 Feb 2015, 23:45
2^15 * 25^S = 5 * 10^m

2^15 * (5^2)^S=5 * 10^m

2^15 * 5^2S=5 * 10^m

2^15 * 5^2S-1=2^m * 5^m

to be equal m=15, s=8

C
Intern
Joined: 26 Jan 2015
Posts: 9
Re: If (2^15)(25^S) = 5(10^m) what is the value of m ? [#permalink]

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09 Feb 2015, 07:14
EMPOWERgmatRichC wrote:
Hi sauberheine1,

This question is all about how you "rewrite" exponents. Before I go through the explanation, I have to ask if this question was transcribed correctly - are we supposed to solve for the value of M or the value of S?

Here, we're given (2^15)(25^S) = 5(10^M). Here's how we can solve for the value of M.

On the "left side":
(2^15) we'll leave alone
(25^S) can be rewritten as (5^2)^S = 5^(2S)

On the "right side":
5 can be written as 5^1
(10^M) can be rewritten as [(2)(5)]^M = (2^M)(5^M)

So now the overall equation is...
(2^15)[5^(2S)] = (5^1)(5^M)(2^M)

Looking at the "base 2" part of each side, we have...(2^15) and (2^M), so M MUST = 15

If we're solving for M, then the answer is
[Reveal] Spoiler:
C

Using M = 15, we can now figure out the value of S.....

[5^(2S)] = (5^1)(5^15)
[5^(2S)] = (5^16)
2S = 16
S = 8

If we're solving for S, then the answer is
[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich

Thanks a lot ! Yes the question asked for the value of m.

I didn't know that you can compare the two bases even though there is one more 5 on the right side.

Problem solved and understood. Thank you all!
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Posts: 696
Location: India
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Schools: ISB '19, IIMA , IIMB, XLRI
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Re: If (2^15)(25^S) = 5(10^m) what is the value of m ? [#permalink]

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21 Aug 2017, 23:16
sauberheine1 wrote:
If (2^15)(25^S) = 5(10^m) what is the value of m ?

A) 7
B) 8
C) 15
D) 16
E) 23

$$(2^{15})(25^S) = 5(10^m)$$

$$(2^{15})(5^{2S}) = (5)(5*2)^m$$

$$(2^{15})(5^{2S}) = (5)(5^m)(2^m)$$

$$(2^{15})(5^{2S}) = (5^{m+1})(2^m)$$

$$2^{15} = 2^m$$

$$m = 15$$

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Re: If (2^15)(25^S) = 5(10^m) what is the value of m ? [#permalink]

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24 Aug 2017, 16:14
sauberheine1 wrote:
If (2^15)(25^S) = 5(10^m) what is the value of m ?

A) 7
B) 8
C) 15
D) 16
E) 23

We can simplify the given equation:

(2^15)(25^S) = 5(10^m)

(2^15)(5^2S) = 5(5^m x 2^m)

(2^15)(5^2S) = (5^m+1)(2^m)

Thus:

2^15 = 2^m

15 = m

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Re: If (2^15)(25^S) = 5(10^m) what is the value of m ?   [#permalink] 24 Aug 2017, 16:14
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