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If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is

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Joined: 02 Sep 2009
Posts: 53004
If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is  [#permalink]

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New post 28 Jan 2019, 00:44
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

91% (00:52) correct 9% (00:00) wrong based on 15 sessions

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Location: India
Concentration: Operations, Finance
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Re: If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is  [#permalink]

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New post 28 Jan 2019, 01:15
Bunuel wrote:
If \(\frac{5^7}{5^{-4}}=5^a\), \(\frac{2^{-3}}{2^{-2}}=2^b\), and \(3^8(3) = 3^c\), what is the value of \(a + b + c\)?

A. 18
B. 19
C. 20
D. 21
E. 22


\(\frac{5^7}{5^{-4}}=5^a\) => , a=11

\(\frac{2^{-3}}{2^{-2}}=2^b\) =>, b=-1

\(3^8(3) = 3^c\) => \(3^(8+1) = 3^c\) => c=9

a+b+c =>11-1+9 = 19

Hence B
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If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is  [#permalink]

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New post 28 Jan 2019, 01:25
Bunuel wrote:
If \(\frac{5^7}{5^{-4}}=5^a\), \(\frac{2^{-3}}{2^{-2}}=2^b\), and \(3^8(3) = 3^c\), what is the value of \(a + b + c\)?

A. 18
B. 19
C. 20
D. 21
E. 22



\(\frac{5^7}{5^{-4}}=5^a\)

\(\frac{5^7*5^4=5^a\)

\(5^11 = 5^a\)

a = 11.

Again ,

\([fraction]2^{-3}}{2^{-2}}=2^b\)

\(\frac{2^{2}}{2^{3}}=2^b\)

\(2^{-1} = 2^b\)

b = -1.

\(3^8(3) = 3^c\)

\(3^9 = 3^c\)

c = 9.

a + b + c = 11 + 9 -1 = 19.

The best answer is B.
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If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is  [#permalink]

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New post 28 Jan 2019, 03:19
Bunuel wrote:
If \(\frac{5^7}{5^{-4}}=5^a\), \(\frac{2^{-3}}{2^{-2}}=2^b\), and \(3^8(3) = 3^c\), what is the value of \(a + b + c\)?

A. 18
B. 19
C. 20
D. 21
E. 22


\(5^7 * 5^4 => 5^{11} = 5^a => a = 11\)

\(2^{-3 + 2} => 2^{-1} = 2^b => b = -1\)

\(3^9 => 9 = c\)

11 - 1 + 9

19

B
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Re: If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is  [#permalink]

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New post 28 Jan 2019, 03:48
Bunuel wrote:
If \(\frac{5^7}{5^{-4}}=5^a\), \(\frac{2^{-3}}{2^{-2}}=2^b\), and \(3^8(3) = 3^c\), what is the value of \(a + b + c\)?

A. 18
B. 19
C. 20
D. 21
E. 22



solving we get
a= 11
b=-1
c=9
sum = 19
IMO B
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Re: If 5^7/5^(-4) = 5^a, 2^(-3)/2^(-2) = 2^b, and 3^8(3) = 3^c, what is   [#permalink] 28 Jan 2019, 03:48
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