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If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value

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If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post Updated on: 30 Jul 2018, 21:23
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A
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D
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  35% (medium)

Question Stats:

76% (02:19) correct 24% (02:39) wrong based on 111 sessions

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If \(3^{y + 1} + 3^{y − 2} + 3^{y − 3} = 85(3^{x + 5})\), what is the value of y in terms of x?


A. x
B. x + 2
C. x − 2
D. x + 8
E. x − 8

Originally posted by gsingh0711 on 30 Jul 2018, 15:59.
Last edited by Bunuel on 30 Jul 2018, 21:23, edited 2 times in total.
Renamed the topic and edited the question.
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Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 30 Jul 2018, 16:00
1
Explanation:

3y+1+3y−2+3y−3=85(3x+5)

⇒ 3y(31+3−2+3−3)=85(3x+5)

⇒ 3y(3+19+127)=85(3(x+5)) )

⇒ 3y(8527)=85(3(x+5))

⇒ 3y=27(3x+5)=33×3x+5

⇒ 3y=3x+8

⇒ y = x + 8

Answer: D.

I think, I deserve a kudus LoL
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If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 30 Jul 2018, 21:11
4
gsingh0711 wrote:
If \(3y + 1 + 3y − 2 + 3y − 3 = 85(3x + 5)\), what is the value of y in terms of x?


A. x
B. x + 2
C. x − 2
D. x + 8
E. x − 8



Poor question at the first look itself..

All the choices have coefficient of X and y same as y=X or y=X+2
But the two sides tell us that y has 9 as coefficient and X has 85*3, so can never be equal

\(3y + 1 + 3y − 2 + 3y − 3 = 85(3x + 5)........9y-4=255x+425.......9y=255x+429........y=85x/3 + 143/3...\)

If it is
Question is
\(3^{y + 1} + 3^{y − 2} + 3^{y − 3} = 85(3^{x + 5})...................
3^{y-3}(3^4+3+1)=85(3^{X+5}...................
3^{y-3}*85=85*3^{X+5}......................
3^{X+5}=3^{y-3}\)

Equating the powers
x+5=y-3.......y=x+8

D
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Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 30 Jul 2018, 21:24
1
chetan2u wrote:
gsingh0711 wrote:
If \(3y + 1 + 3y − 2 + 3y − 3 = 85(3x + 5)\), what is the value of y in terms of x?


A. x
B. x + 2
C. x − 2
D. x + 8
E. x − 8



Poor question at the first look itself..

All the choices have coefficient of X and y same as y=X or y=X+2
But the two sides tell us that y has 9 as coefficient and X has 85*3, so can never be equal

\(3y + 1 + 3y − 2 + 3y − 3 = 85(3x + 5)........9y-4=255x+425.......9y=255x+429........y=85x/3 + 143/3...\)


Yes. The formatting in the question as well in the "solution" was all messed up. I guess the guy just copy pasted both from some source without checking. I fixed it.
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Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 31 Jul 2018, 04:12
Bunuel wrote:
chetan2u wrote:
gsingh0711 wrote:
If \(3y + 1 + 3y − 2 + 3y − 3 = 85(3x + 5)\), what is the value of y in terms of x?


A. x
B. x + 2
C. x − 2
D. x + 8
E. x − 8



Poor question at the first look itself..

All the choices have coefficient of X and y same as y=X or y=X+2
But the two sides tell us that y has 9 as coefficient and X has 85*3, so can never be equal

\(3y + 1 + 3y − 2 + 3y − 3 = 85(3x + 5)........9y-4=255x+425.......9y=255x+429........y=85x/3 + 143/3...\)


Yes. The formatting in the question as well in the "solution" was all messed up. I guess the guy just copy pasted both from some source without checking. I fixed it.


I think system failed the read the raised to the powers and that is why formatting looked messed up.
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Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 28 Aug 2018, 03:23
1
gsingh0711 wrote:
If \(3^{y + 1} + 3^{y − 2} + 3^{y − 3} = 85(3^{x + 5})\), what is the value of y in terms of x?


A. x
B. x + 2
C. x − 2
D. x + 8
E. x − 8


Dear Moderator,
Found this PS question , in the DS section, hope you will do the needful. Thank you.
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Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 28 Aug 2018, 04:59
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If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 28 Aug 2018, 06:30
gsingh0711 wrote:
Explanation:

3y+1+3y−2+3y−3=85(3x+5)

⇒ 3y(31+3−2+3−3)=85(3x+5)

⇒ 3y(3+19+127)=85(3(x+5)) )

⇒ 3y(8527)=85(3(x+5))

⇒ 3y=27(3x+5)=33×3x+5

⇒ 3y=3x+8

⇒ y = x + 8

Answer: D.

I think, I deserve a kudus LoL



gsingh0711 hey there :) thank you for your explanation :-) To deserve kudos please make explanation clear and math friendly :) (explain with words step by step) :grin: :-)

Use math formatting tools express exponent like this \(3^2\) :-)
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If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 28 Aug 2018, 07:49
chetan2u wrote:
gsingh0711 wrote:
If \(3y + 1 + 3y − 2 + 3y − 3 = 85(3x + 5)\), what is the value of y in terms of x?


A. x
B. x + 2
C. x − 2
D. x + 8
E. x − 8



Poor question at the first look itself..

All the choices have coefficient of X and y same as y=X or y=X+2
But the two sides tell us that y has 9 as coefficient and X has 85*3, so can never be equal

\(3y + 1 + 3y − 2 + 3y − 3 = 85(3x + 5)........9y-4=255x+425.......9y=255x+429........y=85x/3 + 143/3...\)

If it is
Question is
\(3^{y + 1} + 3^{y − 2} + 3^{y − 3} = 85(3^{x + 5})...................
3^{y-3}(3^4+3+1)=85(3^{X+5}...................
3^{y-3}*85=85*3^{X+5}......................
3^{X+5}=3^{y-3}\)

Equating the powers
x+5=y-3.......y=x+8

D



chetan2u can you please explain how from this \(3^{y-3}(3^4+3+1)=85(3^{X+5}\) you got this \(3^{y-3}*85=85*3^{X+5}\) ? :-) what happened to this \((3^4+3+1)\) ? :?
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Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 28 Aug 2018, 08:04
1
dave13 wrote:
chetan2u wrote:
gsingh0711 wrote:
If \(3y + 1 + 3y − 2 + 3y − 3 = 85(3x + 5)\), what is the value of y in terms of x?


A. x
B. x + 2
C. x − 2
D. x + 8
E. x − 8



Poor question at the first look itself..

All the choices have coefficient of X and y same as y=X or y=X+2
But the two sides tell us that y has 9 as coefficient and X has 85*3, so can never be equal

\(3y + 1 + 3y − 2 + 3y − 3 = 85(3x + 5)........9y-4=255x+425.......9y=255x+429........y=85x/3 + 143/3...\)

If it is
Question is
\(3^{y + 1} + 3^{y − 2} + 3^{y − 3} = 85(3^{x + 5})...................
3^{y-3}(3^4+3+1)=85(3^{X+5}...................
3^{y-3}*85=85*3^{X+5}......................
3^{X+5}=3^{y-3}\)

Equating the powers
x+5=y-3.......y=x+8

D



chetan2u can you please explain how from this \(3^{y-3}(3^4+3+1)=85(3^{X+5}\) you got this \(3^{y-3}*85=85*3^{X+5}\) ? :-) what happened to this \((3^4+3+1)\) ? :?


Hi..
3^4+3+1=81+3+1=85
So 3^4+3+1 is replaced with 85
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If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post Updated on: 10 Feb 2019, 21:40
1
\(3^{y + 1} + 3^{y − 2} + 3^{y − 3} = 85(3^{x + 5})\)

\(3^{y + 1} ( 1 + 3^{− 3} + 3^{− 4}) = (5)(17)(3^{x + 5})\)

\(3^{y + 1} ( 1 + {1/27} + {1/81}) = (5)(17)(3^{x + 5})\)

\(3^{y + 1} ( {85/81}) = (5)(17)(3^{x + 5})\)

\(3^{y + 1} ( 85 * 3^{− 4}) = (85)(3^{x + 5})\)

y + 1 + ( - 4 ) = x + 5

y = x + 8

D

Originally posted by jfranciscocuencag on 10 Feb 2019, 21:22.
Last edited by jfranciscocuencag on 10 Feb 2019, 21:40, edited 5 times in total.
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If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 10 Feb 2019, 21:31
1
gsingh0711 wrote:
If \(3^{y + 1} + 3^{y − 2} + 3^{y − 3} = 85(3^{x + 5})\), what is the value of y in terms of x?


A. x
B. x + 2
C. x − 2
D. x + 8
E. x − 8


\(3^y\) [ 3 + 1/9 +1/27 ] = 85 \((3^{x + 5})\)

take \(3^y\) common

\(3^y\) [ 85/27] = 85 \((3^{x + 5})\)

\(3^y\) = \((3^{x + 8})\)

y = x+8

D
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Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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New post 24 Mar 2019, 04:53
3^Y•3 + 3^Y•3^-2 + 3^Y•3^-3 = 85•3^X•3^5
3^Y ( 3 + 1/9 +1/27) =85•3^5•(3^X)
3^Y (85/27) = 85•3^5•(3^X)
3^Y = 3^3•3^5•3^X
Y= 3+5 +X
Y = X +8

Answer D
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Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value   [#permalink] 24 Mar 2019, 04:53
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