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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
00:00
A
B
C
D
E

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  35% (medium)

Question Stats:

80% (01:51) correct 20% (02:53) wrong based on 20 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
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
1
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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Manager
Manager
User avatar
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Joined: 02 Mar 2018
Posts: 70
Location: India
Schools: IIMA , IIMA PGPX"20
GMAT 1: 640 Q51 V26
GPA: 3.1
CAT Tests
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.
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value &nbs [#permalink] 31 Jul 2018, 04:12
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