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Manager  S
Joined: 02 Mar 2018
Posts: 59
Location: India
GMAT 1: 640 Q51 V26 GPA: 3.1
If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 77% (02:21) correct 23% (02:39) wrong based on 118 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.
Math Expert V
Joined: 02 Aug 2009
Posts: 8302
If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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
_________________
Manager  S
Joined: 02 Mar 2018
Posts: 59
Location: India
GMAT 1: 640 Q51 V26 GPA: 3.1
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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

I think, I deserve a kudus LoL
Math Expert V
Joined: 02 Sep 2009
Posts: 59674
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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.
_________________
Director  V
Joined: 27 May 2012
Posts: 947
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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.
_________________
- Stne
Math Expert V
Joined: 02 Aug 2009
Posts: 8302
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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
_________________
Senior Manager  G
Joined: 12 Sep 2017
Posts: 308
If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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.
Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

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Manager  S
Joined: 02 Mar 2018
Posts: 59
Location: India
GMAT 1: 640 Q51 V26 GPA: 3.1
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 59674
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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stne wrote:
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.

___________________
Done. Thank you.
_________________
VP  D
Joined: 09 Mar 2016
Posts: 1229
If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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

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)  Use math formatting tools express exponent like this $$3^2$$ VP  D
Joined: 09 Mar 2016
Posts: 1229
If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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 $$(3^4+3+1)$$ ? Intern  B
Joined: 20 Jan 2019
Posts: 2
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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 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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