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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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Manager
Joined: 02 Mar 2018
Posts: 66
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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Updated on: 30 Jul 2018, 21:23
1
8
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Difficulty:

35% (medium)

Question Stats:

76% (02:19) correct 24% (02:39) wrong based on 113 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
Joined: 02 Aug 2009
Posts: 7742
If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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
_________________
Manager
Joined: 02 Mar 2018
Posts: 66
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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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

I think, I deserve a kudus LoL
Math Expert
Joined: 02 Sep 2009
Posts: 55614
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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.
_________________
Director
Joined: 27 May 2012
Posts: 800
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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.
_________________
- Stne
Math Expert
Joined: 02 Aug 2009
Posts: 7742
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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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Senior Manager
Joined: 12 Sep 2017
Posts: 262
If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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.
VP
Joined: 09 Mar 2018
Posts: 1004
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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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
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
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Manager
Joined: 02 Mar 2018
Posts: 66
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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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.
Math Expert
Joined: 02 Sep 2009
Posts: 55614
Re: If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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28 Aug 2018, 04:59
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
Joined: 09 Mar 2016
Posts: 1279
If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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

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
Joined: 09 Mar 2016
Posts: 1279
If 3^(y + 1) + 3^(y − 2) + 3^(y − 3) = 85(3^(x + 5), what is the value  [#permalink]

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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 $$(3^4+3+1)$$ ?
Intern
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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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

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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