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Math Expert V
Joined: 02 Sep 2009
Posts: 58113
If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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4
6 00:00

Difficulty:   35% (medium)

Question Stats: 71% (01:47) correct 29% (02:16) wrong based on 317 sessions

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If 9^y + 3^b = 10*3^b, then 2y ='

(A) b – 2
(B) b – 1
(C) b
(D) b + 1
(E) b + 2

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CEO  D
Status: GMATINSIGHT Tutor
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Posts: 2972
Location: India
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Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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3
1
Bunuel wrote:
If 9^y + 3^b = 10*3^b, then 2y ='

(A) b – 2
(B) b – 1
(C) b
(D) b + 1
(E) b + 2

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Math Expert V
Joined: 02 Aug 2009
Posts: 7830
Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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1
Bunuel wrote:
If 9^y + 3^b = 10*3^b, then 2y ='

(A) b – 2
(B) b – 1
(C) b
(D) b + 1
(E) b + 2

Hi,

9^y + 3^b = 10*3^b
3^2y=9*3^b..
3^2y=3^2*3^b
3^2y=3^(b+2).. so 2y = b+2.. ans E
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Math Expert V
Joined: 02 Sep 2009
Posts: 58113
Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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1
Bunuel wrote:
If 9^y + 3^b = 10*3^b, then 2y ='

(A) b – 2
(B) b – 1
(C) b
(D) b + 1
(E) b + 2

MANHATTAN GMAT OFFICIAL SOLUTION:

Manipulate:

$$9^y + 3^b = 10(3^b)$$

$$3^{2y} + 3^b = 10(3^b)$$

$$3^{2y} = 10(3^b) - 3^b$$

$$3^{2y} = 3^b(10 - 1)$$

$$3^{2y} = 3^b(3^2)$$

$$3^{2y} = 3^{b + 2}$$

$$2y = b + 2$$

The correct answer is E.
_________________
CEO  D
Status: GMATINSIGHT Tutor
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Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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Bunuel wrote:
If 9^y + 3^b = 10*3^b, then 2y ='

(A) b – 2
(B) b – 1
(C) b
(D) b + 1
(E) b + 2

I think this question should be Sub 600 level due to following reasons:

1) It comes from the topic Exponents which is a very basic topic of Math's
2) This question just deals with Simple arrangement and then comparison of powers and doesn't include much complexities.

Just an Opinion _________________
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Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

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Math Expert V
Joined: 02 Sep 2009
Posts: 58113
Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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GMATinsight wrote:
Bunuel wrote:
If 9^y + 3^b = 10*3^b, then 2y ='

(A) b – 2
(B) b – 1
(C) b
(D) b + 1
(E) b + 2

I think this question should be Sub 600 level due to following reasons:

1) It comes from the topic Exponents which is a very basic topic of Math's
2) This question just deals with Simple arrangement and then comparison of powers and doesn't include much complexities.

Just an Opinion The difficulty level will be automatically calibrated based on users timer sessions.
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Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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9^y + 3^b = 10(3^b)
3^2y + 3^b = 10(3^b)
(3^2y)/(3^b) +1=10
(3^2y)/(3^b) = 9
3^(2y-b) = 3^2
y = 1 & b = 0

2y = 2 --> b+2
Non-Human User Joined: 09 Sep 2013
Posts: 12393
Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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_________________ Re: If 9^y + 3^b = 10*3^b, then 2y ='   [#permalink] 27 Feb 2018, 06:52
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