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

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

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05 Jun 2015, 06:13
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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Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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05 Jun 2015, 06:55
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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Posts: 7830
Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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06 Jun 2015, 07:44
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
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Posts: 58113
Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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08 Jun 2015, 05:46
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:

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

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

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

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

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

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

$$2y = b + 2$$

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Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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05 Jun 2015, 06:58
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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Math Expert
Joined: 02 Sep 2009
Posts: 58113
Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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05 Jun 2015, 07:03
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

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Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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28 Oct 2016, 19:00
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
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Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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27 Feb 2018, 06:52
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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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