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

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Bunuel
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If 9^y + 3^b = 10*3^b, then 2y =' [#permalink] New post   05 Jun 2015, 06:13
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25% (medium)

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76% (01:46) correct 24% (02:19) wrong based on 645 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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E
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GMATinsight
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Re: If 9^y + 3^b = 10*3^b, then 2y =' [#permalink] New post   05 Jun 2015, 06:55
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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


Answer: Option
Show Spoiler
E

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Re: If 9^y + 3^b = 10*3^b, then 2y =' [#permalink] New post   05 Jun 2015, 06:58
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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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Re: If 9^y + 3^b = 10*3^b, then 2y =' [#permalink] New post   05 Jun 2015, 07:03
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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 :)


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chetan2u
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If 9^y + 3^b = 10*3^b, then 2y =' [#permalink] New post   06 Jun 2015, 07:44
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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


Hi,

\(9^y + 3^b = 10*3^b\)
\(9^y = 10*3^b-3^b\)
\(3^{2y}=9*3^b\)..
\(3^{2y}=3^2*3^b\)
\(3^{2y}=3^{(b+2)}\)..
so 2y = b+2..


ans E
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Re: If 9^y + 3^b = 10*3^b, then 2y =' [#permalink] New post   08 Jun 2015, 05:46
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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


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.
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Re: If 9^y + 3^b = 10*3^b, then 2y =' [#permalink] New post   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] New post   15 Sep 2020, 10:51
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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


Since \(9^y\) is a power of 9, let \(b=2\), with the result that \(3^b = 3^2 = 9\).
Substituting \(b=2\) into \(9^y + 3^b = 10*3^b\), we get:
\(9^y + 3^2 = 10*3^2\)
\(9^y + 9 = 90\)
\(9^y = 81\)
\(y = 2\)
\(2y = 4\)

The correct answer must yield 4 when b=2.
Only E works:
\(b+2 = 2+2 = 4\)

Show Spoiler
E
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If 9^y + 3^b = 10*3^b, then 2y =' [#permalink] New post   20 Sep 2020, 04:33
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


Given ,
9^y + 3^b = 10*3^b

(3)^2y + 3^b = 10*3^b

(3)^2y-b + 1 = 10 ( by dividing both sides by 3^b )

(3)^2y - b = 3^2

2y - b = 2

2y = b + 2

E is the best answer.
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Re: If 9^y + 3^b = 10*3^b, then 2y =' [#permalink] New post   02 Jan 2023, 08:11
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