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

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

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New post 05 Jun 2015, 05:13
4
6
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:47) correct 30% (02:19) wrong based on 285 sessions

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

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New post 05 Jun 2015, 05:55
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


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

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

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New post 05 Jun 2015, 06:03
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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New post 06 Jun 2015, 06:44
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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Re: If 9^y + 3^b = 10*3^b, then 2y ='  [#permalink]

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New post 08 Jun 2015, 04:46
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:

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

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

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

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

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

\(3^{2y} = 3^{b + 2}\)

\(2y = b + 2\)

The correct answer is E.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 28 Oct 2016, 18:00
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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Re: If 9^y + 3^b = 10*3^b, then 2y =' &nbs [#permalink] 27 Feb 2018, 05:52
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