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

Question

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

GMATinsight · Accepted Answer

Answer: Option  E

GMATinsight · Answer

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

Bunuel · Answer

The difficulty level will be  automatically  calibrated based on users timer sessions.

chetan2u · Answer

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

Bunuel · Answer

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.

law258 · Answer

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

GMATGuruNY · Answer

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

E

KSBGC · Answer

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.

HRX273 · Answer

why cancel out does not work for 3b??

Bunuel · Answer

Can you please elaborate what you mean by "cancel out 3^b"?

HRX273 · Answer

So basically I meant is we have 3b on the right side so i took that from right to left for bit simplify equation and I cancel the 3b.... Let me know where I went wrong thank you in advance

Bunuel · Answer

I think that method is shown above but here it is again:

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

9^y = 10*3^b - 3^b

9^y = 9*3^b

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

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

2y = 2 + b

HRX273 · Answer

I got it now 🙂 thank you

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

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

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