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

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by [email protected] » Fri Dec 01, 2017 4:15 pm
Hi LUANDATO,

While this question might look 'scary', it can be solved rather easily by TESTing VALUES.

Since B appears on both sides of the equation, we'll TEST a value for B and then solve for Y....

IF...
B = 0
(9^Y) + (3^0) = (10)(3^0)
(9^Y) + 1 = (10)(1)
(9^Y) = 9
Y = 1

The question asks for the value of 2Y, so we're looking for an answer that equals 2 when B=0. There's only one answer that matches...

Final Answer: E

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by EconomistGMATTutor » Sat Dec 02, 2017 12:43 pm
$$If\ \ 9^y+3^b=10*3^b,\ \ then\ \ 2y=?$$

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

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
Hi LUANDATO,
Lets take a look at your question.

$$9^y+3^b=10\times3^b$$
$$\left(3^2\right)^y+3^b=10\times3^b$$
$$\left(3^2\right)^y=10\times3^b-3^b$$
$$3^{2y}=10\times3^b-3^b$$
$$3^{2y}=3^b\left(10-1\right)$$
$$3^{2y}=3^b\left(9\right)$$
$$3^{2y}=3^b\left(3^2\right)$$
$$3^{2y}=3^{b+2}$$
Since bases are equivalent, therefore, exponents will be equal as well,
$$2y=b+2$$

Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any followup.
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by Scott@TargetTestPrep » Sun Sep 29, 2019 6:19 pm
BTGmoderatorLU 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

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
Simplifying, we have:

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

3^(2y) = 3^b x (10 - 1)

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

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

2y = b + 2

Answer: E

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