If a is a positive integer then 3^(2a) + 36^a/2^(2a) =

Question

If a is a positive integer then  3^{(2a)} + \frac{36^a}{2^{(2a)}} =

A.  (\frac{9}{4})^a + 9^a 
 
B.  9^a + 18^a

C.  18^a

D.  0

E.  2*9^a

ENGRTOMBA2018 · Accepted Answer

I am quoting the same question with a bit more formatting:

3^{2a} + \frac{36^a}{2^{2a}}  ----> Let go of the variables and plug in a =1 as this statement must be true for all values of a (even 0).

Thus with a =1 we get,  3^{2} + \frac{36^1}{2^{2}}  = 2* 9 =18---> Now plug in a =1 in the options and we see that options C and E satisfy this. To eliminate C, use a =0. Thus E is the correct answer.

sanket1991 · Answer

3^(2a) + 36^a/2^(2a) = 9^a + (9^a*4^a/ 4^a) = 9^a + 9^a = 2*9^a

ashokk138 · Answer

Given:
3^(2a) can be written as 9^a
Similarly,2^(2a) can be written as 4^a

Rearranging the eq:

9^a + (36^a / 4^a) => 9^a + (36/4) ^ a => 9^a + 9^a => 2 x 9^a.

Option E

ashokk138 · Answer

Given:
3^(2a) can be written as 9^a
Similarly,2^(2a) can be written as 4^a

Rearranging the eq:

9^a + (36^a / 4^a) => 9^a + (36/4) ^ a => 9^a + 9^a => 2 x 9^a.

Option E

Bunuel · Answer

800score Official Solution:

3^(2a) + 36^a/ 2^(2a) = 9^a + 36^a/4^a = 9^a + (36/4)^a = 9^a + 9^a = 2 × 9^a,  choice (E) .

Plugging in different values for a until all choices except one are eliminated is also an option.

mvictor · Answer

the fraction can be rewritten as:
(4*9)^a/2^2a

now, numerator can be rewritten as:
2^2a * 3^2a / 2^2a.

simplify 2^2a from numerator and denominator

we are left with 3^2a * 3^2a
rewrite 3^2a(1+1)
3^2a(2)
since no answer matches, let's raise 3 to the second power:
9^a * 2
E is the answer.

redone the question sept 9/28/16
same approach used.

stne · Answer

Thought the question to be :  \frac{3^{2a} + 36^a}{2^{2a}} and ended up getting A.

Question actually means  3^{2a} + \frac{36^a}{2^{2a}}

Perhaps moderator could format in a different way to make the question less confusing. Thank you.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a is a positive integer then 3^(2a) + 36^a/2^(2a) =

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a is a positive integer then 3^(2a) + 36^a/2^(2a) =

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards