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

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If a is a positive integer then 3^(2a) + 36^a/2^(2a) =  [#permalink]

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New post 15 Jul 2015, 03:12
1
8
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (02:01) correct 36% (02:10) wrong based on 220 sessions

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Re: If a is a positive integer then 3^(2a) + 36^a/2^(2a) =  [#permalink]

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New post 15 Jul 2015, 04:06
3^(2a) + 36^a/2^(2a) = 9^a + (9^a*4^a/ 4^a) = 9^a + 9^a = 2*9^a
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Re: If a is a positive integer then 3^(2a) + 36^a/2^(2a) =  [#permalink]

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New post 15 Jul 2015, 04:36
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Bunuel wrote:
If a is a positive integer then 3^(2a) + 36^a/2^(2a) =

A. (9/4)^a + 9^a
B. 9^a + 18^a
C. 18^a
D. 0
E. 2 × 9^a

Kudos for a correct solution.


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.
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Re: If a is a positive integer then 3^(2a) + 36^a/2^(2a) =  [#permalink]

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New post 17 Jul 2015, 23:46
1
Bunuel wrote:
If a is a positive integer then 3^(2a) + 36^a/2^(2a) =

A. (9/4)^a + 9^a
B. 9^a + 18^a
C. 18^a
D. 0
E. 2 × 9^a

Kudos for a correct solution.


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
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Re: If a is a positive integer then 3^(2a) + 36^a/2^(2a) =  [#permalink]

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New post 17 Jul 2015, 23:47
Bunuel wrote:
If a is a positive integer then 3^(2a) + 36^a/2^(2a) =

A. (9/4)^a + 9^a
B. 9^a + 18^a
C. 18^a
D. 0
E. 2 × 9^a

Kudos for a correct solution.


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
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Re: If a is a positive integer then 3^(2a) + 36^a/2^(2a) =  [#permalink]

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New post 19 Jul 2015, 13:14
Bunuel wrote:
If a is a positive integer then 3^(2a) + 36^a/2^(2a) =

A. (9/4)^a + 9^a
B. 9^a + 18^a
C. 18^a
D. 0
E. 2 × 9^a

Kudos for a correct solution.


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.
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If a is a positive integer then 3^(2a) + 36^a/2^(2a) =  [#permalink]

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New post 30 Dec 2015, 20:53
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.
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Re: If a is a positive integer then 3^(2a) + 36^a/2^(2a) =  [#permalink]

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New post 30 Jun 2018, 04:54
Bunuel wrote:
If a is a positive integer then 3^(2a) + (36^a)/(2^(2a)) =

A. (9/4)^a + 9^a
B. 9^a + 18^a
C. 18^a
D. 0
E. 2 × 9^a

Kudos for a correct solution.


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.
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Re: If a is a positive integer then 3^(2a) + 36^a/2^(2a) = &nbs [#permalink] 30 Jun 2018, 04:54
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