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4^(2x)

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4^(2x) [#permalink] New post 27 Jul 2016, 15:14
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Expert's post
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Question Stats:

68% (00:28) correct 31% (00:49) wrong based on 70 sessions
Quantity A
Quantity B
4^(2x)
16^x


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Note: These questions are designed to help students master the quantitative comparison questions on our site: https://www.greenlighttestprep.com/modu ... comparison
[Reveal] Spoiler: OA

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Last edited by Carcass on 28 Jul 2016, 02:26, edited 1 time in total.
Adding the tags
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Re: 4^(2x) [#permalink] New post 28 Jul 2016, 10:18
Expert's post
GreenlightTestPrep wrote:
Quantity A
Quantity B
4^(2x)
16^x



If you're not sure where to start, you can always start with PLUGGING IN NUMBERS.

Let's start with an easy value for x. How about x = 0
We get:
Quantity A: 4^(2x) = 4⁰ = 1
Quantity B: 16^x = 16⁰ = 1
Okay, the quantities are EQUAL

At this point, we know the correct answer is C or D

Now try some other value for x.
How about: x = 1
We get:
Quantity A: 4^(2x) = 4² = 16
Quantity B: 16^x = 16¹ = 16
The quantities are still EQUAL

Let's try x = -1
We get:
Quantity A: 4^(2x) = 4ˉ² = 1/4² = 1/16
Quantity B: 16^x = 16ˉ¹ = 1/16
The quantities are still EQUAL

Let's try one more value for x. How about x = 2
We get:
Quantity A: 4^(2x) = 4⁴ = 256
Quantity B: 16^x = 16² = 256
The quantities are still EQUAL

At this point, we might be reasonably convinced that the two quantities will always be equal. So, you might submit this as the correct answer and move on.
In my next post, I'll show you why the correct answer is C

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Last edited by GreenlightTestPrep on 30 Jul 2016, 05:57, edited 1 time in total.
GRE Instructor
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Joined: 10 Apr 2015
Posts: 3535
Followers: 134

Kudos [?]: 4020 [0], given: 65

CAT Tests
Re: 4^(2x) [#permalink] New post 28 Jul 2016, 10:22
Expert's post
GreenlightTestPrep wrote:
Quantity A
Quantity B
4^(2x)
16^x




NOTE: If you've just begun preparing for the GRE, you might not yet be familiar with the laws of exponents. Nevertheless, here's another approach.
Take 16 in Quantity B and rewrite it as

We get:
Quantity A: 4^(2x)
Quantity B: ()^x

Now apply the POWER OF A POWER Law to Quantity B to get:
Quantity A: 4^(2x)
Quantity B: 4^(2x)

At this point can be certain that the two quantities will always be equal
Answer:
[Reveal] Spoiler:
C


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Intern
Intern
Joined: 30 Jul 2016
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 3

Re: 4^(2x) [#permalink] New post 30 Jul 2016, 04:36
I am confused on this one you did:
"Let's try one more value for x. How about x = 1
We get:
Quantity A: 4^(2x) = 4⁴ = 256
Quantity B: 16^x = 16² = 256"
The quantities are still EQUAL"

If x=1, then 4^(2(1))= 4^2= 16
and 16^1=16. How did you get 4^4 and 16^2?
Manager
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Joined: 23 Jan 2016
Posts: 133
Followers: 4

Kudos [?]: 145 [0], given: 15

Re: 4^(2x) [#permalink] New post 30 Jul 2016, 05:40
Faye214 wrote:
I am confused on this one you did:
"Let's try one more value for x. How about x = 1
We get:
Quantity A: 4^(2x) = 4⁴ = 256
Quantity B: 16^x = 16² = 256"
The quantities are still EQUAL"

If x=1, then 4^(2(1))= 4^2= 16
and 16^1=16. How did you get 4^4 and 16^2?


I guess he meant x = 2, but might mistakenly typed 1.

Anyway the best way to solve this is using algebra than plugging in
GRE Instructor
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Joined: 10 Apr 2015
Posts: 3535
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Kudos [?]: 4020 [0], given: 65

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Re: 4^(2x) [#permalink] New post 30 Jul 2016, 05:58
Expert's post
Faye214 wrote:
I am confused on this one you did:
"Let's try one more value for x. How about x = 1
We get:
Quantity A: 4^(2x) = 4⁴ = 256
Quantity B: 16^x = 16² = 256"
The quantities are still EQUAL"

If x=1, then 4^(2(1))= 4^2= 16
and 16^1=16. How did you get 4^4 and 16^2?


Good catch!
I have edited my response accordingly.

Cheers,
Brent
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Re: 4^(2x)   [#permalink] 30 Jul 2016, 05:58
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