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4^(2x)
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Updated on: 28 Jul 2016, 02:26
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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.
Re: 4^(2x)
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Updated on: 30 Jul 2016, 05:57
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
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 4²
We get: Quantity A: 4^(2x) Quantity B: (4²)^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:
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 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
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.
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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