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nth root of n greater than the cube root of 3?

Problem Solving — algebra and arithmetic
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by rainac » Wed Sep 10, 2014 1:07 pm
Is the nth root of n greater than the cube root of 3?

The nth root of n is equal to the 4th root of 4
The nth root of n is equal to the square root of 2

OA: D
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by Brent@GMATPrepNow » Wed Sep 10, 2014 1:46 pm
rainac wrote:Is the nth root of n greater than the cube root of 3?

The nth root of n is equal to the 4th root of 4
The nth root of n is equal to the square root of 2

OA: D
IMPORTANT: This question illustrates a situation in which we need not perform any calculations. Instead, we need only recognize that we COULD perform calculations, which would allow us to determine whether or not a statement is sufficient.

Target question: Is (nth root of n) greater than (cube root of 3)?

Statement 1: The nth root of n is EQUAL TO the 4th root of 4
"EQUAL TO" is key here.
Since we COULD determine the exact value of the 4th root of 4 (which is equal to nth root of n), and we COULD determine the exact value of the cube root of 3, we could definitely determine whether (nth root of n) is greater than (cube root of 3)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The nth root of n is EQUAL TO the square root of 2
Once again, we have "EQUAL TO"
So, we COULD determine the exact value of the √2 (which is equal to nth root of n), and we COULD determine the exact value of the cube root of 3.
So, we could definitely determine whether (nth root of n) is greater than (cube root of 3)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by gmatcracker0123 » Sun Sep 28, 2014 8:07 pm
I started solving this question just to realize that I could not solve it. However when I read the solution what I did realize was the IMPORTANCE OF READING THE QUESTION and UNDERSTANDING IT completely before approaching towards the solution.

Not reading the question correctly can be the biggest drawback in finding the correct solution.

Thanks Brent for reminding me about the importance of reading the question before starting off with the solution.
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