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nth root

by j_shreyans » Wed Sep 17, 2014 2:00 am
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

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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Sep 17, 2014 3:28 am
j_shreyans 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
Question stem: Is n^(1/n) > 3^(1/3)?

Statement 1:
n^(1/n) = 4^(1/4).
Since the value of n^(1/n) is known, we can determine whether n^(1/n) > 3^(1/3).
SUFFICIENT.

Statement 2:
n^(1/n) = 2^(1/2).
Since the value of n^(1/n) is known, we can determine whether n^(1/n) > 3^(1/3).
SUFFICIENT.

The correct answer is D.
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by Brent@GMATPrepNow » Wed Sep 17, 2014 6:09 am
j_shreyans 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

OAD
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

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