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

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Sep 20, 2014 6:40 am
gmat_guy666 wrote:Is the nth root of n greater than the cube root of 3?

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

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
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by sushantsahaji » Sat Apr 16, 2016 1:46 am
Dear Brent,

In statement 1, nth root of n is equal to the 4th root of 4.

As the 4th root is even, will it not have dual roots,+&-?
And if so, then how can we be sure of unique soln as the target question is considering cube root of 3,which will provide only 1 solition?

Thanks
&
Regards,

Sushant
Brent@GMATPrepNow wrote:
gmat_guy666 wrote:Is the nth root of n greater than the cube root of 3?

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

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
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by Brent@GMATPrepNow » Sat Apr 16, 2016 7:10 am
sushantsahaji wrote:Dear Brent,

In statement 1, nth root of n is equal to the 4th root of 4.

As the 4th root is even, will it not have dual roots,+&-?
And if so, then how can we be sure of unique soln as the target question is considering cube root of 3,which will provide only 1 solition?

Thanks
&
Regards,

Sushant
The rules for the 4th root notation are the same for the square root notation.
For example, the square root notation (e.g. √n) tells us to find the non-negative value (k) such that k² = n
So, √9 = 3 (and not -3)

Likewise, ∜n tells us to find the non-negative value (j) such that j� = n
So, ∜16 = 2 (and not -2)

The same applies to the notation for 6th roots, 8th roots, etc.

Cheers,
Brent
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