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

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

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

by Vincen » Tue Jan 16, 2018 8:47 am

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

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

The OA is the option D.

How can I use each statement to get an answer here? Experts, I would appreciate your help. Thanks

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Source: Beat The GMAT — Data Sufficiency | Tue Jan 16, 2018 8:47 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Jan 16, 2018 8:55 am

Vincen wrote:Is the nth root of n greater than the cube root of 3?

1) The nth root of n is equal to the 4th root of 4
2) 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 since 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 âˆš2 (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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jan 18, 2018 1:43 pm

Vincen wrote:Is the nth root of n greater than the cube root of 3?

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

We need to determine whether ^nâˆšn > ^3âˆš3.

Statement One Alone:

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

Since ^nâˆšn = ^4âˆš4, the question becomes: is ^4âˆš4 > ^3âˆš3?

Let's raise both sides to the 12th power:

(^4âˆš4)^12 > (^3âˆš3)^12 ?

4^3 > 3^4 ?

64 > 81 ?

We see that the answer is no. Statement one alone is sufficient to answer the question.

Statement Two Alone:

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

Thus, we know that:

Since ^nâˆšn = âˆš2, the question becomes: is âˆš2 > ^3âˆš3?

Let's raise both sides to the 6th power:

(âˆš2)^6 > (^3âˆš3)^6 ?

2^3 > 3^2 ?

8 > 9 ?

We see that the answer is no again. Statement two alone is also sufficient to answer the question.

Answer: D

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