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

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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


When you modify the original condition and the question, n^3>3^n? is calculated by multiplying 3n to the both equation, n^1/n>3^1/3. Then, there is 1 variable(n), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), when n=4, 4^3>3^4, which is no and sufficient.
For 2), when m=2, 4^2>2^4, which is also no and sufficient.
Therefore, the answer is D.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

I completely agree this is an odd question and I haven't found anything like it in the OG questions. Having said so:

1. It clearly identifies what The nth root of n is equal to, therefore you could check the inequility of the steam SUFFICIENT
2. It clearly identifies what The nth root of n is equal to, therefore you could check the inequility of the steam SUFFICIENT

ANSWER D

We need to determine whether ^n√n > ^3√3.

Statement One Alone:

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

Since ^n√n = ^4√4, the question becomes: is ^4√4 > ^3√3?

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

(^4√4)^12 > (^3√3)^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 ^n√n = √2, the question becomes: is √2 > ^3√3?

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

(√2)^6 > (^3√3)^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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