Last visit was: 24 Jul 2024, 13:54 It is currently 24 Jul 2024, 13:54
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Manager
Manager
Joined: 06 Jun 2014
Posts: 72
Own Kudos [?]: 566 [7]
Given Kudos: 109
Location: United States
Concentration: Finance, General Management
GMAT 1: 450 Q27 V21
GPA: 3.47
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30863 [2]
Given Kudos: 799
Location: Canada
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6031
Own Kudos [?]: 13827 [2]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10133
Own Kudos [?]: 17060 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: Is the nth root of n greater than the cube root of 3? [#permalink]
Expert Reply
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.
User avatar
Intern
Intern
Joined: 06 Jan 2015
Posts: 48
Own Kudos [?]: 67 [0]
Given Kudos: 7
Send PM
Re: Is the nth root of n greater than the cube root of 3? [#permalink]
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

GMATinsight wrote:
zxcvbnmas 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


Question : Is \(n^{1/n} > n^{1/3}\)?

HINT: To answer the question we require some information about sign of n and range of values of n

Statement 1: \(n^{1/n} = 4^{1/4}\)
This is possible only for n = 4, Hence
SUFFICIENT

Statement 2: \(n^{1/n} = 2^{1/2}\)
This is possible only for n = 4, Hence
SUFFICIENT

Answer: option D



IMPORTANT: I would like to mark this question as BAD and INVALID question for a test like GMAT.

GMAT never gives information in two statements that have even possibility of contradicting with each other i.e. value of n as per 2nd statement can't be 4 if the first statement has already brought it as 4. However 2nd statement may have more possible value of n in addition to 4 if the 1st statement has already brought us to get the value of n as 4
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19191
Own Kudos [?]: 22718 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: Is the nth root of n greater than the cube root of 3? [#permalink]
Expert Reply
zxcvbnmas 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 ^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
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34075
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: Is the nth root of n greater than the cube root of 3? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: Is the nth root of n greater than the cube root of 3? [#permalink]
Moderator:
Math Expert
94609 posts