January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Nov 2010
Posts: 186
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)

If @(n) is defined as the product of the cube root of n and
[#permalink]
Show Tags
Updated on: 10 Feb 2014, 00:50
Question Stats:
68% (02:04) correct 32% (02:32) wrong based on 622 sessions
HideShow timer Statistics
If @(n) is defined as the product of the cube root of n and the positive square root of n, then for what number n does @(n)=50 percent of n? A. 16 B. 64 C. 100 D. 144 E. 729
Official Answer and Stats are available only to registered users. Register/ Login.
Attachments
n integer.JPG [ 13.49 KiB  Viewed 7764 times ]
_________________
The proof of understanding is the ability to explain it.
Originally posted by GMATD11 on 28 Feb 2011, 02:12.
Last edited by Bunuel on 10 Feb 2014, 00:50, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 52294





Manager
Joined: 14 Feb 2011
Posts: 175

for 16, cube root is 2* cube root of 2 and positive square root is 4, so @n = 2*2^(1/3)*4 = 8 *2(1/3) so greater than 8 or greater than 0.5n
Similarly for 64, it is 4*8 = 32 = 0.5*64, so B is correct.
For E, the cube root is 9 and positive square root is 27, so 27*9 is not equal to 0.5*729, so incorrect



Intern
Joined: 28 Feb 2011
Posts: 6

n pow(1/3)* n pow(1/2)=0.5n
n pow (5/6)= 0.5n
n pow(1/6)=2
n= 64



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8795
Location: Pune, India

GMATD11 wrote: From B and E whts wrong with E Just follow the rules of exponents. Answer will follow. Cube root is the power of 1/3. Square root is the power of 1/2 \(n^{\frac{1}{3}}*n^{\frac{1}{2}} = \frac{n}{2}\) You need to find n. So bring all n's together on one side of the equation and everything else on the other side. Adding the exponents, \(n^{\frac{5}{6}} = \frac{n}{2}\) Clubbing n's together, \(2 = n^{1\frac{5}{6}}\) \(n = 2^6 = 64\) Hence it cannot be 729. If in the question, rather than half, we had a third, answer would have been 729.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 14 Apr 2011
Posts: 11

the cube root of what integer power of 2 is closest to 50?
1)16 2) 17 3)18 4 ) 19 5) 20
can u pls help me in this by a quicker solution???????



Director
Joined: 01 Feb 2011
Posts: 658

n^(5/6) = (1/2)n
=> n^62^6*n^5 = 0
=> n =0 or 64.
Answer is B.



Intern
Joined: 27 Feb 2011
Posts: 40

GMATD11 wrote: From B and E whts wrong with E 50% of 729 is not an integer .. whereas @(729) is an integer



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8795
Location: Pune, India

sushantarora wrote: the cube root of what integer power of 2 is closest to 50?
1)16 2) 17 3)18 4 ) 19 5) 20
can u pls help me in this by a quicker solution??????? Look at the powers of 2. 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 Since it is an exponential increase, the result increases much more as you go to higher and higher powers. Which powers of 2 are around 50? 2^5 = 32 2^6 = 64 50 is almost in the middle of the two of them but closer to 64. Also, the result increases more with higher powers so I would expect 50 to be almost 2^(5.6) or a little higher. If you find the cube root of 2^18, you will get (2^18)^(1/3) = 2^6 If you find the cube root of 2^17, you will get (2^17)^(1/3) = 2^(5.667) This is the closest. Answer is 17.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 14 Apr 2011
Posts: 11

hi karishma,
seems like the best and easiest ans .. thank you so much .



Manager
Joined: 26 Feb 2015
Posts: 115

Re: If (n) is defined as the product of the cube root of n and
[#permalink]
Show Tags
10 Mar 2015, 02:31
VeritasPrepKarishma wrote: GMATD11 wrote: From B and E whts wrong with E Just follow the rules of exponents. Answer will follow. Cube root is the power of 1/3. Square root is the power of 1/2 \(n^{\frac{1}{3}}*n^{\frac{1}{2}} = \frac{n}{2}\) You need to find n. So bring all n's together on one side of the equation and everything else on the other side. Adding the exponents, \(n^{\frac{5}{6}} = \frac{n}{2}\) Clubbing n's together, \(2 = n^{1\frac{5}{6}}\) \(n = 2^6 = 64\) Hence it cannot be 729. If in the question, rather than half, we had a third, answer would have been 729. I really need to study these formulas, where do I suggest I go?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8795
Location: Pune, India

Re: If (n) is defined as the product of the cube root of n and
[#permalink]
Show Tags
10 Mar 2015, 05:05
erikvm wrote: VeritasPrepKarishma wrote: GMATD11 wrote: From B and E whts wrong with E Just follow the rules of exponents. Answer will follow. Cube root is the power of 1/3. Square root is the power of 1/2 \(n^{\frac{1}{3}}*n^{\frac{1}{2}} = \frac{n}{2}\) You need to find n. So bring all n's together on one side of the equation and everything else on the other side. Adding the exponents, \(n^{\frac{5}{6}} = \frac{n}{2}\) Clubbing n's together, \(2 = n^{1\frac{5}{6}}\) \(n = 2^6 = 64\) Hence it cannot be 729. If in the question, rather than half, we had a third, answer would have been 729. I really need to study these formulas, where do I suggest I go? Here are the basics of exponents and roots: http://www.veritasprep.com/blog/2011/07 ... eparation/http://www.veritasprep.com/blog/2011/07 ... rationii/http://www.veritasprep.com/blog/2011/07 ... sapplied/http://www.veritasprep.com/blog/2011/08 ... thegmat/http://www.veritasprep.com/blog/2011/08 ... exponents/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4551
Location: United States (CA)

Re: If (n) is defined as the product of the cube root of n and
[#permalink]
Show Tags
28 Jun 2017, 16:01
GMATD11 wrote: If @(n) is defined as the product of the cube root of n and the positive square root of n, then for what number n does @(n)=50 percent of n?
A. 16 B. 64 C. 100 D. 144 E. 729 We are given that @(n) is defined as the product of the cube root of n and the positive square root of n. We need to determine for what number n does @(n) = 50 percent of n. We see that @n = (∛n)(√n) = (n^(⅓))(n^(½)) = n^(⅓ + ½) = n^(⅚) We need to determine a value for n when: n^(⅚) = 0.5n 2n^(⅚) = n 2 = n/n^(⅚) 2 = n^(⅙) 2^6 = n n = 64 Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 9450

Re: If @(n) is defined as the product of the cube root of n and
[#permalink]
Show Tags
19 Sep 2018, 08:22
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If @(n) is defined as the product of the cube root of n and &nbs
[#permalink]
19 Sep 2018, 08:22






