Last visit was: 24 Jul 2024, 05:13 It is currently 24 Jul 2024, 05:13
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
User avatar
Manager
Manager
Joined: 10 Nov 2010
Posts: 129
Own Kudos [?]: 2678 [50]
Given Kudos: 22
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE:Information Technology (Computer Software)
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94605
Own Kudos [?]: 643495 [31]
Given Kudos: 86734
Send PM
Tutor
Joined: 16 Oct 2010
Posts: 15148
Own Kudos [?]: 66828 [13]
Given Kudos: 436
Location: Pune, India
Send PM
General Discussion
User avatar
Manager
Manager
Joined: 14 Feb 2011
Posts: 103
Own Kudos [?]: 404 [0]
Given Kudos: 3
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
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
avatar
Intern
Intern
Joined: 28 Feb 2011
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
n pow(1/3)* n pow(1/2)=0.5n

n pow (5/6)= 0.5n

n pow(1/6)=2

n= 64
avatar
Intern
Intern
Joined: 14 Apr 2011
Posts: 6
Own Kudos [?]: 5 [0]
Given Kudos: 0
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
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???????
User avatar
Senior Manager
Senior Manager
Joined: 01 Feb 2011
Posts: 305
Own Kudos [?]: 328 [0]
Given Kudos: 42
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
n^(5/6) = (1/2)n

=> n^6-2^6*n^5 = 0

=> n =0 or 64.

Answer is B.
User avatar
Intern
Intern
Joined: 27 Feb 2011
Posts: 22
Own Kudos [?]: 9 [1]
Given Kudos: 9
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
1
Kudos
GMATD11 wrote:
From B and E whts wrong with E


50% of 729 is not an integer .. whereas @(729) is an integer
Tutor
Joined: 16 Oct 2010
Posts: 15148
Own Kudos [?]: 66828 [2]
Given Kudos: 436
Location: Pune, India
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
2
Kudos
Expert Reply
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.
avatar
Intern
Intern
Joined: 14 Apr 2011
Posts: 6
Own Kudos [?]: 5 [0]
Given Kudos: 0
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
hi karishma,

seems like the best and easiest ans .. thank you so much .
User avatar
Manager
Manager
Joined: 26 Feb 2015
Posts: 94
Own Kudos [?]: 207 [0]
Given Kudos: 43
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
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?
Tutor
Joined: 16 Oct 2010
Posts: 15148
Own Kudos [?]: 66828 [0]
Given Kudos: 436
Location: Pune, India
Send PM
If @(n) is defined as the product of the cube root of n and [#permalink]
Expert Reply
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?


Check out the blog posts on the link given in my signature below.

Originally posted by KarishmaB on 10 Mar 2015, 06:05.
Last edited by KarishmaB on 17 Oct 2022, 01:51, edited 1 time in total.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19189
Own Kudos [?]: 22706 [1]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
1
Bookmarks
Expert Reply
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
Current Student
Joined: 10 Sep 2019
Posts: 137
Own Kudos [?]: 33 [0]
Given Kudos: 59
Location: India
Concentration: Social Entrepreneurship, Healthcare
GMAT 1: 680 Q49 V33
GMAT 2: 720 Q50 V37
GRE 1: Q167 V159
GPA: 2.59
WE:Project Management (Non-Profit and Government)
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
This can be written as (n)^1/3 * (n)^1/2 = 0.5n

= (n)^5/6 = 0.5n

= (n)^1/6 = 2

=> n = 2^6

=> n = 64

Ans B
Senior Manager
Senior Manager
Joined: 28 Feb 2014
Posts: 470
Own Kudos [?]: 591 [0]
Given Kudos: 74
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE:Engineering (Education)
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#permalink]
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

@(n) = n^1/3 x n^1/2 = n^5/6

According to the condition
n^5/6 = n/2
--> 2 = n^1/6
--> n =64

B is correct.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34061
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: If @(n) is defined as the product of the cube root of n and [#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: If @(n) is defined as the product of the cube root of n and [#permalink]
Moderator:
Math Expert
94605 posts