If @(n) is defined as the product of the cube root of n and : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 18:42

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If @(n) is defined as the product of the cube root of n and

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 10 Nov 2010
Posts: 267
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 301 [0], given: 22

If @(n) is defined as the product of the cube root of n and [#permalink]

### Show Tags

28 Feb 2011, 02:12
7
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

67% (03:05) correct 33% (02:10) wrong based on 439 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
[Reveal] Spoiler: OA

Attachments

n integer.JPG [ 13.49 KiB | Viewed 5202 times ]

_________________

The proof of understanding is the ability to explain it.

Last edited by Bunuel on 10 Feb 2014, 00:50, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 14 Feb 2011
Posts: 196
Followers: 4

Kudos [?]: 126 [0], given: 3

### Show Tags

28 Feb 2011, 02:19
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
Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93212 [6] , given: 10553

### Show Tags

28 Feb 2011, 02:27
6
KUDOS
Expert's post
6
This post was
BOOKMARKED
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

Given: $$@(n)=\sqrt[3]{n}*\sqrt[2]{n}$$. Question: if $$@(n)=0.5n$$ then $$n=?$$

So we have that $$\sqrt[3]{n}*\sqrt[2]{n}=\frac{1}{2}*n$$ --> $$2*\sqrt[3]{n}*\sqrt[2]{n}=n$$ --> take to the 6th power --> $$64*n^2*n^3=n^6$$ --> $$n=64$$.

_________________
Intern
Joined: 28 Feb 2011
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 0

### Show Tags

28 Feb 2011, 06:20
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: 7125
Location: Pune, India
Followers: 2136

Kudos [?]: 13655 [1] , given: 222

### Show Tags

28 Feb 2011, 18:51
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
GMATD11 wrote:
From B and E whts wrong with E

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
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 14 Apr 2011 Posts: 11 Followers: 0 Kudos [?]: 1 [0], given: 0 Re: n [#permalink] ### Show Tags 01 Aug 2011, 08:44 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: 755 Followers: 14 Kudos [?]: 115 [0], given: 42 Re: n [#permalink] ### Show Tags 01 Aug 2011, 10:50 n^(5/6) = (1/2)n => n^6-2^6*n^5 = 0 => n =0 or 64. Answer is B. Intern Joined: 27 Feb 2011 Posts: 48 Followers: 0 Kudos [?]: 3 [0], given: 9 Re: n [#permalink] ### Show Tags 01 Aug 2011, 12:43 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: 7125 Location: Pune, India Followers: 2136 Kudos [?]: 13655 [1] , given: 222 Re: n [#permalink] ### Show Tags 01 Aug 2011, 20:08 1 This post received KUDOS Expert's post 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 My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Intern
Joined: 14 Apr 2011
Posts: 11
Followers: 0

Kudos [?]: 1 [0], given: 0

### Show Tags

01 Aug 2011, 22:35
hi karishma,

seems like the best and easiest ans .. thank you so much .
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13459
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If @(n) is defined as the product of the cube root of n and [#permalink]

### Show Tags

19 Jul 2014, 08:36
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.
_________________
Manager
Joined: 26 Feb 2015
Posts: 127
Followers: 0

Kudos [?]: 9 [0], given: 43

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

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: 7125
Location: Pune, India
Followers: 2136

Kudos [?]: 13655 [0], given: 222

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

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 ... ration-ii/
http://www.veritasprep.com/blog/2011/07 ... s-applied/
http://www.veritasprep.com/blog/2011/08 ... -the-gmat/
http://www.veritasprep.com/blog/2011/08 ... exponents/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13459
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If @(n) is defined as the product of the cube root of n and [#permalink]

### Show Tags

10 May 2016, 00:01
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.
_________________
Re: If @(n) is defined as the product of the cube root of n and   [#permalink] 10 May 2016, 00:01
Similar topics Replies Last post
Similar
Topics:
20 For each positive integer n, p(n) is defined to be the product of.. 9 05 May 2016, 09:16
5 The function F(n) is defined as the product of all the conse 7 15 Oct 2012, 10:16
72 For any positive integer n, the length of n is defined as 13 29 Jan 2012, 16:15
A function g(n), where n is an integer, is defined as the product of 1 22 Jan 2011, 05:30
A sequence is defined as follows: a(n)= (n)/(n+1) If n is a 8 12 Oct 2008, 05:01
Display posts from previous: Sort by