Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 19 Jun 2013, 23:22

# A third Problem Solving question

Author Message
TAGS:
Intern
Joined: 06 Oct 2010
Posts: 41
Followers: 0

Kudos [?]: 1 [0], given: 29

A third Problem Solving question [#permalink]  06 Oct 2010, 12:26
00:00

Question Stats:

80% (02:37) correct 20% (01:11) wrong based on 10 sessions
Please explain how to solve the following question. It was listed in one of the GMAT Paper Tests.

16. For all real numbers v, the operation is defined by the equation v* = v - v/3. If (v*)* = 8, then v=

(A) 15
(B) 18
(C) 21
(D) 24
(E) 27

My problem is that I don't know how to interpret the following symbols: (v*)*. Hopefully someone can help. Thanks.
[Reveal] Spoiler: OA
 Kaplan Promo Code Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes
Senior Manager
Joined: 06 Jun 2009
Posts: 335
Location: USA
WE 1: Engineering
Followers: 1

Kudos [?]: 36 [2] , given: 0

Re: A third Problem Solving question [#permalink]  06 Oct 2010, 12:42
2
KUDOS
niheil wrote:
Please explain how to solve the following question. It was listed in one of the GMAT Paper Tests.

16. For all real numbers v, the operation is defined by the equation v* = v - v/3. If (v*)* = 8, then v=

(A) 15
(B) 18
(C) 21
(D) 24
(E) 27

My problem is that I don't know how to interpret the following symbols: (v*)*. Hopefully someone can help. Thanks.

v* = v - v/3

For sake of understanding, let v* = B

B = v - v/3

Therefore, (v*)* = B* = B-B/3

Or, (v*)* = [v- v/3] - [v- v/3]/3

8 = 2v/3 - 2v/9
v = 18
_________________

All things are possible to those who believe.

GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879

Kudos [?]: 10133 [1] , given: 965

Re: A third Problem Solving question [#permalink]  06 Oct 2010, 12:52
1
KUDOS
niheil wrote:
Please explain how to solve the following question. It was listed in one of the GMAT Paper Tests.

16. For all real numbers v, the operation is defined by the equation v* = v - v/3. If (v*)* = 8, then v=

(A) 15
(B) 18
(C) 21
(D) 24
(E) 27

My problem is that I don't know how to interpret the following symbols: (v*)*. Hopefully someone can help. Thanks.

Given: v*=v-\frac{v}{3}=\frac{2}{3}v and (v*)*=8.
Question: v=?

(v*)*=(\frac{2}{3}v)*=\frac{2}{3}*(\frac{2}{3}v)=8 --> \frac{4}{9}v=8 --> v=18.

_________________
Intern
Joined: 06 Oct 2010
Posts: 41
Followers: 0

Kudos [?]: 1 [0], given: 29

Re: A third Problem Solving question [#permalink]  06 Oct 2010, 13:06
Bunuel, how did you know that (2v/3)* = 2/3 x (2v/3)?
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879

Kudos [?]: 10133 [0], given: 965

Re: A third Problem Solving question [#permalink]  06 Oct 2010, 13:14
niheil wrote:
Bunuel, how did you know that (2v/3)* = 2/3 x (2v/3)?

v*=v-\frac{v}{3}=\frac{2}{3}v so v* is \frac{2}{3}rd of v. So (\frac{2}{3}v)* is \frac{2}{3}rd of \frac{2}{3}v.
_________________
Intern
Joined: 06 Oct 2010
Posts: 41
Followers: 0

Kudos [?]: 1 [0], given: 29

Re: A third Problem Solving question [#permalink]  06 Oct 2010, 13:22
Awesome! I understand. Thanks Bunuel! And thanks again adishail!
Intern
Joined: 31 Oct 2010
Posts: 32
Followers: 0

Kudos [?]: 1 [0], given: 25

new [#permalink]  11 Dec 2010, 09:36
ywilfred wrote:
For all real numbers v, the operation v* is defined by the equation v* = v - v/3 . If (v*)* = 8, what is the value of v.

Since v* = v - v/3,

(v*)* = (v - v/3) - (v - v/3)/3
= (3v-v)/3 - [(3v-v)/3]/3
= 2v/3 - (2v/3)/3
= 2v/3 - 2v/9
= (6v - 2v)/9
= 4v/9

We also know that (v*)* = 8, so (v*)* = 8 = 4v/9 and v = 18.

(v-v/3) did you just multiply by three to just make the v/3 go away? but then why does the first part get divided by three, its late here so the synapses arent firing at full speed scotty.

im losing the progression from (v-v/3) - (v-v/3)/3 --------> (3v-v)/3 - [(3v-v)/3]/3
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879

Kudos [?]: 10133 [1] , given: 965

Re: new [#permalink]  11 Dec 2010, 09:52
1
KUDOS
Merging similar topics. Refer to the solutions above. Please ask if anything remains unclear.
_________________
Current Student
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 410
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross) - Class of 2014
GMAT 1: 730 Q49 V39
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)
Followers: 6

Kudos [?]: 42 [0], given: 46

Re: A third Problem Solving question [#permalink]  13 Dec 2010, 08:42
Thanks for the explanation.
_________________
Re: A third Problem Solving question   [#permalink] 13 Dec 2010, 08:42
Similar topics Replies Last post
Similar
Topics:
Problem Solving Question 8 20 Oct 2008, 14:19
2 Problem Solving Question 3 02 Nov 2009, 20:18
problem solving - 700+ question 3 18 May 2010, 18:30
Quant Question - Problem Solving 2 02 Jul 2010, 23:35
Display posts from previous: Sort by