GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Oct 2019, 04:52

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

For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 15 Dec 2015
Posts: 34
For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)  [#permalink]

Show Tags

New post Updated on: 24 Dec 2015, 21:09
4
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

38% (02:18) correct 62% (02:12) wrong based on 85 sessions

HideShow timer Statistics

For any numbers W and Z, W∙Z=Wˆ3 * Z(8-Wˆ2) . If both Z and W∙Z are positive numbers, which of the following could be a value of W ?

(A) 9

(B) 3

(C) 0

(D) -2

(E) -9

Originally posted by sara86 on 24 Dec 2015, 16:51.
Last edited by sara86 on 24 Dec 2015, 21:09, edited 3 times in total.
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7987
Re: For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)  [#permalink]

Show Tags

New post 24 Dec 2015, 20:18
sara86 wrote:
For any numbers W and Z, \(W•Z=Wˆ3 Z(8-Wˆ2)\) . If both Z and W•Z are positive numbers, which of the following could be a value of W ?

(A) 9

(B) 3

(C) 0

(D) -2

(E) -9


Hi,
it is given that both Z and W•Z are positive numbers and \(W•Z=Wˆ3 Z(8-Wˆ2)\)..
this means Wˆ3 Z(8-Wˆ2) must be positive..
we know Z is positive, so Wˆ3 *(8-Wˆ2) must be positive...
in other words, Wˆ3 and (8-Wˆ2) must be of the same sign..
lets see the two cases ..

1) Both positive..
W^3 is positive, so 8-W^2>0..
or W^2<8....or W < 3 as 3^2=9...
eliminate 9 and 3 that is A and B...

2) both negative..
W^3 is negative, so 8-W^2<0..
or W^2>8....or W <- 2 or W>2..
W>2 can be discarded as here W is taken as negative
D can be eliminated since it is -2,
E is the answer..

Note :- C which is 0 can be eliminated initially itself as W.Z will become 0 in that case.
and after initial steps We can substitute the values and find the answer, especially so, since it is asking " which of the following could be a value of W ?".
_________________
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2596
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)  [#permalink]

Show Tags

New post 24 Dec 2015, 20:43
chetan2u wrote:
sara86 wrote:
For any numbers W and Z, \(W•Z=Wˆ3 Z(8-Wˆ2)\) . If both Z and W•Z are positive numbers, which of the following could be a value of W ?

(A) 9

(B) 3

(C) 0

(D) -2

(E) -9


Hi,
it is given that both Z and W•Z are positive numbers and \(W•Z=Wˆ3 Z(8-Wˆ2)\)..
this means Wˆ3 Z(8-Wˆ2) must be positive..
we know Z is positive, so Wˆ3 *(8-Wˆ2) must be positive...
in other words, Wˆ3 and (8-Wˆ2) must be of the same sign..
lets see the two cases ..

1) Both positive..
W^3 is positive, so 8-W^2>0..
or W^2<8....or W < 3 as 3^2=9...
eliminate 9 and 3 that is A and B...

2) both negative..
W^3 is negative, so 8-W^2<0..
or W^2>8....or W <- 2 or W>2..
W>2 can be discarded as here W is taken as negative
D can be eliminated since it is -2,
E is the answer..

Note :- C which is 0 can be eliminated initially itself as W.Z will become 0 in that case.
and after initial steps We can substitute the values and find the answer, especially so, since it is asking " which of the following could be a value of W ?".


IMO, W can not be <0 in this question as it is given that both z and w*z are >0 ---> w>0. The question needs to be reformatted as it is mentioning W and w and the RHS is not clearly written.
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7987
Re: For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)  [#permalink]

Show Tags

New post 24 Dec 2015, 20:58
1
Engr2012 wrote:
chetan2u wrote:
sara86 wrote:
For any numbers W and Z, \(W•Z=Wˆ3 Z(8-Wˆ2)\) . If both Z and W•Z are positive numbers, which of the following could be a value of W ?

(A) 9

(B) 3

(C) 0

(D) -2

(E) -9


Hi,
it is given that both Z and W•Z are positive numbers and \(W•Z=Wˆ3 Z(8-Wˆ2)\)..
this means Wˆ3 Z(8-Wˆ2) must be positive..
we know Z is positive, so Wˆ3 *(8-Wˆ2) must be positive...
in other words, Wˆ3 and (8-Wˆ2) must be of the same sign..
lets see the two cases ..

1) Both positive..
W^3 is positive, so 8-W^2>0..
or W^2<8....or W < 3 as 3^2=9...
eliminate 9 and 3 that is A and B...

2) both negative..
W^3 is negative, so 8-W^2<0..
or W^2>8....or W <- 2 or W>2..
W>2 can be discarded as here W is taken as negative
D can be eliminated since it is -2,
E is the answer..

Note :- C which is 0 can be eliminated initially itself as W.Z will become 0 in that case.
and after initial steps We can substitute the values and find the answer, especially so, since it is asking " which of the following could be a value of W ?".


IMO, W can not be <0 in this question as it is given that both z and w*z are >0 ---> w>0. The question needs to be reformatted as it is mentioning W and w and the RHS is not clearly written.


Hi Engr2012,
The Question is correct as it is and yes it is possible to read the Q the way you are reading it as I too did think the same way for a minute..
W•Z does not mean W*Z but the "•" is basically a symbol telling us a relation.. it could have been #, @ etc to avoid confusion..
_________________
Intern
Intern
avatar
Joined: 15 Dec 2015
Posts: 34
Re: For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)  [#permalink]

Show Tags

New post 24 Dec 2015, 21:08
Hi,

Yes, 'W' and 'w' are the same variable. Both should be in capital letters. It's just a typo. My bad.


Sent from my iPhone using Tapatalk
Intern
Intern
avatar
Joined: 15 Dec 2015
Posts: 34
Re: For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)  [#permalink]

Show Tags

New post 24 Dec 2015, 21:26
Thanks a lot Chetan2u ! You answered it in a very clever way!


Sent from my iPhone using Tapatalk
Manager
Manager
avatar
B
Joined: 14 Jul 2014
Posts: 158
Location: United States
Schools: Duke '20 (D)
GMAT 1: 600 Q48 V27
GMAT 2: 720 Q50 V37
GPA: 3.2
Reviews Badge
Re: For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)  [#permalink]

Show Tags

New post 31 Jan 2016, 14:54
W∙Z=Wˆ3 * Z(8-Wˆ2)

If both Z and WZ are positive, then w^3(8-w^2) must be positive. Only E will satisfy this condition. (-9)^3 is negative and (8-81) is negative so this will result in a positive product. D does not satisfy this condition.
Intern
Intern
avatar
Joined: 23 Sep 2018
Posts: 1
Re: For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)  [#permalink]

Show Tags

New post 30 Sep 2018, 12:10
sara86 wrote:
For any numbers W and Z, W∙Z=Wˆ3 * Z(8-Wˆ2) . If both Z and W∙Z are positive numbers, which of the following could be a value of W ?

(A) 9

(B) 3

(C) 0

(D) -2

(E) -9


Looks like you have a mistake.
It is said, "both Z and W∙Z are positive numbers".
If Z is positive, then W*Z can be positive only when W also positive.
-9 * [positive] != positive.
GMAT Club Bot
Re: For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)   [#permalink] 30 Sep 2018, 12:10
Display posts from previous: Sort by

For any numbers W and Z, W•Z=Wˆ3 * Z(8-Wˆ2)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne