Last visit was: 23 Apr 2026, 01:20 It is currently 23 Apr 2026, 01:20
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,763
Own Kudos:
810,716
 [12]
Given Kudos: 105,850
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,763
Kudos: 810,716
 [12]
For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po Updated on: 24 Mar 2026, 02:12
Originally posted by Bunuel on 25 Aug 2016, 01:32.
Last edited by Bunuel on 24 Mar 2026, 02:12, edited 1 time in total.
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

65% (02:06) correct 35% (01:57) wrong based on 374 sessions

History

Date
Time
Result
Not Attempted Yet
For any numbers w and z, \(w\#z = w^3z(8 - w^2)\). 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
ShowHide Answer
Official Answer
E
User avatar
abhimahna
User avatar
Board of Directors
Joined: 18 Jul 2015
Last visit: 06 Jul 2024
Posts: 3,481
Own Kudos:
5,779
 [2]
Given Kudos: 346
Status:Emory Goizueta Alum
Products:
My Reviews
Expert
Expert reply
Posts: 3,481
Kudos: 5,779
 [2]
For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po 25 Aug 2016, 10:06
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
For any numbers w and z, \(w#z = w^3z(8 - w^2)\). 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
Show more

Answer is E.

Since w#Z and w are positive, we need to take the value of w such that w#z or w^3z(8 - w^2) is positive.
User avatar
msk0657
User avatar
Retired Moderator
Joined: 26 Nov 2012
Last visit: 14 Feb 2020
Posts: 455
Own Kudos:
569
 [1]
Given Kudos: 46
Posts: 455
Kudos: 569
 [1]
For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po 25 Aug 2016, 21:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
For any numbers w and z, \(w#z = w^3z(8 - w^2)\). 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
Show more

Given z is positive and w#z is positive

Now we need to find the value of w, let's assume z = 1.

From options.

A. 9 if we sub w as 9 in the equation we get w#z as -ve.
B. 3 if we sub w as 3 in the equation we get w#z as -ve
C. 0 Here we get result as 0, 0 is even but not positive. so w#z is not positive.
D. −2 if we sub w as -2 in the equation we get w#z as -ve
E. −9 if we sub w as 3 in the equation we get w#z only +ve value.


Option E is correct.
User avatar
Tobybun
User avatar
Joined: 17 Mar 2016
Last visit: 16 Apr 2017
Posts: 12
Own Kudos:
21
Given Kudos: 30
Location: Singapore
GPA: 3.5
WE:Business Development (Energy)
Posts: 12
Kudos: 21
For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po 26 Aug 2016, 01:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
For any numbers w and z, \(w#z = w^3z(8 - w^2)\). 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
Show more

To satisfy the condition we have two scenarios:
1. w^3 & (8-w^2) both need to be +ve. So A & B are out

2. w^3 & (8-w^2) both need to be -ve. -2 makes (8-w^2) +ve, so D is out. -9 satisfies the requirements, E is the correct answer
User avatar
Nunuboy1994
User avatar
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 554
Own Kudos:
126
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 554
Kudos: 126
For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po 20 Feb 2017, 20:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How did you guys figure out that in order for the answer to be correct the result must be positive? I kind of thought that but didn't understand how you could derive that from the question.
avatar
adityapareshshah
avatar
Joined: 17 Apr 2016
Last visit: 14 Nov 2017
Posts: 59
Own Kudos:
46
Given Kudos: 254
Posts: 59
Kudos: 46
For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po 21 Feb 2017, 06:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Nunuboy1994
How did you guys figure out that in order for the answer to be correct the result must be positive? I kind of thought that but didn't understand how you could derive that from the question.
Show more


Hi Nunuboy1994,

It is mentioned in the question that w#z is positive. Also we are given the equation w#z = w^3z(8 - w^2) to figure out the value of w. Hence using we have to use the fact that w#z should be positive and only one option will satisfy this condition. Hence the option that satisfies the condition , is the correct answer.

Hope it is clear.


Thanks,
Aditya
avatar
adityapareshshah
avatar
Joined: 17 Apr 2016
Last visit: 14 Nov 2017
Posts: 59
Own Kudos:
46
Given Kudos: 254
Posts: 59
Kudos: 46
For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po 21 Feb 2017, 06:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi @Bunnuel,

I used the following approach.
Since w#z is positive,w#z = w^3z(8 - w^2),
8w^3z- w^5z is positive.

Solving we get the following inequality--> w^2<8. Only Option D fulfils this condition.

What am I missing? Kindly help.
User avatar
Kurtosis
User avatar
Current Student
Joined: 13 Apr 2015
Last visit: 10 Nov 2021
Posts: 1,384
Own Kudos:
5,236
 [1]
Given Kudos: 1,228
Location: India
Products:
My Reviews
Posts: 1,384
Kudos: 5,236
 [1]
For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po 21 Feb 2017, 08:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
adityapareshshah
Hi @Bunnuel,

I used the following approach.
Since w#z is positive,w#z = w^3z(8 - w^2),
8w^3z- w^5z is positive.

Solving we get the following inequality--> w^2<8. Only Option D fulfils this condition.

What am I missing? Kindly help.
Show more

You have considered only one aspect i.e. (8 - w^2) > 0. However, (8 - w^2) can be negative too.
w^3z(8 - w^2) is positive.
Since we know that z is positive, the contributing expressions are w^3 and (8 - w^2). Either both can be negative or both can be positive.
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,710
 [1]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,710
 [1]
For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po 23 Feb 2017, 10:35
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
For any numbers w and z, \(w#z = w^3z(8 - w^2)\). 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
Show more

We have to go through the answer choices. Remember, we want w#z to be positive.

A. 9

If w = 9, then 9#z = (9^3)z(8 - 9^2) is negative, since 9^3 and z are positive, but 8 - 9^2 is negative.

B. 3

If w = 3, then 3#z = (3^3)z(8 - 3^3) is negative, since 3^3 and z are positive, but 8 - 3^2 is negative.

C. 0

If w = 0, then 0#z = (0^3)z(8 - 0^2) is zero, since 0^3 = 0.

D. -2

If w = -2, then -2#z = ((-2)^3)z(8 - (-2)^2) is negative, since z and 8 - (-2)^2 are positive, but (-2)^3 is negative.

E. -9

If w = -9, then -9#z = ((-9)^3)z(8 - (-9)^2) is positive, since z is positive, but (-9)^3 and 8 - (-9)^2 are negative. Notice that negative x positive x negative is positive.

Answer: E
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,959
Own Kudos:
1,117
Posts: 38,959
Kudos: 1,117
For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po 13 Aug 2025, 08:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109763 posts
Krunaal
Tuck School Moderator
853 posts