Last visit was: 25 Apr 2026, 22:22 It is currently 25 Apr 2026, 22:22
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: 25 Apr 2026
Posts: 109,830
Own Kudos:
811,300
 [12]
Given Kudos: 105,886
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: 109,830
Kudos: 811,300
 [12]
If a is a multiple of 3 and a = yz^2, where y and z are prime numbers, 13 Dec 2016, 10:55
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

68% (01:46) correct 32% (01:42) wrong based on 273 sessions

History

Date
Time
Result
Not Attempted Yet
If a is a multiple of 3 and a = y*z^2, where y and z are prime numbers, which of the following must be a multiple of 9 ?

A. y^2
B. z^2
C. yz
D. y^2*z^2
E. y^3*z
ShowHide Answer
Official Answer
D
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,902
Own Kudos:
5,456
 [2]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,902
Kudos: 5,456
 [2]
If a is a multiple of 3 and a = yz^2, where y and z are prime numbers, 13 Dec 2016, 12:16
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If a is a multiple of 3 and a = y*z^2, where y and z are prime numbers, which of the following must be a multiple of 9 ?

A. y^2
B. z^2
C. yz
D. y^2*z^2
E. y^3*z
Show more

Given a = y*z^2 and a is a multiple of 3

There can be 3 possibilities -

1. Either y = 3k
2. Or z = 3k
3. Both y & z are multiple of 3k

(A) Not possible if z is a multiple of 3 and y is not a multiple of 3
(B) Not possible if y is a multiple of 3 and z is not a multiple of 3
(C) Not possible if either y or z is a multiple of 3 alone
(D) Possible, if y = miltiple y^2 = Miltiple of 9 & if if z = miltiple z^2 = Miltiple of 9
(E) Not possible if y is a multiple of 3 and z is not a multiple of 3

Hence, correct answer will definitely be (D)
User avatar
Alexey1989x
User avatar
Joined: 05 Dec 2016
Last visit: 20 May 2023
Posts: 187
Own Kudos:
98
 [1]
Given Kudos: 49
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
GMAT 1: 620 Q46 V29
Posts: 187
Kudos: 98
 [1]
If a is a multiple of 3 and a = yz^2, where y and z are prime numbers, 15 Dec 2016, 05:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
"a" is a multiple of 3, so 3 is a factor of "a". Given "a" = yz^2 then it's a prime factorization of "a". Taken that 3 is a prime number and it's a factor of "a" then 3 should be either y or z.Taken that prime factorization of 9 = 3^2, so to be the multiple of 9 "a" should contain at least 3^2, therefore it should be either y^2*z or y*z^2 or y^2*z^2, only answer "D" conforms to the basic terms.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 25 Apr 2026
Posts: 22,286
Own Kudos:
26,537
 [3]
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,286
Kudos: 26,537
 [3]
If a is a multiple of 3 and a = yz^2, where y and z are prime numbers, 19 Dec 2016, 10:53
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If a is a multiple of 3 and a = y*z^2, where y and z are prime numbers, which of the following must be a multiple of 9 ?

A. y^2
B. z^2
C. yz
D. y^2*z^2
E. y^3*z
Show more

We are given that a is a multiple of 3 and a = y(z^2), in which y and z are prime numbers. Thus, either y or z MUST be 3. We need to determine which of the answer choices MUST be true.

A) y^2

Answer choice A does not have to be true. For instance, if y = 2 and z = 3, then the given statement is satisfied and y^2 = 2^2 is not a multiple of 9.

B) z^2

Answer choice B does not have to be true. For instance, if y = 3 and z = 2, then the given statement is satisfied and z^2 = 2^2 is not a multiple of 9.

C) yz

Answer choice C does not have to be true. For instance, if y = 2 and z =3, then the given statement is satisfied and 2 x 3 = 6 is not a multiple of 9.

D) (y^2)(z^2)

Answer choice D will always be true. In order for a to be a multiple of 3 in the equation a = y(z^2), in which y and z are prime numbers, either y or z MUST be 3. If y = 3, then y^2 = 9, and hence regardless what z is, (y^2)(z^2) is a multiple of 9. If y ≠ 3, then z = 3. If z = 3, then z^2 = 9, and hence (y^2)(z^2) is a multiple of 9. Thus (y^2)(z^2) will ALWAYS be a multiple of 9. We can stop here.

Answer: D
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,987
Own Kudos:
1,118
Posts: 38,987
Kudos: 1,118
If a is a multiple of 3 and a = yz^2, where y and z are prime numbers, 12 Nov 2024, 07:06
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
109830 posts
Krunaal
Tuck School Moderator
852 posts