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

 It is currently 17 Nov 2019, 22:44 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Is the square of positive integer Z divisible by 9?

Author Message
TAGS:

### Hide Tags

SVP  P
Joined: 03 Jun 2019
Posts: 1844
Location: India
Is the square of positive integer Z divisible by 9?  [#permalink]

### Show Tags

3 00:00

Difficulty:   55% (hard)

Question Stats: 57% (02:11) correct 43% (01:56) wrong based on 21 sessions

### HideShow timer Statistics

Is the square of positive integer Z divisible by 9?
(1) The sum of the digits of Z^3 is divisible by 9
(2) 3Z^4 + 16 leaves a remainder of 7 when divided by 9

_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Director  V
Joined: 28 Jul 2016
Posts: 650
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: Is the square of positive integer Z divisible by 9?  [#permalink]

### Show Tags

Is the square of positive integer Z divisible by 9?
(1) The sum of the digits of Z^3 is divisible by 9
(2) 3Z^4 + 16 leaves a remainder of 7 when divided by 9
1) The sum of the digits of Z^3 is divisible by 9 hence z^3 is divisible by 9 . z^3 means three powers of 3 atleast . therefoew z^2 will definitely be divisible by 3. take an example 3^3 will be divisible by 9. if 111^3 is divisible by 9 then 111^2 is also divisible by 9
sufficient

2) 3Z^4 + 16 = 9l+7 simplify it
3Z^4 + 9 = 9l since 9 is divisible by 9 l that means 3Z^4 should be divisible by 9
and since z is an integer z^2 will also be divisible
sufficient
GMAT Tutor S
Joined: 17 Sep 2014
Posts: 239
Location: United States
GMAT 1: 780 Q51 V45 GRE 1: Q170 V167 Is the square of positive integer Z divisible by 9?  [#permalink]

### Show Tags

Kinshook wrote:
Is the square of positive integer Z divisible by 9?
(1) The sum of the digits of Z^3 is divisible by 9
(2) 3Z^4 + 16 leaves a remainder of 7 when divided by 9

Analyzing the question:
For the square of Z to be divisible by 9, Z itself only needs to be divisible by 3. So we just need to find if Z has a factor of 3.

Statement 1:
This means $$Z^3$$ is divisible by 9. Z must have a factor of 3 for $$Z^3$$ to have a factor of 9. Hence this statement also tells us $$Z^3$$ has a factor of 27. Sufficient.

Statement 2:
$$3Z^4 + 7$$ has a remainder of 7 when divided by 9
-> $$3Z^3$$ is divisible by 9
-> $$Z^3$$ is divisible by 3.
For $$Z^3$$ to have a factor of 3, Z itself must have a factor of 3. Sufficient.

Ans: D
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
Intern  B
Joined: 06 May 2019
Posts: 40
Location: India
Schools: LBS '22
GPA: 4
WE: Information Technology (Computer Software)
Re: Is the square of positive integer Z divisible by 9?  [#permalink]

### Show Tags

1- Z^3 ----divisible by 9 --- so z^2 is also divisible by 9 --- Sufficient
2)3Z^4 + 16 , when divide 9 remainder comes 7 --- 16/9 --- remainder = 7 , hence 3z^4 is divisible by 9...so z^2 is also divisible by 9---sufficient

-------------------------
If u liked solution please appreciate with kudos.
_________________
Dear Aspirants,

If you liked my post , Pleas appreciate me Kudos...it's a motivation for me...Never Say Never..

- With regards your Buddy Jai Re: Is the square of positive integer Z divisible by 9?   [#permalink] 28 Oct 2019, 02:38
Display posts from previous: Sort by

# Is the square of positive integer Z divisible by 9?   