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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If z is a multiple of 24, what is the remainder when z^2 is

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Manager  Joined: 21 Jul 2009
Posts: 126
Location: New York, NY
If z is a multiple of 24, what is the remainder when z^2 is  [#permalink]

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1 00:00

Difficulty:   15% (low)

Question Stats: 79% (01:10) correct 21% (01:17) wrong based on 165 sessions

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If z is a multiple of 24, what is the remainder when z^2 is divided by 9?

(A) 0
(B) 1
(C) 2
(D) 4
(E) 6

Originally posted by mendelay on 04 Sep 2009, 07:24.
Last edited by mendelay on 17 Sep 2009, 08:07, edited 2 times in total.
Director  Joined: 04 Jan 2008
Posts: 595

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is it
A--0?

z=24(K)=2^3(3)(k)

z^2=2^6(9)(k^2)

now z^2/9= 2^6(k^2)==multiple of 2^6

mendelay wrote:
If z is a multiple of 24, what is the remainder when z^2 is divided by 9?

(A) 0
(B) 1
(C) 2
(D) 4
(E) 6

Intern  Joined: 27 Aug 2009
Posts: 23

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24= (8*3)n
the resultant number will be multiplied by 3^2 for sure... hence z^2/9 will have its remiander as 0...

wats the OA?
Manager  Joined: 25 Aug 2009
Posts: 130

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1
this question will hardly take more than 30 seconds..

this is not data sufficiency problem, in which you have to test the answer by plugging different values..

this is problem solving question asking for a definite answer..So, the answer would be same whether z is 24 or any other multiple of 24.

Let z = 24 ; =>$$z^2 = 24*24$$

=>$$z^2 = 9*64$$ ( divisible by 9)
Manager  Joined: 22 Dec 2009
Posts: 231

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1
1
mendelay wrote:
If z is a multiple of 24, what is the remainder when z^2 is divided by 9?

(A) 0
(B) 1
(C) 2
(D) 4
(E) 6

z = 24 * K = 8 * 3 * k
z^2 = 8^2 * 9 * k^2

Therefore z^2 Mod 9 = 0 ( as 9 is a factor in the same)

Intern  Joined: 17 Nov 2009
Posts: 29
Schools: University of Toronto, Mcgill, Queens

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jeeteshsingh wrote:
mendelay wrote:
If z is a multiple of 24, what is the remainder when z^2 is divided by 9?

(A) 0
(B) 1
(C) 2
(D) 4
(E) 6

z = 24 * K = 8 * 3 * k
z^2 = 8^2 * 9 * k^2

Therefore z^2 Mod 9 = 0 ( as 9 is a factor in the same)

nice explanation but also you can do the other way by calculating square of 24 and then divide by 9.
Director  Joined: 03 Aug 2012
Posts: 651
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)

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Easy one:

Z=24A

Z^2 = 24*24* A^2

REM(24/9) = 6

Rem (Z^2/9) = REM (6*6* A^2)/9
= REM(36*A^2)/9
= REM(0*A^2)/9

=0

Rgds,
TGC!
Senior Manager  Joined: 10 Jul 2013
Posts: 279

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mendelay wrote:
If z is a multiple of 24, what is the remainder when z^2 is divided by 9?

(A) 0
(B) 1
(C) 2
(D) 4
(E) 6

........
z=24k
or, z = 8×3×k
or, z^2 = 64 × 9 × k^2

So remainder is 0 (A)
Intern  Joined: 31 Aug 2013
Posts: 12
Re: If z is a multiple of 24, what is the remainder when z^2 is  [#permalink]

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If z is a multiple of 24, what is the remainder when z^2 is divided by 9?

(A) 0
(B) 1
(C) 2
(D) 4
(E) 6

z =24k

z^2= 24*24
ie 24*24/9 = 64

So,the remainder is 0.

SVP  Joined: 06 Sep 2013
Posts: 1514
Concentration: Finance
Re: If z is a multiple of 24, what is the remainder when z^2 is  [#permalink]

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For this problem I just did the following

Took z = 24

Then 24/9 remainder is 6
Do this twice and you will get 6*6 / 9

Remainder of 36/9 is zero

Cheers!
J Math Expert V
Joined: 02 Sep 2009
Posts: 61549
Re: If z is a multiple of 24, what is the remainder when z^2 is  [#permalink]

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1
mendelay wrote:
If z is a multiple of 24, what is the remainder when z^2 is divided by 9?

(A) 0
(B) 1
(C) 2
(D) 4
(E) 6

z is a multiple of 24, means that z is a multiple of 3, therefore z^2 must be a multiple of 9.

_________________
Intern  Joined: 05 Dec 2013
Posts: 28
Concentration: Technology
GMAT Date: 02-01-2014
GPA: 3.95
WE: Information Technology (Venture Capital)
Re: If z is a multiple of 24, what is the remainder when z^2 is  [#permalink]

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24 = 2^3 * 3. Any multiple of this could be 2^4 * 3, 2^3 *3^2, etc.

Let's assume z = 24 for now. So z = 2^3 * 3. Then z^2 = 2^6 * 3^2. If we divide this by 9 or 3^2 we will end up with no denominator, meaning there is no remainder.
Non-Human User Joined: 09 Sep 2013
Posts: 14155
Re: If z is a multiple of 24, what is the remainder when z^2 is  [#permalink]

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_________________ Re: If z is a multiple of 24, what is the remainder when z^2 is   [#permalink] 06 Jan 2020, 07:26
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