NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 11:14 It is currently 26 Apr 2024, 11:14
Decision Tracker
My Rewards
New posts
New comers' posts

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

Remainder

User avatar
arturo2021
Intern
Intern
Joined: 10 Sep 2013
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Remainder [#permalink] New post   10 Sep 2013, 17:53
Hi guys, I have this question:

If x has a remainder of 4 when divided by 9 and y has a reminder of 3 when divided by 9, what's the remainder when xy is divided by 9?

Thanks in advance for the attention received!!!!



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4452
Own Kudos [?]: 28574 [0]
Given Kudos: 130
Re: Remainder [#permalink] New post   10 Sep 2013, 18:12
Expert Reply
arturo2021 wrote:
Hi guys, I have this question:

If x has a remainder of 4 when divided by 9 and y has a reminder of 3 when divided by 9, what's the remainder when xy is divided by 9?

Thanks in advance for the attention received!!!!

Dear arturo2021,
I'm happy to respond :-), but I'm a little confused because you appear to have posted the solution to the question about which you are asking. Are you suggesting that this particular explanation does not make sense to you?

First of all, here's a blog on remainders.
https://magoosh.com/gmat/2012/gmat-quant ... emainders/

My explanation will not be all that different from what is said in that explanation you posted, but perhaps a different way of saying it will resonate.

The first statement ("x has a remainder of 4 when divided by 9") implies:

x = (some THING divisible by 9) + 3 = A + 3

and the second implies

y = (some OTHER THING divisible by 9) + 4 = B + 4

I abbreviated those long phrases with A & B for algebraic clarity. Now we multiply --- for the two expressions with addition, we have to FOIL. See this blog on FOILing:
https://magoosh.com/gmat/2012/foil-on-th ... expanding/

x*y = (A + 3)*(B + 4) = A*B + 4A + 3B + 12

Since A & B are both divisible by 9, any term with either an A or a B in it will be divisible by 9 --- that's the first three terms. Since those first three terms are divisible by 9, by definition they have a remainder of zero. The only term that could possibly leave a remainder is the last term.

12 divided by 9 has a remainder of 3.

Does all this make sense?
Mike :-)
User avatar
rrsnathan
Manager
Manager
Joined: 30 May 2013
Posts: 126
Own Kudos [?]: 358 [0]
Given Kudos: 72
Location: India
Concentration: Entrepreneurship, General Management
Schools: Booth '16 Carroll '16 ESADE '16 Foster '16 HEC Jan'16 Haas EWMBA '16 Tuck '16
GPA: 3.82
Send PM
GMAT ToolKit User
Re: Remainder [#permalink] New post   10 Sep 2013, 19:48
arturo2021 wrote:
Hi guys, I have this question:

If x has a remainder of 4 when divided by 9 and y has a reminder of 3 when divided by 9, what's the remainder when xy is divided by 9?

Thanks in advance for the attention received!!!!


Hi Arturo2021,

Another Method of solving:

For this type of question u can take example values

as x=12 (13/9 = 1 (quotient) + 4 (Remainder)) and y =12 (12/9 = 1 (quotient) + 3 (Remainder))

So xy = 156
xy/9 = 17 (Quotient) + 3(Remainder)
So answer is 3.

Thanks,
Rrsnathan.

Presssssss kudos if helped
User avatar
B
mau5
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 485
Own Kudos [?]: 3093 [0]
Given Kudos: 141
Send PM
Re: Remainder [#permalink] New post   10 Sep 2013, 21:42
arturo2021 wrote:
Hi guys, I have this question:

If x has a remainder of 4 when divided by 9 and y has a reminder of 3 when divided by 9, what's the remainder when xy is divided by 9?

Thanks in advance for the attention received!!!!


Once you read such questions, it would be better to understand that the remainder when xy is divided by 9, would be the SAME, for any values of x and y, given the fact that they individually adhere to the conditions given. Thus, just pick up numbers for x and y.

For x=4, the remainder when 4 is divided by 9=4(Condition 1 met,Check)
For y=3, the remainder when 3 is divided by 9=3(Condition 2 met,Check)

Thus, xy=12, and when 12 is divided by 9, the remainder is 3.
You can plug in ANY relevant values for (x,y) and will still get the remainder as 3.

Hope this helps.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: Remainder [#permalink]
10 Sep 2013, 21:42
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions