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

It is currently 18 Oct 2019, 19:14

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.

Close

Request Expert Reply

Confirm Cancel

When 15 is divided by y, the remainder is y-3. If y must be

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 14 May 2009
Posts: 124
Schools: AGSM '16
When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

Show Tags

New post 03 Jun 2012, 00:28
5
14
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

65% (01:14) correct 35% (02:02) wrong based on 68 sessions

HideShow timer Statistics

When 15 is divided by y, the remainder is y-3. If y must be an integer, what are all the possible values of y?

OA:
3, 6, 9 and 18
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

Show Tags

New post 03 Jun 2012, 03:32
6
2
AceofSpades wrote:
When 15 is divided by y, the remainder is y-3. If y must be an integer, what are all the possible values of y?

OA:
3, 6, 9 and 18


Note: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, we have that \(15=qy+(y-3)\) and \(remainder=y-3\geq{0}\) --> \(y\geq{3}\). From \(15=qy+(y-3)\) --> \(y(q+1)=18\) --> \(y\) must be factor of 18 but greater than or equal to 3. Thus \(y\) can be: 3, 6, 9, or 18.
_________________
General Discussion
Current Student
User avatar
V
Joined: 19 Mar 2012
Posts: 4263
Location: India
GMAT 1: 760 Q50 V42
GPA: 3.8
WE: Marketing (Non-Profit and Government)
Re: Number properties  [#permalink]

Show Tags

New post 03 Jun 2012, 01:04
2
2
Manager
Manager
avatar
Joined: 12 May 2012
Posts: 67
Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
GMAT 2: 730 Q50 V38
GPA: 4
WE: General Management (Transportation)
Re: When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

Show Tags

New post 03 Jun 2012, 04:02
AceofSpades wrote:
When 15 is divided by y, the remainder is y-3. If y must be an integer, what are all the possible values of y?

OA:
3, 6, 9 and 18


Nice one.
I had left out 3. :oops:

Remainder 0 is a possibility too.
Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 649
Re: When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

Show Tags

New post 04 May 2017, 10:59
Bunuel wrote:
AceofSpades wrote:
When 15 is divided by y, the remainder is y-3. If y must be an integer, what are all the possible values of y?

OA:
3, 6, 9 and 18


Note: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, we have that \(15=qy+(y-3)\) and \(remainder=y-3\geq{0}\) --> \(y\geq{3}\). From \(15=qy+(y-3)\) --> \(y(q+1)=18\) --> \(y\) must be factor of 18 but greater than or equal to 3. Thus \(y\) can be: 3, 6, 9, or 18.


I directly solved it.

18=y(q+1)
As y is an integer, it should divide 18 i.e. it has to be a factor of 18.

Total values y can take are 6

Why do we have to consider y>=3 ?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

Show Tags

New post 04 May 2017, 11:43
Shiv2016 wrote:
Bunuel wrote:
AceofSpades wrote:
When 15 is divided by y, the remainder is y-3. If y must be an integer, what are all the possible values of y?

OA:
3, 6, 9 and 18


Note: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, we have that \(15=qy+(y-3)\) and \(remainder=y-3\geq{0}\) --> \(y\geq{3}\). From \(15=qy+(y-3)\) --> \(y(q+1)=18\) --> \(y\) must be factor of 18 but greater than or equal to 3. Thus \(y\) can be: 3, 6, 9, or 18.


I directly solved it.

18=y(q+1)
As y is an integer, it should divide 18 i.e. it has to be a factor of 18.

Total values y can take are 6

Why do we have to consider y>=3 ?


Please re-read the highlighted part.

Hope it helps.
_________________
Intern
Intern
avatar
B
Joined: 14 May 2015
Posts: 47
Re: When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

Show Tags

New post 04 May 2017, 14:52
15=ya+y-3
18=y(a+1)
factors of 18 are 1,2,3,6,9,18
y can take 3,6,9,18
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13262
Re: When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

Show Tags

New post 24 Oct 2018, 03:26
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: When 15 is divided by y, the remainder is y-3. If y must be   [#permalink] 24 Oct 2018, 03:26
Display posts from previous: Sort by

When 15 is divided by y, the remainder is y-3. If y must be

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne