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Manager  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]

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

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

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6
2
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.
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Current Student V
Joined: 19 Mar 2012
Posts: 4263
Location: India
GMAT 1: 760 Q50 V42 GPA: 3.8
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Re: Number properties  [#permalink]

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Think of it this way
15=ky+y-3
Where k is an integer
I.e y=18/(k+1)
Now put values of k such that y is an integer
I.e k = 0,1,2,5
Y= 3,6,9,18
However, for k=8 the equation holds but the remainder in that case is 1 not -1(thats when y=2)
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Manager  Joined: 12 May 2012
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GMAT 1: 650 Q51 V25 GMAT 2: 730 Q50 V38 GPA: 4
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Re: When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

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

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Bunuel 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 V
Joined: 02 Sep 2009
Posts: 58453
Re: When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

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Shiv2016 wrote:
Bunuel 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 ?

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

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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 Joined: 09 Sep 2013
Posts: 13262
Re: When 15 is divided by y, the remainder is y-3. If y must be  [#permalink]

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_________________ Re: When 15 is divided by y, the remainder is y-3. If y must be   [#permalink] 24 Oct 2018, 03:26
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