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If x and y are positive integers, what is the remainder when

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If x and y are positive integers, what is the remainder when [#permalink]

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22 Apr 2005, 10:46
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If x and y are positive integers, what is the remainder when x is divided by y?

(1) When x is divided by 2y, the remainder is 4
(2) When x + y is divided by y, the remainder is 4

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-integers-what-is-the-remainder-when-98567.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Oct 2013, 08:51, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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22 Apr 2005, 12:17
Look at it this way
x = ay + r where r < y

1. leads to x = 2by + 4, it is insufficient however, take y < 4 with 2y > 4

2. lead to x+y = cy + 4 => x = (c+1) y + 4 in this case because 4 is said to be reminder after dividing by y, y cannot be less then 4.

Thus 2 is sufficient, 1 is not.
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22 Apr 2005, 12:45
Tyr wrote:
Look at it this way
x = ay + r where r < y

1. leads to x = 2by + 4, it is insufficient however, take y < 4 with 2y > 4

2. lead to x+y = cy + 4 => x = (c+1) y + 4 in this case because 4 is said to be reminder after dividing by y, y cannot be less then 4.

Thus 2 is sufficient, 1 is not.

I did get answer B. But I approached it be inserting numbers, which took a while. I did not follow the above explanation. Can you please restate how 2 is sufficient from above.
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22 Apr 2005, 13:21
aks720 wrote:
I did get answer B. But I approached it be inserting numbers, which took a while. I did not follow the above explanation. Can you please restate how 2 is sufficient from above.

2 means that x can be represented in the form a*y + r and 0 <= (r = 4) < y, those two together mean that r=4 will be a reminder x/y

Last edited by Tyr on 22 Apr 2005, 16:57, edited 1 time in total.
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Re: What is the reminder for x/y? 1. Reminder for x/(2y) is 4. [#permalink]

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10 Jun 2012, 19:17
What is the reminder for x/y?

1. Reminder for x/(2y) is 4.
2. Reminder for (x+y)/y is 4.

we want to find x = yz + R (R=?)

Vote for C

(A) x = 2y + 4 = {4,6,8,10,------}

therefore, for x = yz + R when (Dont know anything about z)
--> y=0 x=4 z=3 then R = 4
--> y=1 x=6 z=3 then R = 3
not sufficient

(B) (x+y) = yz + 4
x = yz-y + 4
x = y(z-1) + 4 = {4,z+3,2z+2,3z+1,4z}
x = 4z x={0,4,8,12,....}

(c)
x = 2y + 4 = {4,6,8,10,------} - (I)
x = 4z x={0,4,8,12,....} - (II)

therefore remainder should be 4
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Re: What is the reminder for x/y? [#permalink]

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10 Jun 2012, 23:18
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Statement 1 is insuff.
x=4/3, y=3/2, x=8, y=9.......

Statement 2:
(x+y)/y has remainder as 4
this can be written as.......(x/y + 1)
as 1 is a whole number the fraction comes from x/y.......which is 4

Hence SUFF.

Ans B
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Re: What is the reminder for x/y? [#permalink]

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11 Jun 2012, 05:19
manulath wrote:
Statement 1 is insuff.
x=4/3, y=3/2, x=8, y=9.......

Statement 2:
(x+y)/y has remainder as 4
this can be written as.......(x/y + 1)
as 1 is a whole number the fraction comes from x/y.......which is 4

Hence SUFF.

Ans B

Hey there,
Can u please explain concept behind statement 2 : "as 1 is a whole number the fraction comes from x/y.......which is 4"
How do you know x/y will always give same remainder?
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Re: What is the reminder for x/y? [#permalink]

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11 Jun 2012, 07:33
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kuttingchai wrote:
manulath wrote:
Statement 1 is insuff.
x=4/3, y=3/2, x=8, y=9.......

Statement 2:
(x+y)/y has remainder as 4
this can be written as.......(x/y + 1)
as 1 is a whole number the fraction comes from x/y.......which is 4

Hence SUFF.

Ans B

Hey there,
Can u please explain concept behind statement 2 : "as 1 is a whole number the fraction comes from x/y.......which is 4"
How do you know x/y will always give same remainder?

The idea used here is that any number can be written in form of a fraction. (Integers can be the number divided by 1)

eg 0.111 = 111/1000

9.99 = 999/100 = 9 + 99/100 = 9 + 0.99

There are two numbers = x and y
Let x be a*y + c (where a and c are integers)

What is the remainder of x/y?

x/y = (a*y + c)/y = a + c/y
We see that c is the remainder and a is quotient.
We have to find c

Given (x + y) /y has remainder as 4
(x+y)/y => (a*y + c + y)/y => a + c/y + 1 =>
The quotient is (a+1) and remainder is c. (Already given as 4)

Any whole number will be added to the quotient and not remainder.

EG.

5/4 = 1 + 1/4 => 1 is remainder

(5 + 4) / 4 = 5/4 + 4/4 = 1 + 1/4 + 1 = 2 + 1/4 => 1 is remainder

5/2 + 1 = 7/2 or 3 + 1/2

Even if x and y are not integers, but fractions, then also x/y will have same remainder as x/y + 1

Hope that Helps.

5/4 + 1 = 1 + 1/4 + 1
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Re: What is the reminder for x/y? [#permalink]

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12 Oct 2013, 07:02
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raviatreya wrote:
What is the reminder for x/y?

(1) Reminder for x/(2y) is 4.
(2) Reminder for (x+y)/y is 4.

Answer is (B) this is pretty straightforward.

Statement 1: x= 2y+4 and we also know that we want to find x=4+r so if we equal both we get y+4 = r. We don't know 'y' so not good enough
Statement 2: x+y/y remainder is 4. y/y has no remainder so x/y will have remainder 4.

Hence it is (B)
Hope it helps
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Re: If x and y are positive integers, what is the remainder when [#permalink]

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12 Oct 2013, 08:51
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-integers-what-is-the-remainder-when-98567.html
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Re: If x and y are positive integers, what is the remainder when   [#permalink] 12 Oct 2013, 08:51
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