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

Question

If x and y are positive integer, what is the remainder when x is divided by y ?

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

Bunuel · Accepted Answer

x=yn+r. Question is r=?

(1) This statement is clearly insufficient, no info about y.
Maybe there is a typo? If it were: "When x is divided by  2y , the remainder is 4." It would make more sense, though still would be insufficient.

But still let's consider this case too:
x=2yk+4. x=20 y=8 --> x/2y=20/16 remainder 4 and x/y=20/8  remainder also 4 , BUT x=10 y=3 --> x/2y=10/6 remainder 4 and x/y=10/3  remainder 1 . Two different remainders: not sufficient.

(2) x+y=yp+4 --> x=y(p-1)+4 --> this statement directly gives a remainder of 4 upon dividing x by y. Sufficient.

Answer: B.

Hussain15 · Answer

Hi Bunuel!,

Look at the red coloured equation above.

x= 2yk + 4
=> x= y(2k) + 4
=> x divided by y has a remainder of 4. Is my understanding correct?

2nd query: For first equation (the red one mentioned above) x= 2yk + 4, you solved it by plugging in the numbers while for second correct equation x= y(p-1) + 4 you didn't solve it by plugging the numbers. Why did you not plug the numbers in equation 2? I mean how did you find out without counter checking that equation 2 will be true for all positive integers???

Thanks in Advance!!!

Bunuel · Answer

That's a good question. 
A. x=y(2k)+4, k any integer >=0.
B. x=y(p-1)+4, p any integer >=0.

Why A is not sufficient to determine the remainder and B is? Why did I use number plugging to show this in the first case and didn't in the second?

If we are told that x divided by y gives a remainder of 4, means x=yp+4 where p is integer >=0. We don't know x and y so p (coefficient) can be any integer.

Look at equation A, the coefficient is 2k, 2k is even. It can be rephrased as x divided by y will give the remainder of 4 IF coefficient is even. But what about the cases when coefficient is odd? We don't know that so we must check to determine this.

As for B. Coefficient here is (p-1), which for integer values of p can give us ANY value: any even as well as any odd. So basically x=y(p-1)+4 is the same as x=yp+4. No need for double checking.

Hope it's clear.

Hussain15 · Answer

Thanks boss!!! You will score +50 in your test definitely.

Kinshook · Answer

Asked: If x and y are positive integer, what is the remainder when x is divided by y ?

(1) When x is divided by 2x, the remainder is 4.
x = 4
Since y is unknown
NOT SUFFICIENT

(2) When x + y is divided by y, the remainder is 4.
Remainder when x is divided by y, the remainder will be 4.
SUFFICIENT

IMO B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards