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# if X and Y are non-zero integers, what is the remainder when

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Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
if X and Y are non-zero integers, what is the remainder when [#permalink]

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24 Jun 2005, 12:03
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if X and Y are non-zero 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....

Show the working...I know (2) is so simple but putup the explanations...
VP
Joined: 30 Sep 2004
Posts: 1480
Location: Germany

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24 Jun 2005, 12:30
first statement is insufficient. x/2y=z+4 => x=2yz+4. thats not enough to find the remainder of x/y. try y=3 and z=2 or y=5 and z=2. but you dont need to pick number. in the eq above are just to many unknown variables. second statement is sufficient. x+y/y => x/y +y/y => x/y + 1 has remainder 4. so its clear that x/y has a remainder of 4 as well.
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Director
Joined: 18 Apr 2005
Posts: 545
Location: Canuckland

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24 Jun 2005, 13:46
fresinha12 wrote:
if X and Y are non-zero 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....

Show the working...I know (2) is so simple but putup the explanations...

B

1) x = y*2k + 4 works only for even multipliers => insuff
2) x+y = y*m + 4 => x = y(m-1) +4 => works y>4
Senior Manager
Joined: 30 May 2005
Posts: 276

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20 Jul 2005, 14:28
hello
can anyone plz explains me why statement 1 is insufficient thanks

regards

mandy
Senior Manager
Joined: 04 May 2005
Posts: 279
Location: CA, USA

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29 Jul 2005, 13:21
B for me

1) insufficient
if one know X/(2Y) remainder is a, then he cannot
derive anything about the result of X/Y's remainder

Example:
if you know 4/10 remainder is 3, will you know 4/5's remainder (1)?
OR if you know 3/10 remainder is 3, will you know 3/5's remainder (3) ?

I cannot deduce it using formula though.
Senior Manager
Joined: 29 Nov 2004
Posts: 483
Location: Chicago

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29 Jul 2005, 17:34
Agree with B, christoph has good explation thanks
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29 Jul 2005, 17:34
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