If X and Y are nonzero integers, what is the remainder when : DS Archive
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# If X and Y are nonzero integers, what is the remainder when

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If X and Y are nonzero integers, what is the remainder when [#permalink]

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16 Jul 2003, 03:48
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If X and Y are nonzero 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

A. if statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not;
B. if statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not;
C. if statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient;
D. if EITHER statement BY ITSELF is sufficient to answer the question;
E. if statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
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16 Jul 2003, 05:57

(1) says, X = 2KY + 4

and (2) says, X = Y(M-1) + 4.

The quotient in in above case are, 2K and M-1 and remainder is 4.

Is that correct?
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16 Jul 2003, 07:29
my solution is the same. I vote for D but still doubt.

consider an example:

22=2*3*3+4 when divided by 2Y (2*3)
22=3*7+1 when divided by Y (3)
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16 Jul 2003, 09:23
Sorry boys, the answer is NOT D.

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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
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16 Jul 2003, 13:15
Okay, here is a hint.

It is obvious that the expression "When A is divided by B you get a remainder of R" can be restated by saying "there exists an integer Q such that A = B*Q + R." However, there is a condition that must hold in order for the reverse to be true. Do you know what it is?
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16 Jul 2003, 19:05

A fails:

10/(2*3) remainder = 4.
10/3 , remainder = 1.

20(2*8) remainder = 6.
20/8 remainder = 4.
clearly not suffiecient.

but B looks to hold good.
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16 Jul 2003, 21:33
When you say A divided by B has remainder R and restate it as A = BQ + R, you must remember that B must be > R for this to make sense.

In (1), restated, we have X = Y*2*K + 4. We know that 2*Y > 4, but we don't know if Y > 4 so we go the other way. For example, if X = 10, Y = 3, then 2Y > 4 and 10 mod 6 = 4, but 10 mod 3 = 1. Hence, it is not sufficient.

In (2) we have X = Y*K - Y + 4 = Y * (K - 1) * 4. We already know that Y must be > 4 so we can say that X divided by Y has remainder 4.

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AkamaiBrah
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16 Jul 2003, 21:43
evensflow wrote:

(1) says, X = 2KY + 4

and (2) says, X = Y(M-1) + 4.

The quotient in in above case are, 2K and M-1 and remainder is 4.

Is that correct?

That is correct, but in (1) you cannot show that Y > 4 (only that 2Y > 4), hence you cannot conclude that X mod Y = 4. Try examples when Y = 3. If we set constraint of Y > 4, then (1) would be sufficient.

Got it?
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AkamaiBrah
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MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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18 Jul 2003, 17:42
Perfect!!!

I realized my mistake after i posted the answer..

Also to my understanding the answer A would be incorrect,

since it get reduces to X = 2(YK + 2)

So therefore again no chance of getting a remainder 4 always.

Thanks for pointing out...
18 Jul 2003, 17:42
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