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

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Kudos [?]: 52 [0], given: 0

If X and Y are nonzero integers, what is the remainder when [#permalink]  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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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Kudos [?]: 8 [0], given: 0

(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?
SVP
Joined: 03 Feb 2003
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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)
GMAT Instructor
Joined: 07 Jul 2003
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Kudos [?]: 52 [0], given: 0

Sorry boys, the answer is NOT D.

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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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Kudos [?]: 52 [0], given: 0

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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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Kudos [?]: 0 [0], given: 0

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.
GMAT Instructor
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Kudos [?]: 52 [0], given: 0

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
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
Followers: 13

Kudos [?]: 52 [0], given: 0

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?
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Manager
Joined: 08 Apr 2003
Posts: 149
Followers: 1

Kudos [?]: 8 [0], given: 0

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...
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