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

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16 Jul 2003, 04:48

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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.
_________________

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

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

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

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.

Hence, B is the answer.
_________________

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

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