For integers x and y, when x is divided by y, the remainder

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For integers x and y, when x is divided by y, the remainder [#permalink]

28 Feb 2013, 05:27

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For integers x and y, when x is divided by y, the remainder is odd. Which of the following must be true?

A. x is odd
B. xy is odd
C. x and y share no common factors other than 1
D. The sum x + y is odd
E. At least one of x and y is odd

[Reveal] Spoiler: OA

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Last edited by Bunuel on 28 Feb 2013, 05:52, edited 1 time in total.

Edited the question and the tags.

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Re: For integers x and y, when x is divided by y, the remainder [#permalink]

28 Feb 2013, 06:02

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For integers x and y, when x is divided by y, the remainder is odd. Which of the following must be true?

A. x is odd. Not necessarily true. Consider x=4 and y=3.

B. xy is odd. Not necessarily true. Consider x=4 and y=3.

C. x and y share no common factors other than 1. Not necessarily true. Consider x=3 and y=6.

D. The sum x + y is odd. Not necessarily true. Consider x=1 and y=3.

E. At least one of x and y is odd. If both x and y were even, then the remainder when x is divided by y would be even, not odd. Hence at least one of x and y is odd.

Answer: E.

Hope it's clear.
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Re: For integers x and y, when x is divided by y, the remainder [#permalink]

28 Feb 2013, 07:02

For integers x and y, when x is divided by y, the remainder is odd. Which of the following must be true?

A. x is odd. May be. not must.
B. xy is odd. x= 6, y =5 R= 1. xy is not odd
C. x and y share no common factors other than 1. x=12 , y=9. r= 3. common factor = 3, 1
D. The sum x + y is odd. x= 3, y=5. r= 3. x+y = 8 even
E. At least one of x and y is odd. correct
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Re: For integers x and y, when x is divided by y, the remainder [#permalink] 28 Feb 2013, 07:02

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For integers x and y, when x is divided by y, the remainder

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For integers x and y, when x is divided by y, the remainder

For integers x and y, when x is divided by y, the remainder

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