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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 [#permalink] New post 28 Feb 2013, 04:27
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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, 04:52, 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] New post 28 Feb 2013, 05:02
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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] New post 28 Feb 2013, 06:02
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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For integers x and y, when x is divided by y, the remainder [#permalink] New post 27 Mar 2014, 21:41
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
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Re: For integers x and y, when x is divided by y, the remainder [#permalink] New post 27 Mar 2014, 23:45
Expert's post
rango wrote:
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


Merging similar topics. Please refer to the discussion above.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: For integers x and y, when x is divided by y, the remainder   [#permalink] 27 Mar 2014, 23:45
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