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If M and N are positive integers, then is M an even integer?

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If M and N are positive integers, then is M an even integer? [#permalink] New post 09 Feb 2012, 16:57
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If M and N are positive integers, then is M an even integer?

(1) M/N is an odd integer.
(2) M + N is an even integer.
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Feb 2012, 17:08, edited 1 time in total.
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Re: Integers [#permalink] New post 09 Feb 2012, 17:06
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If M and N are positive integers, then is M an even integer?

(1) M/N is an odd integer --> m=n*odd --> if n=odd then m=odd but if n=even then m=even. Not sufficient.
(2) M + N is an even integer --> either both are odd or both are even. Not sufficient.

(1)+(2) Still the same two cases: either both are odd (for example m=3 and n=1) or both are even (for example m=2 and n=2). Not sufficient.

Answer: E.
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Re: Integers [#permalink] New post 12 Feb 2014, 11:20
Bunuel wrote:
If M and N are positive integers, then is M an even integer?

(1) M/N is an odd integer --> m=n*odd --> if n=odd then m=odd but if n=even then m=even. Not sufficient.
(2) M + N is an even integer --> either both are odd or both are even. Not sufficient.

(1)+(2) Still the same two cases: either both are odd (for example m=3 and n=1) or both are even (for example m=2 and n=2). Not sufficient.

Answer: E.


Statement 1 says M/N = Odd

Only Odd / Odd can give an odd integer. If M is even then even / even = even or even / odd = not integer.

Statement 1 is sufficient to say that M is not even right?

Can you help with this?
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Re: Integers [#permalink] New post 13 Feb 2014, 00:10
Expert's post
Qoofi wrote:
Bunuel wrote:
If M and N are positive integers, then is M an even integer?

(1) M/N is an odd integer --> m=n*odd --> if n=odd then m=odd but if n=even then m=even. Not sufficient.
(2) M + N is an even integer --> either both are odd or both are even. Not sufficient.

(1)+(2) Still the same two cases: either both are odd (for example m=3 and n=1) or both are even (for example m=2 and n=2). Not sufficient.

Answer: E.


Statement 1 says M/N = Odd

Only Odd / Odd can give an odd integer. If M is even then even / even = even or even / odd = not integer.

Statement 1 is sufficient to say that M is not even right?

Can you help with this?


That's not correct at all! What about 6/2 = even/even = 3 = odd? Also, what about 6/3 = even/odd = 2 = even?
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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: Integers   [#permalink] 13 Feb 2014, 00:10
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