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I dont understand the answer choices here. If I substitute 8 and 4 for a and b, i get both D&E as odd. If I assume D&E to be even, both A and B need to be odd. I just gave up and guessed C (not saying C is the OA)

Re: If a and b are positive integers such that a-b and a/b are [#permalink]
25 Nov 2008, 07:25

2

This post received KUDOS

twilight wrote:

If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2 B. b/2 C. (a+b)/2 D. (a+2)/2 E. (b+2)/2

I dont understand the answer choices here. If I substitute 8 and 4 for a and b, i get both D&E as odd. If I assume D&E to be even, both A and B need to be odd. I just gave up and guessed C (not saying C is the OA)

7-t66732 I think this prob and yours are the same. a/b is even so a must be even a+b is even so b must be even a/b is even while b is even so a must be a multiple of 4. a is a multiple of 4 => a+2 is not a multiple of 4. => (a+2)/2 must be odd.

I dont understand the answer choices here. If I substitute 8 and 4 for a and b, i get both D&E as odd. If I assume D&E to be even, both A and B need to be odd. I just gave up and guessed C (not saying C is the OA)

\(a-b\) even --> either both even or both odd

\(\frac{a}{b}\) even --> either both even or \(a\) is even and \(b\) is odd.

As both statements are true --> \(a\) and \(b\) must be even.

As \(\frac{a}{b}\) is an even integer --> \(a\) must be multiple of 4.

Options A is always even. Options B can be even or odd. Options C can be even or odd. Options D: \(\frac{a+2}{2}=\frac{a}{2}+1\), as \(a\) is multiple of \(4\), \(\frac{a}{2}\) is even integer --> even+1=odd. Hence option D is always odd. Options E can be even, odd.

Re: If a and b are positive integers such that a-b and a/b are [#permalink]
25 Nov 2008, 05:33

twilight wrote:

If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2 B. b/2 C. (a+b)/2 D. (a+2)/2 E. (b+2)/2

I dont understand the answer choices here. If I substitute 8 and 4 for a and b, i get both D&E as odd. If I assume D&E to be even, both A and B need to be odd. I just gave up and guessed C (not saying C is the OA)

I do not have the answer yet but I would like to comment on your reasoning. I think D and E can be odd or even, even when a and b are even. If you take a = 6, then you will have (6+2)/2 = 4 even. Or you can take b = 10, then you will have (10+2)/2 = 6 even.

Re: If a and b are positive integers such that a-b and a/b are [#permalink]
25 Nov 2008, 05:36

Agree with you. What I was poitning out there (with the 8 and 4 example) was that for two even numbers that satisfy the question, I get a situation where two of the choices are potentials answers.

---edit--- but I see the flaw in my reasoning here, since the question asks for a 'must be odd' response, so substitution is not the right way to go.

Re: If a and b are positive integers such that a-b and a/b are [#permalink]
25 Nov 2008, 06:29

Interesting answer, thanks for that. I did not consider that 'a' must not be 2, which is true and your explantion makes sense.

However, theres nothing stopping a from being say a 6 - and in that case (a+2)/2 would be even, and hence would not agree with the requirement of 'must be odd'..

Re: If a and b are positive integers such that a-b and a/b are [#permalink]
25 Nov 2008, 07:40

DavidArchuleta wrote:

7-t66732 I think this prob and yours are the same. a/b is even so a must be even a+b is even so b must be even a/b is even while b is even so a must be a multiple of 4. a is a multiple of 4 => a+2 is not a multiple of 4. => (a+2)/2 must be odd.

Re: If a and b are positive integers such that a-b and a/b are [#permalink]
25 Nov 2008, 20:31

DavidArchuleta wrote:

twilight wrote:

If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2 B. b/2 C. (a+b)/2 D. (a+2)/2 E. (b+2)/2

I dont understand the answer choices here. If I substitute 8 and 4 for a and b, i get both D&E as odd. If I assume D&E to be even, both A and B need to be odd. I just gave up and guessed C (not saying C is the OA)

7-t66732 I think this prob and yours are the same. a/b is even so a must be even a+b is even so b must be even a/b is even while b is even so a must be a multiple of 4. a is a multiple of 4 => a+2 is not a multiple of 4. => (a+2)/2 must be odd.

Re: If a and b are positive integers such that a-b and a/b are [#permalink]
14 Sep 2014, 07:12

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