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Re: Odd / Even question [#permalink]
06 Jul 2008, 00:07

1

This post received KUDOS

nirimblf wrote:

DavidArchuleta wrote:

m/n is even so m must be even m+n is even so n is even too m/n is even while n is even so m is divisible by 4 so m/2 is always even

I. m/2+n/2 (nothing about n) II. m/2 + 1 (always odd) III. n/2+1 (nothing can be determined about n)

My choice is B.

I don't understand. If n is even why nothing can be determined about n?

I'm sorry, nothing can be determined about n/2. I'm careless as usual. Sorry again. m/2 is always even 'coz m is divisible by 4 but n is just even, it can be divisible by 4 or not so n/2 is either even or odd.

Re: Odd / Even question [#permalink]
06 Jul 2008, 04:31

I don't understand why option B should be our answer. If M is even, then it doesn't necessarily mean that m/2 will be even. For example, 10/2 is 5, which is odd. so an even number divided by 2 could yield either even or odd. please explain guys! thanks

Re: Odd / Even question [#permalink]
06 Jul 2008, 05:01

tarek99 wrote:

I don't understand why option B should be our answer. If M is even, then it doesn't necessarily mean that m/2 will be even. For example, 10/2 is 5, which is odd. so an even number divided by 2 could yield either even or odd. please explain guys! thanks

As it was said above, m is not only even, it is also divisible by 4.

Re: Odd / Even question [#permalink]
06 Jul 2008, 15:46

Oski wrote:

tarek99 wrote:

I don't understand why option B should be our answer. If M is even, then it doesn't necessarily mean that m/2 will be even. For example, 10/2 is 5, which is odd. so an even number divided by 2 could yield either even or odd. please explain guys! thanks

As it was said above, m is not only even, it is also divisible by 4.

i'm sorry if i might be asking a stupid question, but how do you know that m is divisible specifically by 4?? all we know is that m is even. So in statement II:

(m+2)/2 = (m/2) + (2/2) = (m/2) + 1

If m/2 is even, then + 1 will be odd

if m/2 is odd, then + 1 will be even. so where from the divisibility by 4??

Re: Odd / Even question [#permalink]
06 Jul 2008, 23:52

tarek99 wrote:

i'm sorry if i might be asking a stupid question, but how do you know that m is divisible specifically by 4?? all we know is that m is even. So in statement II:

(m+2)/2 = (m/2) + (2/2) = (m/2) + 1

If m/2 is even, then + 1 will be odd

if m/2 is odd, then + 1 will be even. so where from the divisibility by 4??

It was said above:

m/n is even => m can be written as m = 2 * K * n, with K an integer i.e. m is even

Then m+n is even: since m is even then it tells us that n is even i.e. n can be written as n = 2 * L, with L an integer

Back to m, we can then write m = 2 * K * (2 * L) i.e. m = 4 * K * L => m is divisible by 4

Re: Odd / Even question [#permalink]
07 Jul 2008, 05:16

tarek99 wrote:

Oski wrote:

tarek99 wrote:

I don't understand why option B should be our answer. If M is even, then it doesn't necessarily mean that m/2 will be even. For example, 10/2 is 5, which is odd. so an even number divided by 2 could yield either even or odd. please explain guys! thanks

As it was said above, m is not only even, it is also divisible by 4.

i'm sorry if i might be asking a stupid question, but how do you know that m is divisible specifically by 4?? all we know is that m is even. So in statement II:

(m+2)/2 = (m/2) + (2/2) = (m/2) + 1

If m/2 is even, then + 1 will be odd

if m/2 is odd, then + 1 will be even. so where from the divisibility by 4??

m /n = even we know n is even m = even * even lest even number we know is 2 m = 2*2 we know m is atleast divisible by 4 Hope thi s helps