Number properties

I think the answer is a+b /2

a and b must both be even for a-b to be even

Lets say a=12 b=2 for a-b and a/b to be even

We can rule out every other choice other than a+b/2

I contradicted my owen example in my previous answer.

Thinking some more I think the answer is D) and I would have missed it in haste.

a-b even means

either both a and b are even
or both are odd


a/b even means
a is even [as a and b are intergers]

hence from two condirions we have a and b are both even



In this case I am able to justify all.
Can anyone help me understand what am I missing?


regarding a=12, b=2
a-b=10
a/b=6

a/2=6
b/2=1
(a+b)/2=7
(a+2)/2=7
(b+2)/2=2

so here BE are true



One observation
we have a/2 and a/2+1
similarly we have b/2 and b/2+1
so one of these has to be odd....

I agree with Stop@800. Something is definitely wrong with the question.

I am able to get all answers choices except for A and B for some or the other number.

I think I was wrong; thanks for catching it!

Either I am confusing myself or I am missing something here.

Stop@800 I agree with you on
a-b even means

either both a and b are even
or both are odd


a/b even means
a is even [as a and b are intergers]


BUT

taking both the facts together a has to be even and if a-b is even b has to be even(addition or subtraction of even and odd is always odd)

Agree or am I mistaken?

In your case a=12 b = 6

B,C,D are all odd and not B,E

Down to 3 choices

Lets say a = 36 b =18

B is ruled out

a=40 b =20

C is ruled out

I just cannot pick numbers where D) can be ruled out. I could very well be missing something here.

The question says must be true so if we can disprove the choices wiht the exception of one then the last one left must be the true one

Stop@800 or Morgoth, feel free to chip in?


Beater whats the OA?

Either I am confusing myself or I am missing something here.

Stop@800 I agree with you on
a-b even means

either both a and b are even
or both are odd


a/b even means
a is even [as a and b are intergers]


BUT

taking both the facts together a has to be even and if a-b is even b has to be even(addition or subtraction of even and odd is always odd)

Agree or am I mistaken?

a=12 b = 6

B,C,D are all odd

Down to 3 choices

a=40 b =20

B is ruled out
C is ruled out

I just cannot pick numbers where D) can be ruled out. I could very well be missing something here.

The question says must be true so if we can disprove the choices wiht the exception of one then the last one left must be the true one

Stop@800 or Morgoth, feel free to chip in?

Looks ok with numbers
Let me try to derive the generic logic

Thanks cramya

a/b is even
means a and b are even and also a is multiple of 4


a/2 will be even so out
b/2 will be even when b is multipole of 4 so out [a=8 b=4]

b/2 + 1 will be even when b is multiple of 2
bcoz b/2 will be odd so b/2 + 1 will be even [OUT]

(a+b)/2 will be odd whn b is also multiple of 4 so OUT


since a/2 is even [as a is multiple of 4]
so a/2 + 1 will always be odd

Stop@800 - I'm confused could you please explain your answer..Thanks

beater wrote:Stop@800 - I'm confused could you please explain your answer..Thanks

Confused at what point??