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
Number properties
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Source: Beat The GMAT — Problem Solving |
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....
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....
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cramya
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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?
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?
-
cramya
- Legendary Member
- Posts: 2467
- Joined: Thu Aug 28, 2008 6:14 pm
- Thanked: 331 times
- Followed by:11 members
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?
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?
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
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
