rahul16singh28 wrote:
chetan2u wrote:
Is a an even integer, if a,b and c are positive integers?
(1) (a+b)*c is odd
(2) (a+c)*b is odd
New question
source-self
Hi
chetan2u &
amanvermagmatCan you help me to clarify my doubt.
I got the answer as C by combining both statements via one approach. However, when I do it with the below approach I am getting different answer.
\(a * c + b * c = odd\)
\(a * b + c * b = odd\)
Subtract the above two equations, we get
\(a (c-b) = even\)... As
c & b are already odd as per the two statements
We can have
a = odd or even.
Not sure where i am going wrong.
Hi Rahul
I think your approach is not wrong, its just that here this approach is incomplete.
Because this approach does not tell us what 'a' will be - odd or even?
However, as 'b' and 'c' are already odd as per statements, then instead of subtracting the two equations, why not use this for any one equation only: say first equation.
a*c + b*c = Odd, now b & c are both odd so b*c is odd. So a*c = Odd - Odd = even.
Product of a & c is even, but since c is odd, 'a' definitely has to be even.
(we can do the same thing for second equation also and we will get the same result)
What you have done is not wrong, but not very useful towards the required answer. Consider this:- say we are given
x+y = 5
2x + y = 9 and say we have to find x.
If I subtract first equation from second, I will straight away get x.
But instead if I add the two equations, I will get 3x + 2y = 14. What I have now done is not wrong, but it doesnt help me get x. I will have to do something more with this, or do something else to get x.