If x,y and z are integers
If x, y and z are integers and xy + z is an odd integer, is x an even integer?
I. xy + xz is an even integer II. y + xz is an odd integer
my ques: How do i solve this within 2 mins? Pluggin values is confusing me
There is no need for plugging values in this question. It can be easily solved algebraically and some logic.
Remember,
Odd – Even = Odd
Even x Odd =Even
Odd x Odd = Odd
- xy + xz is an even integer – SUFFICIENT , answer will be A or D
Given:
xy + z is odd …(i)
xy + xz is even …(ii)
Subtracting (ii) from (i)
we get xz – z, which should be odd
=> z(x-1) is odd
=> both z and (x-1) is odd
=> since (x-1) is odd, x must be even.
- y + xz is an odd integer -INSUFFICIENT
Given:
xy + z is odd …(i)
y + xz is odd …(ii)
Subtracting (ii) from (i)
we get xy + z – y – xz
= (x-1)(y-z) , which should be even
=> Either (x-1) is even or (y-z) is even ….insufficient to determine
Hence, answer is option A.
