hongwang9703 wrote:OG pg 282, question 106
If x and y are integers, is xy even?
1. x=y+1
2. x/y is an even integer.
answer: D
however, from 1. X could be 0, and y could be -1, which 0 x -1 = 0, which is neither even nor odd. 0 is an integer, and so is -1, so no rules are violated and it makes statement 1 a maybe, thus answer should be B!
please explain....i must be missing an important peice of information somewhere!
Lets not get in to 0 is odd or even argument .
Here is a simple way to solve this problem :
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If x and y are integers, is xy even?
1. x=y+1
2. x/y is an even integer.
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we are given x and y are integers .
We need to know if xy = even .
For xy to be even we need to find if either x or y is even .
So the question is - IS any of the numbers x OR y even ?
Lets look at the statements .
1. x=y+1
x - y = 1 Rephrase x - y = odd .
Rule : Even +/- Odd = Odd .
So we can tell any one of x or y is odd and the other even.
Thus we can say xy will be even .
Sufficient .
Now lets look at statement 2 .
x/y is an even integer .
x/ y = even .
Multiply y both sides .
x= even(y).
Rephrase x = even .
Thus we can say xy will be even .
Sufficient .
Hence D .
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Now to answer the 0 is odd or even .
0 is considered even . Why?
Reason : Integers range from 0 , 1, 2, ......... N .
Similarly integers can be - ve also -N ...............-3,-2,-1,0,1,2........N
Property Of Integers : Integers alternate between odd and even numbers .
That is ever alternate digit will be Odd or Even depending upon the starting digit .
So keeping this in mind -1 is odd so 0 should be even .
And 1 is odd , 2 is even so 0 should be even .
Hope this helps.
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