I see no know discussion for M#04 ,Q- 13.
If a and b are integers, is x even?
1. x = a/b, where the division leaves no remainder and b is odd.
2. x= a/b, where the division leaves no remainder and both a and b are odd
I think the answer should be E.
We dont know the values of a and b. All we know is they are odd
x = a/b
if a = 9, b=3 ->x=3 odd
a= 3,b=9 ->x=1/3 Not odd
Therefor B is not suff
1 and 2 are not suff together => answer is E
when you pick numbers, you have to follow the rules that you've been given. The second set of numbers you chose for statement (2) contradict the statement, so those numbers are "illegal".
In terms of quotients and remainders, 3/9 has a quotient of 0 and a remainder of 3; since (2) tells us that a/b leaves no remainder, you cannot choose those numbers.
The only way to get no remainder is for a to be a multiple of b; if a and b are both odd, then we have an odd divided by an odd which, if it's an integer, must be odd (and we know that it has to be an integer, since there's no remainder). Accordingly, (2) tells us that x is definitely NOT even and is therefore sufficient.
As an aside, even with the illegal numbers you chose you should have arrived at (b) as the correct answer. The question is "is x even?" and if you plug in x = 1/3 the question becomes "is 1/3 even?", which also has a "no" answer. A statement is only insufficient if it can generate both a "yes" and a "no" answer to the original question.
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