Is z an odd integer?

[vsrc100]

Is z an odd integer?

1. z/3 is odd
2. 3z is odd

[Hashim B]

Aha ...

CAVEAT LECTOR: I am delirious from sleep deprivation.

Sheesh. I love this DS stuff.

Is z an odd integer is really TWO questions. Is z odd and is z an integer. Not that it matters because odd and even only apply to integers. But its good to break down what the GMAT throws at you anyway.

Alright, on DS that throw defintions at you, you should make sure you pull out the definitions and have them close to hand. There is no defintion for odd that means anything much. The defintion is for even. Even is defined to be any number divisible by two. Odd just means not even. So let's change up the question to be
Is z even?
Is z divisible by two?

We have changed their questions and made it our own it is time to take a look at our statements.
(1) z/3 = odd.
We know that z/3 is not divisible by two.
Since no twos came out of z for us to worry about, the 3 is just slight of hand ...
If the result is odd then we know that z must have been odd.
Otherwise, the two would still be 'left in' (be a factor of) z.
"look into my eyes... you are getting sleepy ...."
Sufficient.

(2) 3z is odd.
Which tells us that zis not even.
If z were even, 3z would also have been even.
Suffcient.

You may want to learn the following.

E x E = E
E x O = E
O X E = E
O x O = O.

(Send me your money you have a 3/4 chance of being even afterwards)
Similar to above for division, but with far less certainty:
(Assuming the top number is greater in each.)

E / E = could be even or odd, or fraction.
O / O = O
E / O = E
O / E = non-integer/fraction/decimal

[vsrc100]

1 is sufficent. I agree.
For 2, if z = 1/3, does it suffice?

[Hashim B]

1 is sufficent. I agree.
For 2, if z = 1/3, does it suffice?

Does it really matter? (Rhetorical question)
No, it does not.
We would still know that z is not even.

[gmat168]

Didn't you just contradict yourself in your last answer, Hashim?

So 2 is NOT sufficient. Only 1 in sufficient.

[Hashim B]

Didn't you just contradict yourself in your last answer, Hashim?

So 2 is NOT sufficient. Only 1 in sufficient.

I think so, I do tend to make lots of careless errors. I always wonder how I get my math scores.

Hence CAVEAT LECTOR.

The explanation from this this morning assumes that z is an integer and all good test-takers know that we make NO ASSUMPTION in DS. This is actually an extremely sloppy error that would earn any of my students many frowns because assuming the integer ignores one and one and zero are fodder for all sorts of sneaky stuff on the GMAT.

[gmat168]

Where do you teach, if I may ask?

[gmatguy]

A it is

[DEVIKA]

why can't the answer be D
since 3 is odd z has to be odd for 3z to be odd, right!
if i am wrong please explain

[gmat168]

z= 1/3