Is z an odd integer? (1) z/3 is odd. (2) 3z is odd.

Question

Is z an odd integer?

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

kevincan · Answer

(1) z/3 is an odd integer, so we can write z/3=k for some odd integer k
Thus z=3k, which is an odd integer. SUFF

(2) 3z is an odd integer m. Thus z=m/3. If m is a multiple of 3, z is an odd integer. However, if m is not a multiple of 3, z will not be an integer.

NOT SUFF

A

Fig · Answer

(A) for me

From 1 z/3 = 2*k+1 where k is an integer <=> z = 3*(2*k + 1) = ODD*ODD = ODD SUFF. From 2 3*z = 2*k+1 <=> z= (2*k+1)/3 So, o If 2*k+1 = 3*n (n an ODD integer), then: z = 3*n / 3 and z is an ODD o If 2*k+1 is not a multiple of 3, then: z is even not an integer. INSUFF.

Mishari · Answer

No, odds and evens are only for integers. While the question asks about whether Z is odd, statements 1 and 2 gives clue some fractions that contain z.

Statemnet 1 confirms that Z is indeed an integer, while statement 2 does not neccessarily indicate that Z is an integer, regardless whether odd or even.

My updated Answer:  A

umbdude · Answer

Crazy...it's like playing word games. Is Z odd AND integer?

(1) Z/3=Odd -> Z=3*Odd -> Z=Odd*Odd, so Z must be Odd. SUFF.

(2) 3Z=Odd -> Z=Odd/3. So Z could be 7/3 or 15/3, one is integer another one isn't. Or you can look at it as 3*(5)=Odd (yes, Z is an odd integer); but 3*(1/3) = Odd (no, Z is neither odd nor an integer). -___-

So the answer is A I guess.

DavidTutorexamPAL · Answer

The Alternative approach to this question is to try to find specific numbers that would eliminate certain answers because they lead to more than one option.
Statement (1) works for 3,9,15,21... all odd. Since z/3 equals odd, z = 3 times odd, so it must be odd. Statement (1) is sufficient, so (B), (C) and (E) are eliminated.
Statement (2) works for 1,3,5,7... but also for 1/3, so there's more than one option. Answer choice (D) is eliminated. The correct answer is (A).

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keshavmishra · Answer

Is z an odd integer?

a) z/3 is odd integer
z=3*odd = odd*odd = odd {sufficient, cancel (BCE)}

b)3z= odd integer
z= odd integer /3 
it may or may not be integer. Not sufficient

Answer A

dhwanit2412 · Answer

the logic which people are using to negate B is the same logic which can be used to negate A, as if Z is something like a 5.1 now divide by 3 it will give you a odd figure. which is 1.7

Bunuel · Answer

No. Only integers can be even or odd. 1.7 is not odd becasue it's not an integer.

Is z an odd integer? (1) z/3 is odd. (2) 3z is odd.

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