Is z an odd integer?

Question

Tough and Tricky questions: Word Problems.

(1) z is divisible by 3.
(2) The square root of z is an integer divisible by 3.

Kudos for a correct  solution .

littlewarthog · Answer

We can solve this one easily by picking numbes.

Statement 1: if we could fine one odd and one even integer, both divisible by 3, we could show that this statement is insufficient. 3 and 6 are such numbers. To prove it by using number properties, we can just write 3as 1*3 and 6 as 2*3. As 3 is odd, multiplying it with odd and even numbers will have odd and even results. Insufficient.

Statement 2: With the same approach, we can show that the second statement is also insufficient. We just need to square 3 and 6. As 3is odd, it's square,9, must also be odd. As 6 can be written as 2*3, it's square is  (2*3)^2=2^2*3^3=36 , it must be even. Therefore statement 2is also insufficient.

Both taken together: as we see from the factorization, the numbers picked for statement 2 (9 and 36) already fulfill both statements and still do not allow a clear conclusion whether z is odd or even. Answer E.

sunaimshadmani · Answer

St (1) : 3 has both odd and even multiples, so z can be odd or even..... Insufficient.

St (2): Z can be 9 or 36, according to this statement.....Insufficient.

Combining both statements, still 9 AND 36 satisfy both statements......Answer is E.

Bunuel · Answer

OFFICIAL SOLUTION:

Statement (1) tells us that z a multiple of 3. 3 and 6 are both multiples of 3, but 3 is odd and 6 is even. So Statement (1) is insufficient.

Statement (2) tells us that z must be a perfect square that is also a multiple of 3. Some possible values for z are 9 and 36. 9 is odd and 36 is even, so Statement (2) is also insufficient.

When combined, the statements still do not provide sufficient information. If z is equal to either 9 or 36, both statements are true, so we do not know whether z was odd.

Since the statements are both insufficient, even when combined, the correct answer is choice (E).

TheNightKing · Answer

Statement 1 : z can be 9 or 36
Statement 2: z can be 36 or 81.

Both combined, we cannot find a unique answer since z can be even or odd.
Hence E

bumpbot · Answer

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Is z an odd integer?

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Is z an odd integer?

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