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vivek920368
zhanbo
If z~=1, then 1<=z<2

(1)Only
We should be able to solve for z, and then surely we can answer the question.
Sufficient. No need to actually solve for z.

Now, Let's actually solve for z.
3z=-12
z=-4
We can answer "No" to the question: is z~ = 1

(2)Only
We can answer "YES" to the question.

So, while the answer is thus "(D)", the contradiction between (1) and (2) is unexpected for a GMAT DS question.
zhanbo in the 2nd statement, the answer is always "No" because according to the statement z will always be greater than 1, which is quite the opposite to the stem.

vivek920368 Please note that the stem asks for z~, with the "strange symbol" ~. The strange symbol ~ is defined as "the greatest integer less than or equal to z", which is a complicated way of saying that it rounds DOWN to the nearest integer. It's helpful to become comfortable with this language, because it appears occasionally on official questions, and of course it's much easier to process quickly and accurately if you've done this before.

So, for statement 2, z~ rounds the z value down to 1, and we get a YES answer.

zhanbo is indeed correct that the contradiction between (1) and (2) is unexpected for a GMAT DS question.
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