Gmat_mission wrote:If \(z\) is an odd integer, is \(300z > 1500?\)

\((1 )\ 0 < \sqrt{z} < 8 \)
\((2) \ 1 < z^2 < 45\)

[spoiler]OA=B[/spoiler]

Source: Veritas Prep

Hi Gmat_mission. This is how I would solve this DS question.

Statement 1:
\((1 )\ 0 < \sqrt{z} < 8 \)

Since \(0 < \sqrt{z} < 8 \) then we have that \(0 < z < 64 \). Now:
- If z=1 then \(300z < 1500,\) and so the answer is NO.
- If z=63 then \(300z > 1500,\) and so the answer is YES.
We've got two different answers, then this statement is Not Sufficient.

Statement 1:
\((2) \ 1 < z^2 < 45\)

Since \(z\) is an odd integer and \(1 < z^2 < 45\) then \(1 < z < 7\) which implies that \(z=3\) or \(z=5\). Here, in any case, we will get that \(300z \leq 1500,\) and so, the answer is NO.
Here, we've got a unique answer. Therefore, this statement is Sufficient.

In conclusion, the correct answer is _B_.

I hope it helps you. <i class="em em-sunglasses"></i>