Is p > q (1) 2p/3 < 3q/8 (2) 7p/11 < 4q/5

Statement 1: \(\frac{2}{3}p < \frac{3}{8}q\)
Multiplying by the LCM of the two denominators -- 24 -- we get:
16p < 9q
\(p < \frac{9}{16}q\)

Case 1: q=1, implying that p < 9/16
If p=0, then p<q, so the answer to the question stem is NO.
Case 2: q=-16, implying that p < -9
If p=-10, then p>q, so the answer to the question stem is YES.
INSUFFICIENT.

Statement 2: \(\frac{7}{11}p < \frac{4}{5}q\)
Multiplying by the LCM of the two denominators -- 55 -- we get:
35p < 44q
\(p < \frac{44}{35}q\)

Case 1: q=1, implying that p < 44/35
If p=0, then p<q, so the answer to the question stem is NO.
Case 2: q=35, implying that p < 44
If p=40, then p>q, so the answer to the question stem is YES.
INSUFFICIENT.

Statements combined:
16p < 9q --> difference between the coefficients = 16-9 = 7
35p < 44q --> difference between the coefficients = 44-35 = 9

To combine the two inequalities so that p and q are ISOLATED, the difference between the coefficients must be THE SAME in each inequality.
The LCM of the two differences in blue is 63.
To yield a difference of 63 in each inequality, multiply the first by 9 and the second by 7:
9*16p < 9*9q --> 144p < 81q --> difference between the coefficients = 144-81 = 63
7*35p < 7*44q --> 245p < 308q --> difference between the coefficients = 308-245 = 63

Adding together the resulting inequalities in green, we get:
144p + 245p < 81q + 308q
389p < 389q
p < q
Thus, the answer to the question stem is NO.
SUFFICIENT.