Evaluating data sufficiency to determine if a number is prime

Translate the operators into standard mathematical inequalities [cite: 2549, 2550]: `P` is `>`, `Q` is `<`, `R` is `≤` (not greater means less than or equal), `S` is `≥` (not less means greater than or equal), and `T` is `=` [cite: 2549, 2550].

Evaluate Statement 1: 2x \ge 3y \implies x \ge 1.5y. 3x = 4z \implies x = 4/3z. Substitute x: 4/3z \ge 1.5y \implies 4z \ge 4.5y \implies 8z \ge 9y, which is 9y \le 8z. The statement claims 9y(P)8z, which translates to 9y > 8z[cite: 2549, 2551]. Since our derived relation is \le, Statement 1 is Incorrect.

Evaluate Statement 2: x < 2y y \le z \implies 2y \le 2z. Combining them gives x < 2y \le 2z \implies x < 2z. The statement claims x(R)z, which means x \le z[cite: 2550, 2552]. If x < 2z, x could easily be greater than z (e.g., if z=2, then 2z=4; x could be 3, where 3 < 4 holds but 3 \le 2 is false). Statement 2 is Incorrect.

Answer: (d).