If P means 'greater than (>)'; Q means 'less than (<)'; R means 'not greater than'; S means 'not less than'…
If P means 'greater than (>)'; Q means 'less than (<)'; R means 'not greater than'; S means 'not less than' and T means 'equal to (=)', then consider the following statements:
1. If 2x(S)3y and 3x(T)4z, then 9y(P)8z.
2. If x(Q)2y and y(R)z, then x(R)z.
Which of the statements given above is/are correct?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Solution
Statement 1: $2x \ge 3y$ and $3x = 4z$. From these, $x \ge 3y/2$ and $x = 4z/3$, so $4z/3 \ge 3y/2$, giving $8z \ge 9y$, i.e. $9y \le 8z$, not $9y > 8z$ - so statement 1 is incorrect. Statement 2: $x < 2y$ and $y \le z$ gives $2y \le 2z$, so $x < 2z$, but this does not establish $x \le z$ - statement 2 is incorrect. Hence neither statement is correct.