Given that x > y and 3 < y, which of the following is/are true? i. y > 3 ii. x < 3 iii. x > y > 3

Analyze the question: We are given two facts:

• x > y
• 3 < y

We need to decide which of the statements i, ii and iii must be true.

Concept: The inequality a < b can be rewritten as b > a. Inequalities are also transitive: if x > y and y > 3, then x > 3.

Step-by-step:

1. Statement i: y > 3. The given condition 3 < y is just y > 3 written the other way round. So i is true.

2. Statement ii: x < 3. We know x > y and y > 3, so x > 3. That means x cannot be less than 3. So ii is false.

3. Statement iii: x > y > 3. Combining x > y with y > 3 gives x > y > 3. So iii is true.

Only i and iii are true.

Answer: Option C.

Tip: When you see an inequality like 3 < y, flip it so the variable comes first (y > 3). Then chain the inequalities together in one line (x > y > 3). This makes it easy to check each statement quickly.