**Rule: Understanding Idiomatic Expressions.** The idiom 'at the mercy of' means to be in the power of someone or something, with no way to protect oneself from their potentially harmful actions. A small country is often in this vulnerable position relative to larger, more powerful ones. Option (a) is the correct definition. Option (b) is a possible but not necessary outcome. Option (c) and (d) are the opposite.

**Rule: Understanding Phrasal Verbs.** The phrasal verb 'add up' in this context means to seem reasonable or consistent; to make sense. The sentence uses the negative ('don't add up') to indicate that the stories are contradictory, which is why the police are suspicious. Option (a) is the correct definition. Option (b) is a literal misinterpretation. Option (c) is the opposite. Option (d) is an unrelated quality.

**Rule: Understanding Idiomatic Expressions.** The idiom 'a feather in one's cap' refers to a significant achievement that brings credit and honor to a person. A company's success would be a proud accomplishment for its leader. Option (c) is the correct definition. Option (a) is the literal origin. Option (b) is the opposite. Option (d) is an understatement.

**Rule: Understanding Idiomatic Expressions.** The idiom 'on cloud nine' describes a state of extreme happiness. The birth of a child is a life event that typically brings such joy. Option (a) is the correct definition. Option (b) and (d) are literal misinterpretations. Option (c) is the opposite.

**Rule: Understanding Idiomatic Expressions.** The idiom 'an ace up one's sleeve' comes from card games and refers to a hidden advantage that is kept in reserve until the opportune moment. In a debate, this could be a powerful, unexpected argument. Option (b) is the correct definition. Option (a) is the literal origin. Option (c) is the opposite. Option (d) is a profession that uses similar tricks, but it is not the meaning of the idiom.

**Rule: Understanding Idiomatic Expressions.** The idiom 'blow a fuse' means to lose one's temper and become very angry. It is a metaphor based on an electrical fuse blowing when overloaded. A cancelled flight is a common trigger for such an outburst. Option (a) is the correct definition. Option (b) and (d) are literal misinterpretations. Option (c) is the opposite.

**Rule: Understanding Idiomatic Expressions.** The idiom 'in the firing line' means to be in a position where one is vulnerable to attack, criticism, or dismissal. A team's poor performance often puts its coach or captain in this position. Option (a) is the correct definition. Option (b) is a literal interpretation. Option (c) is the opposite. Option (d) is an incorrect interpretation of 'firing'.

**Rule: Understanding Idiomatic Expressions.** The idiom 'bounce ideas off someone' means to share one's ideas with another person to get their feedback and opinion. This is a common practice in creative collaboration, such as between comedians. Option (b) is the correct definition. Option (a) is a similar but different idiom ('throw something at the wall...'). Option (c) is the opposite. Option (d) is an incorrect interpretation of 'chemistry'.

**Rule: Understanding Idiomatic Expressions.** The idiom 'live from hand to mouth' describes a precarious existence of having only enough resources to satisfy immediate needs, with no money left for the future. Being worried about one's next meal is a hallmark of this situation. Option (b) is the correct definition. Option (a) and (d) are the opposite. Option (c) is a literal misinterpretation.

**Rule: Understanding Idiomatic Expressions.** The idiom 'a rough patch' (or 'a bad patch') refers to a period of time marked by problems or hardship. A company facing financial or operational trouble would be going through a rough patch. Option (a) is the correct definition. Option (b) and (d) are literal misinterpretations. Option (c) is the opposite.