**Rule: Understanding Idiomatic Expressions.** The idiom 'barking up the wrong tree' means to be following a false lead or misdirecting one's efforts or blame. It comes from hunting, where a dog might bark at the base of a tree where it thinks its quarry is, even after the animal has escaped. Blaming the wrong department for one's own error is a perfect example. Option (b) is the correct definition. Option (a) is a literal interpretation. Option (c) is the opposite. Option (d) is an unrelated profession.

**Rule: Understanding Idiomatic Expressions.** The idiom 'hang in the balance' means that the future of something is uncertain and depends on the outcome of a particular event. Awaiting a crucial court decision would put a company's future in this precarious state. Option (c) is the correct definition. Option (a) is a literal misinterpretation. Options (b) and (d) are the opposite.

**Rule: Understanding Idiomatic Expressions.** The idiom 'a way with words' describes a person who has a talent for using language effectively and eloquently. The ability to make a boring subject interesting is a clear demonstration of this skill. Option (a) is the correct definition. Option (b) is a literal misinterpretation. Option (c) is the opposite. Option (d) is a profession related to words, but not the meaning of the idiom.

**Rule: Understanding Idiomatic Expressions.** The idiom 'ups and downs' refers to the mixture of good and bad experiences that happen in life or in a relationship. The statement implies that the friendship has endured through both fortunate and difficult periods. Option (b) is the correct definition. Option (a) and (d) are literal misinterpretations. Option (c) is an incomplete picture.

**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.