Exactly one of the following statements is false:

1. Audrey is older than Beatrice.

2. Clement is younger than Beatrice.

3. The sum of the ages of Beatrice and Clement is twice the age of Audrey.

4. Clement is older than Audrey.

Who is the youngest?

Đây là toán Anh

Result: 2 is wrong, Beatrice is the youngest
Step by step:

Let Audrey's age is $a$, Beatrice's age is $b$, Clement's age is $c$ `(a; b; c ∈ N`*`) `

`text{In case statement 1 is false, then the statements:}`

`3. b + c = 2a`

and `2. c < b`

and `4. c > a`

`text{Are all true.}`

From statement `2` and `4` `⇒ b > c > a`

`∴ b + c > 2a` (Eliminate this case ∵ `b + c = 2a`)

`text{In case statement 2 is false, then the statements:}`

`1. a > b`

and `3. b+c = 2a`

and `4. c > a`

`text{Are all true.}`

From statements `1` and `4` `⇒ c > a > b`

`∴ c + b` could equal `2a`

⇒ 2 is the only false statement `∵` Exactly one of the statements is false

`∴ c > a > b` is true `∵ a > b; c > a` is true `⇒ b` is the smallest

∵ Beatrice is the youngest