Question

A zookeeper had \(x\) baboons and \(y\) monkeys in an enclosure. One day, the zookeeper was told that seven of the animals have escaped. From only this information, he was able to deduce that at least one baboon has escaped. Which of the following does not represent a possible \((x, y)\) pair?

• A. (10,8)
• B. (7,2)
• C. (25,6)
• D. (12,4)

Hint:

To verify conditions in word problems, analyze all constraints systematically and eliminate options that fail to satisfy them.

Answer 1

The Correct Option is A

1. For the zookeeper to deduce that at least one baboon has escaped, the number of monkeys (\(y\)) must be less than 7. This ensures that even if all monkeys escape, some baboons must also have escaped.
2. Analyzing the options:
- Option A (10,8): Here, \(y = 8>7\). This means it is possible for all escaped animals to be monkeys, contradicting the zookeeper's conclusion. Hence, \(A\) is not possible.
- Option B (7,2): Here, \(y = 2<7\). The zookeeper can conclude that at least one baboon escaped. Hence, \(B\) is possible.
- Option C (25,6): Here, \(y = 6<7\). The zookeeper can deduce that at least one baboon escaped. Hence, \(C\) is possible.
- Option D (12,4): Here, \(y = 4<7\). The zookeeper can deduce that at least one baboon escaped. Hence, \(D\) is possible.
Conclusion: The pair that does not satisfy the condition is \(A\) (10,8).