Question

Stacy and Ben start packing their books in groups of two. Stacy could pack all her books into groups of two. However, Ben was left with one book which he could not pack in a group of two.
Statement 1: Stacy has an odd number of books.
Statement 2: Ben has an even number of books.

Which of the following options is correct?

• A. Only statement 2 is correct.
• B. Both statements are correct.
• C. Both statements are incorrect.
• D. Only statement 1 is correct.

Answer 1

The correct option is C Both statements are incorrect.

Let us consider a set of $5$ books.


When we group the $5$ books in pairs, we can observe that one book gets left out.
Since all the books cannot be grouped in pairs, $5$ is an odd number.
When we group a certain number of objects in pairs such that one object is left alone after the pairing, the number of objects is odd.

Now, let us consider a set of $6$ books.


Since we can group all $6$ books in pairs, $6$ is an even number.
Hence when we group a certain number of objects in pairs such that all the objects are paired, the number of objects is even.

Therefore, Stacy has an even number of books and Ben has an odd number of books.
Both statements given in the question are incorrect.