If n and k are positive integers and n + k

Question

If n and k are positive integers and n + k < 8, how many different values of the product nk are possible?

Sahil Verma · Accepted Answer

We know that n and k are positive integers, so they can be 1, 2, 3, ...
We also know that n + k < 8. This means the largest possible sum of n and k is 7.
Let's list all possible pairs of (n, k) that satisfy these conditions:(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)(2, 1), (2, 2), (2, 3), (2, 4), (2, 5)(3, 1), (3, 2), (3, 3), (3, 4)(4, 1), (4, 2), (4, 3)(5, 1), (5, 2)(6, 1)
Now, let's calculate the product nk for each pair:1 * 1 = 11 * 2 = 21 * 3 = 31 * 4 = 41 * 5 = 51 * 6 = 62 * 1 = 2 (already counted)2 * 2 = 4 (already counted)2 * 3 = 6 (already counted)2 * 4 = 82 * 5 = 103 * 1 = 3 (already counted)3 * 2 = 6 (already counted)3 * 3 = 93 * 4 = 124 * 1 = 4 (already counted)4 * 2 = 8 (already counted)4 * 3 = 12 (already counted)5 * 1 = 5 (already counted)5 * 2 = 10 (already counted)6 * 1 = 6 (already counted)
Counting the unique products, we get:1, 2, 3, 4, 5, 6, 8, 9, 10, 12
Therefore, there are 10 different possible values for the product nk.