I tried different combos but still couldn’t figure out the number of 25-cent stamps, what’s the right way to approach this?

Question

If each of the stamps Carla bought cost 20, 25, or 30 cents and she bought at least one of each denomination, what is the number of 25-cent stamps that she bought? 
1. She spent a total of $1.45 for stamps. 
2. She bought exactly 6 stamps.

Mohit C · Accepted Answer

This question is about solving for the number of 25-cent stamps (y), knowing that the stamps come in 20c, 25c, and 30c denominations.
Statement 1 tells us the total cost was $1.45, or 145 cents. So the equation is: 20x + 25y + 30z = 145. But there are multiple combinations of positive integers that satisfy this &mdash; for example, x = 3, y = 1, z = 2 and x = 2, y = 3, z = 1 both work. So Statement 1 alone isn&rsquo;t sufficient.
Statement 2 tells us she bought exactly 6 stamps, so x + y + z = 6. But that alone still doesn&rsquo;t tell us y. The same two combinations above both add up to 6 stamps, so Statement 2 alone is also not sufficient.
Even when combined, both equations allow for multiple valid solutions for y. So we still can&rsquo;t uniquely determine the number of 25-cent stamps. The answer is E &mdash; not sufficient even together.

Divakshi Arora · Answer

This one&rsquo;s about checking if the info locks down a unique solution.

Let x, y, z be the number of 20c, 25c, and 30c stamps
Statement 1: Total cost is 145 cents &rarr; 20x + 25y + 30z = 145
Multiple integer solutions exist for this equation &rarr; not sufficient
Statement 2: Total number of stamps = 6 &rarr; x + y + z = 6
Still no way to isolate y &mdash; multiple combinations add to 6
Even together, the same value of y (like y = 3) can appear in different valid sets
So even combined, the statements don&rsquo;t uniquely determine y.
Correct answer is E.