Explanation

In this question, if we call the number of carrots bought C, and the number of onions bought N (so as not to confuse ourselves with zero), then we have



That might not seem like enough to solve, but we know that Pat bought at least one of each. So we can't have or . The fact that both C and N are integers also limits the possibilities. Since C is larger, we can start there and see how it contributes, in various cases to the total of 11. You could write, or partly write and imagine the following table:











This last case is special. Since we have at least one carrot and at least on onion, we need some multiple of their prices to add to eleven dollars. This is the first possibility we've found, since we can't have or . In this case, the number of carrots is 5. The remaining amount of dollars is $5.50, which amounts to 11 onions. The total number of vegetable items purchased is 11+5=16.

The correct answer is (E).