How many jelly beans does each group of four need originally if each of four people consume jelly beans proportional to their original numbers?

How many jelly beans does each group of four need originally if each of four people consume jelly beans proportional to their original numbers?

• A. A multiple of 4
• B. A prime number
• C. 90
• D. None of the above

Answer: (A)

To determine why a multiple of four is the correct answer, we need to consider the context of the question regarding consumption of jelly beans among four individuals. If each person is consuming jelly beans in a way that is proportional to their original numbers, this implies that the total number of jelly beans must be divisible by the number of people sharing them, which in this case is four. When we say each individual is consuming jelly beans proportional to their original amounts, if each person's original count must be a whole number, then the total initial count of jelly beans must also be divisible by four to ensure that every individual can receive whole numbers of jelly beans based on the proportions assigned to them. Thus, if you were to start with any whole number of jelly beans, it would need to be a multiple of four to guarantee that when divided among the four individuals, no one receives a fractional amount. For example, if the total jelly beans were 80, then each person could potentially receive 20 in a 1:1 proportion. If it were 90, it wouldn’t work out evenly since each person would not receive a whole number (22.5 each), leading to fractions which do not fit the requirement of consuming whole jelly beans. Thus, the requirement

To determine why a multiple of four is the correct answer, we need to consider the context of the question regarding consumption of jelly beans among four individuals. If each person is consuming jelly beans in a way that is proportional to their original numbers, this implies that the total number of jelly beans must be divisible by the number of people sharing them, which in this case is four.

When we say each individual is consuming jelly beans proportional to their original amounts, if each person's original count must be a whole number, then the total initial count of jelly beans must also be divisible by four to ensure that every individual can receive whole numbers of jelly beans based on the proportions assigned to them. Thus, if you were to start with any whole number of jelly beans, it would need to be a multiple of four to guarantee that when divided among the four individuals, no one receives a fractional amount.

For example, if the total jelly beans were 80, then each person could potentially receive 20 in a 1:1 proportion. If it were 90, it wouldn’t work out evenly since each person would not receive a whole number (22.5 each), leading to fractions which do not fit the requirement of consuming whole jelly beans.

Thus, the requirement