ISEE Mathematics Achievement Question 326: Answer and Explanation

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Question: 326

10. A group of people are sharing equally the $30 cost of renting a car. If an additional person joined the group, each person would owe $1 less. How many people are in the group currently?

  • A. 5
  • B. 6
  • C. 10
  • D. 12

Correct Answer: A

Explanation:

A Let the choices help here. The choices represent how many people are currently in the group. Eliminate (D) immediately since 30 cannot be divided 12 ways (hopefully there aren't partial people in the car!). Try (B), which is the middle answer of the remaining choices: if there are 6 people renting the car now, the cost would be $5 each since = 5. If a seventh person joined, the cost per person would be , which is not an integer. Since the problem stated that adding 1 person to the group would result in each person owing $1 less, this does not satisfy the question, so eliminate (B) and try another choice. Try (A): if there are 5 people renting the car, they will each pay $6 since = 6. If a sixth person joins, they will each pay $5 because = 5. $5 is exactly one dollar less than $6, so this satisfies the question stem. Choice (A) is correct.

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