SAT Math Multiple Choice Practice Question 169: Answer and Explanation

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Question: 169

15. Sergei decided to give everyone else in his study group 3 candies each, planning to have 2 left over for himself. However, one member of the group was sick; as a result, he gave 4 candies to everyone who showed up, and there was only one left over for him. How many candies were originally in the bag?

A. 5
B. 13
C. 17
D. 29
E. 34

Correct Answer: C


C. Let n stand for the number of people in the study group, aside from Sergei. So Sergei had 3n + 2 candies. When one person didn't show up, he had 4(n - 1) + 1 candies, which is still the same number of candies. So 3n + 2 = 4(n - 1) + 1, and the right side simplifies to 4n - 3. Solving 3n + 2 = 4n - 3 gives you n = 5, but be careful! The problem doesn't ask for the number of people, but for the number of candies. So plug 5 back in to the equation 3n + 2 to get 17.

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