BTGmoderatorLU wrote: ↑

Fri Mar 27, 2020 1:20 pm

Manhattan Prep

Four different children have jelly beans: Aaron has 5, Bianca has 7, Callie has 8, and Dante has 11. How many jelly beans must Dante give to Aaron to ensure that no child has more than 1 fewer jelly beans than any other child?

A. 2
B. 3
C. 4
D. 5
E. 6

The OA is B

Since Bianca’s number of jelly beans and Callie’s number of jelly beans differ by exactly 1, we need to bring Aaron’s number of jelly beans to either Bianca’s or Callie’s. If Aaron’s number is brought up to Bianca’s (i.e., Dante gives Aarron 2 jelly beans), then Aaron, Bianca, Callie, and Dante have 7, 7, 8, and 9 jelly beans, respectively. However, we see that Dante still has 2 more jelly beans than either Aaron or Bianca. On the other hand, if Aaron’s number is brought up to Callie’s (i.e., Dante gives Aarron 3 jelly beans), then Aaron, Bianca, Callie, and Dante have 8, 7, 8, and 8 jelly beans, respectively. We see that in this case, no child has more than 1 fewer jelly beans than any other child.

Answer: B