4. We look at the remainders when the numbers of eggs in the baskets is divided by 4.
Numbers 12 13 14 16 18 19 22 24 29 34
Remainders 0 1 2 0 2 3 2 0 1 2
The sum of the remainders is 1+2+2+3+2+3=13, so that when the total number of
eggs is divided by 4, the remainder will be 1. Since the sum of the numbers of eggs in
the unsold baskets is a multiple of 4, the number of eggs in the basket sold must leave
a remainder of 1 when divided by 4. From the chart above, the only possibility is the
basket with 13 eggs or the basket with 29 eggs. These in fact satisfied the remaining
conditions since 3×(12+16+19)=14+18+22+24+29+34, or
3×(24+19)=12+13+14+16+18+22+34.
ANS: 13 or 29
Section B.
Answer the following 3 questions, and show your detailed solution on the
space provided after each question. Each question is worth 20 points.
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