Track / Stage 4 / 36 of 340 #296 of 2000

Problem 296

AMC 12 late, AIME early

Combinatorics Difficulty 4.6 Find the answer

1. Given the universal set $I=\{1,2,3,4,5\}, A \cap B$ $=\{2\}, \bar{A} \cap B=\{1,4\}$ . Then $\bar{B}$ equals: ( ).
(A) $\{3\}$
(B) $\{5\}$
(C) $\{1,2,4\}$
(D) $\{3,5\}$

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

1. D

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