Category: math competition

Charlyn walks completely around the boundary of a square whose sides are each 5 km long. From any point on her path she can see exactly 1 km horizontally in all directions. What is the area of the region consisting of all points Charlyn can see during her walk, expressed in square kilometers and rounded to the nearest whole number?

(A) 24 (B) 27 (C) 39 (D) 40 (E) 42

ANSWER: C

Mrs.Walter gave an exam in a mathematics class of five students. She entered the scores in random order into s spreadsheet, which recalculated the class average after each score was entered. Mrs.Walter noticed that after each score was entered, the average was always an integer. The scores(listed in a ascending order) were 71,76,80,82,and 91. What was the last score Mrs.Walter entered?

(A) 71 (B) 76 (C) 80 (D) 82 (E) 91

ANSWER: 80

Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?

(A) 21 (B) 60 (C) 119 (D) 180 (E) 231

ANSWER: C

At Wootton High School, 2/5 of the freshmen and 4/5 of the sophomores took the math competition. Given that the number of freshmen and sophomore contestants was the same, which of the following must be true?

(A) There are five times as many sophomore as freshmen.

(B) There are twice as many sophomore as freshmen.

(C) There are as many freshmen as sophomores.

(D) There are twice as many freshmen as sophomore.

(E) There are five times as many freshmen as sophomores.