Let n be the largest integer that is the product of exactly 3 distinct prime number d,e, and 10d+e, where d and e are single digits. What is the sum of the digits of n?
(A) 12 (B) 15 (C) 18 (D) 21 (E) 24
ANSWER: A
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Problem 71
A point (x,y) is randomly picked from inside the rectangle with vertices (0,0), (4,0), (4,1), and (0,1). What is the probability that x< y ?
(A) 1/8 (B) 1/4 (C) 3/8 (D) 1/2 (E) 3/4
ANSWER:B
Problem 70
The sum of the two 5-digit numbers ABC10 and ABC12 is 123422. What is A+B+C ?
(A) 10 (B) 11 (C) 12 (D) 13 (E) 14
ANSWER: E
Problem 69
What is the probability that a randomly drawn positive factor of 60 is less than 7?
(A) 1/10 (B) 1/6 (C) 1/4 (D) 1/3 (E) 1/2
ANSWER: E
Problem 68
How many non-congruent triangles with perimeter 7 have integer side lengths?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
ANSWER: C
Problem 67
It takes Mary 30 minutes to walk uphill 1 km from her home to school, but it takes her only 10 minutes to walk from school to her home along the same route. What is her average speed, in km/hr, for the round trip?
(A) 3 (B) 3.125 (C) 3.5 (D) 4 (E) 4.5
ANSWER: A
Problem 66
A solid box is 15 cm by 10 cm by 8 cm. A new solid is formed by removing a cube 3 cm on a side from each corner of this box. What percent of the original volume is removed?
(A) 4.5 (B) 9 (C) 12 (D) 18 (E) 24
ANSWER: B
Problem 65
Members of the Rock Soccer League buy socks and T-shirts. Socks cost $4 per pair and each T-shirt costs $5 more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games.If the total cost is $2366, how many members are in the League?
(A) 77 (B) 91 (C) 143 (D) 182 (E) 286
ANSWER: B
Problem 64
What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers?
(A) 0 (B) 1 (C) 2 (D) 2003 (E) 4006
ANSWER: B
Problem 63
When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8