Virtual Math Club
Problem Set #1 June 27, 2010
Name:_
1. Points A, B, C, D, and E are points on the circle shown. How many different
triangles can be formed by joining any three of these points? (Note: The
triangle formed by joining A to B to C is the sam
Virtual Math Club
Problem Set #31 February 6, 2011
NO CALCULATOR
Name_
1. Eric ties his dog to the corner of a 10-foot by 15-foot rectangular shed. The
length of the rope from the shed to the dog is 25 feet. Over how many square
feet can the dog roam? (As
Virtual Math Club
Problem Set #29 January 23, 2011
NO CALCULATOR
Name_
1. In simplest terms, what is the value of this radial expression?
Answer:
2. In year N, the 300th day of the year is a Tuesday. In year N+1, the 200th day of
the year is also a Tuesda
Virtual Math Club
Problem Set #25 December 19, 2010
NO CALCULATOR
Name_
1. In this addition problem, different letters represent different digits. Which three
digits are represented by X, Y, and Z?
Answer:
2. Mr. Gideon owns a large piece of land. The exa
Virtual Math Club
Problem Set #30 January 30, 2011
NO CALCULATOR
Name_
1. The points A(-3,6), B(8,6), C(8,-4), and D(-3, -4) are vertices of rectangle
ABCD. A point is selected at random from the interior of the rectangle. What is
the probability that the
Virtual Math Club
Problem Set #26 January 2, 2011
NO CALCULATOR
Name_
1. In the figure below, circle B is tangent to circle A at X, circle C is tangent to
circle A at Y, and circles B and C are tangent to each other. If AB = 6, AC = 5,
and BC = 9, what is
Virtual Math Club
Problem Set #28 January 16, 2011
NO CALCULATOR
Name_
1. Mr. Smith brings home 7 animals for his 7 children. Each child will adopt a pet
to be his or her own. There are 4 different cats (a Siamese, a Persian, a Calico,
and a Tabby), 2 dif
Virtual Math Club
Problem Set #24 December 12, 2010
NO CALCULATOR
Name_
1. The inhabitants of Magrathea use the same mathematical operators that we do
(+, , etc.). They also use and operator, @, that we do not know. The following
properites are true for a
Virtual Math Club
Problem Set #21 November 21, 2010
NO CALCULATOR
Name_
1. If the product (47)(517) is written as an integer, how many digits are in this
integer?
Answer:
2. Words that read the same backward and forward are called palindromes. How
many th
Virtual Math Club
Problem Set #32 February 13, 2011
NO CALCULATOR
Name_
1. A scratch-off lottery ticket has six spaces that can be uncovered. Two of the six
spaces say WIN; the other four say LOSE. A player randomly uncovers two
spaces. If he uncovers bot
Virtual Math Club
Problem Set #35 March 6, 2011
NO CALCULATOR
Name_
1. Five squares are inscribed along the hypotenuse of a right triangle as shown
below. If AB = 3 cm and BC = 6 cm, what is the combined area of the five
squares?
Answer:
2. A positive two
Virtual Math Club
Problem Set #40 April 17, 2011
NO CALCULATOR
Name_
1. The digits 1, 2, 3, 4, 5, 6, 7, and 9 are used to form four two-digit prime
numbers, with each digit used exactly once. What is the sum of these four
primes? (AMC)
Answer:
2. A number
Virtual Math Club
Problem Set #38 April 3, 2011
NO CALCULATOR
Name_
1. The number 25646425 is the square of a positive integer N. In decimal
representation, what is the sum of the digits of N? (AMC)
Answer:
2. The sum of 18 consecutive positive integers i
Virtual Math Club
Problem Set #4 July 25, 2010
Name:_
1. You are given five tiles, each with a single digit printed on it. You have tiles
with the digits 2, 5, 5, 7, and 8 on them. How many ways can you arrange these
tiles, using each tile once, to form a
Virtual Math Club
Problem Set #27 January 9, 2011
NO CALCULATOR
Name_
1. You are given a hundred dollars and told to spend it all purchasing exactly a
hundred animals at the pet store. Dogs cost $15, cats cost $1, and mice are 25
cents each. Also, you mus
Virtual Math Club
Problem Set #33 February 20, 2011
NO CALCULATOR
Name_
1. In the trapezoid ABCD, segment AB is parallel to segment CD, AB = CD,
and point P lies somewhere on segment AB. What is the ratio of the area of
triangle DPC to the area of trapezo
Virtual Math Club
Problem Set #34 February 27, 2011
NO CALCULATOR
Name_
1. Evan is 13 years old, and his aunt Melinda is 31 years old, which is Evans age
with the digits reversed. What is the fewest number of years in which the digits
of their ages will b
Virtual Math Club
Problem Set #36 March 13, 2011
NO CALCULATOR
Name_
1. At Nordic High School, 60% of the students cross-country ski, 40% of the
students play hockey, and 30% of the cross-country skiers also play hockey. Of
the student who dont play hocke
Virtual Math Club
Problem Set #37 March 27, 2011
NO CALCULATOR
Name_
1. How many different sums can be obtained by adding any two different integers
chosen from these thirty-five consecutive integers? (MOEMS)
Answer:
-17, -16, -15,-1, 0, 1, 15, 16, 17
2.
Virtual Math Club
Problem Set #22 November 28, 2010
NO CALCULATOR
Name_
1. Meghana has a bowl of gum drops. She sees Geeta at her door and quickly eats
one gum drop before Geeta enters and takes half of the remaining gum drops.
Then she sees Gauri at the
Virtual Math Club
Problem Set #23 December 5, 2010
NO CALCULATOR
Name_
1. A chef is preparing spaghetti and meatballs. He made two dozen meatballs, each
2 inches in diameter. His sauce is in a 12 inch diameter pot filled to within 2
inches of the top. How
Virtual Math Club
Problem Set #11 September 12, 2010
NO CALCULATOR
Name:_
1. Express as a single fraction in lowest terms:
Answer:
2. Sarahs teacher suggested 8 different novels for her to read this semester for
extra credit. If Sarah picks three novels,
Virtual Math Club
Problem Set #6 August 8, 2010
Name:_
1. How many numbers between 1 and 100 are the product of two even numbers?
Answer:
2. The Springfield city pool city pool is 50 meters long and 25 meters wide. The
water in the shallow end of the pool
Virtual Math Club
Problem Set #9 August 29, 2010
NO CALCULATOR
Name:_
1. What is the difference between the sum of all the even numbers up to 2010 and
the sum of all the odd numbers up to 2010?
Answer:
2. A circle of radius 2 cm is cut into four equal arc
Virtual Math Club
Problem Set #7 August 15, 2010
NO CALCULATOR
Name:_
1. cfw_1, 2, 7, 15, 17, 18 is a set of six data values. Suppose each data value is
multiplied by 3.6 and then 4 is added to each product. What is the mean of the
new set of six data val
Virtual Math Club
Problem Set #2 July 11, 2010
Name:_
1. Amanda arranges the digits 1, 3, 5, and 7 to write a four-digit number. The 7 is
next to the 1, but not to the 5. The 3 is next to the 7, but not to the 5. The fourdigit number is divisible by 5. Wh
Virtual Math Club
Problem Set #8 August 22, 2010
NO CALCULATOR
Name:_
1. What fraction of this regular octagon is shaded?
Answer:
2. Two numbers are such that their difference, their sum, and their product are in
the ratio 1 : 4 : 15. What are the two num
Virtual Math Club
Problem Set #5 August 1, 2010
Name:_
1. Mr. Potato Head has 4 hats, 3 sets of eyes, 2 noses, 3 mouths, one pair of ears, one pair
Answer:
of arms, and 4 sets of shoes. How many ways can Mr. Potato Head be assembled?
Assume that he must h
Virtual Math Club
Problem Set #3 July 18, 2010
Name:_
1. In this multiplication example, different letters represent different digits. What
digit does H represent in the 3-digit number AHA?
Answer:
AHA
xA
TADA
2. Express as a single number:
Answer:
(-2) +
Virtual Math Club
Problem Set #10 September 5, 2010
NO CALCULATOR
Name:_
1. It is now 10:45 a.m. What time will it be in 143,999,999,995 minutes from
now? (Ignore any leap seconds between now and then.)
Answer:
2. In the figure below, ABCD is a unit squar