Divisibility
What is the sum of all two-digit multiples of three that have units digit 1?
153
The ratio of the lengths of the corresponding sides of two similar decagons is 1:2. If the perimeter of
the smaller decagon is 76 cm, what is the perimeter of the larger decagon?
156
Manny has 5 shirts, 3 pairs of pants, 2 ties and 4 pairs of shoes. If Manny’s school uniform consists
of a shirt, a pair of pants, a tie and a pair of shoes, how many different uniforms can he wear to
school?
120
Kris multiplies the first six positive prime numbers together. How many zeros follow the last non-ze-
ro digit of the product?
1 zero
Two triangles are similar. The ratio of their areas is 1:4. If the height of the smaller triangle is 3 cm,
how long is the corresponding height of the larger triangle, in centimeters?
6 cm
How many triangles of any size are in the Belgian truss shown?
23
What is the least positive integer greater than 20 that has exactly three positive factors?
25
The length of a rectangle is increased by 25%. To keep the area of the
rectangle the same, by what percent must the width be decreased?
20%
A fair coin is flipped five times. What is the probability there are at least two tails and at least one head?
at least two tails = not all heads (-1) not four heads (-5)
at least one head = not all tails (-1)
2^5 = 32
(32 - 7)/32 = 25/32
How many positive 3-digit integers are palindromes and multiples of 11?
there are 8 3-digit integer palindromes that are multiples of 11: 121, 242, 363, 484, 616,
737, 858 and 979.
Two small circles with radii 2 cm and 3 cm are externally tangent. A third circle is
circumscribed about the first two as shown. What is the ratio of the area of the
smallest circle to the area of the shaded region? Express your answer as a
common fraction
1/3
Alvin lives 4 blocks west and 3 blocks south of his school. He wants
to take a different route to school each day, but each route must be
exactly 7 blocks long. For how many days can he do this without re-
peating any route
10