In the pattern below, the cat moves clockwise through the four squares and the mouse moves counterclockwise through the eight exterior segments of the four squares.

If the pattern is continued, where would the cat and mouse be after the 247th move?

The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim’s siblings?

Child | Eye Color | Hair Color |
---|---|---|

Benjamin | Blue | Black |

Jim | Brown | Blond |

Nadeen | Brown | Black |

Austin | Blue | Blond |

Tevyn | Blue | Black |

Sue | Blue | Blond |

How many integers between 1000 and 2000 have all three of the numbers 15, 20 and 25 as factors?

The area of trapezoid $ABCD$ is 164 $cm^2$ . The altitude is 8 cm, $AB$ is 10 cm, and $CD$ is 17 cm. What is $BC$, in centimeters?

In the figure, the area of square $WXYZ$ is 25 $cm^2$ . The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In $\triangle{ABC}$, $AB$ = $AC$, and when $\triangle{ABC}$ is folded over side $\overline{BC}$, point $A$ coincides with $O$, the center of square $WXYZ$. What is the area of $\triangle{ABC}$, in square centimeters?

The following figures are composed of squares and circles. Which figure has a shaded region with largest area?

Ali, Bonnie, Carlo and Dianna are going to drive together to a nearby theme park. The car they are using has four seats: one driver’s seat, one front passenger seat and two back seats. Bonnie and Carlo are the only two who can drive the car. How many possible seating arrangements are there?

A ship travels from point A to point B along a semicircular path, centered at Island X. Then it travels along a straight path from B to C. Which of these graphs best shows the ship’s A distance from Island X as it moves along its course?

What is the measure of the acute angle formed by the hands of a clock at 4:20 a.m.?

Each of the twenty dots on the graph below represents one of Sarah’s classmates. Classmates who are friends are connected with a line segment. For her birthday party, Sarah is inviting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not be invited to Sarah’s party?