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In the figure, the square ENFM is inscribed in the rectangle ABCD, E and F are the midpoints of side AB and DC. If the area of ENFM is 64, G and H are the midpoints of AD and BC, and GM=NH=5, then what is the area of ABCD?


The figure above shows five congruent circles each with radius 2 such that each of the five circles is tangent to two other congruent circles and to a smaller inner circle. The perimeter of the figure is composed of 5 line segments of length x and 5 circular arcs of length y. What is the perimeter of the figure?


If 20 red cubes and 7 white cubes, all of equal size, are fitted together to form one large cube, as shown above, what is the greatest fraction of the surface area of the large cube that could be red?
Three students need to read 50 proposals. Each proposal has to be read by at least one student. Student A read 38 of them, Student B read 36 of them, while Student C read 28 of them. At least how many proposals are read by at least two students?
100 cards are marked with 100 numbers from 0 to 99. If a person draws n cards from them, then what`s the value of n such that the sum of all the numbers marked on these cards is 100?
Indicate all such values.
How many integers between 100 and 299 (inclusive) have a units digit between 3 and 9 (inclusive)?
A students selects books for reading material randomly,and which of the following has exactly 10 different ways of selection?
Indicate all such statements.
Two numbers are to be selected at random and without replacement from the set {1,3,5,7,9,11}. What is the probability that the product of the two selected numbers will be greater than 50?
Give your answer as a fraction.
A restaurant has a total of 16 tables, each of which can seat a maximum of 4 people. If 50 people were sitting at the tables in the restaurant, with no tables empty, what is the greatest possible number of tables that could be occupied by just 1 person?
At a toy sale, each toy was sold for either $2 or $3. If a customer bought toys of $15 at the sale, which of the following could have been the total number of toys that the customer bought?

Indicate all such values.
A set consists of all three-digit positive integers with the following properties. Each integer is of the form JKL, where J, K, and L are digits; all the digits are nonzero; and the two-digit integers JK and KL are each divisible by 9. HOW many integers are in the set?
$$d$$ is the greatest common divisor of 36 and 60, $$m$$ is the least common multiple of 36 and 60.

Quantity A

$$\frac{36}{d}$$

Quantity B

$$\frac{m}{60}$$


Two librarians, Robert and Patricia,cataloged a combined total of 180 new books,each of which was cataloged by only one of the two librarians. Although they spent the same amount of time cataloging their books, Robert spent an average of 15 minutes per book whereas Patricia spent an average of 12 minutes per book.

Quantity A

The number of books cataloged by Robert

Quantity B

60


The degree measure of each angle of a regular polygon with n sides is between 100 and 130. Which of the following could be the value of n?

Indicate all such integers.

The figure shown consists of a rectangle with length 14 and width 6, together with three isosceles right triangles. What is the area of the entire figure?

R and r are two radii of the larger and smaller circle, respectively, if the ratio of R to r is 3. The shaded region is what percentage of the larger circle?
Give your answer as a fraction.


In how many ways can letter a b and c be assigned into a nine palace such that no letter is used more than once in each column and each row?
In how many more ways can you select 4 books out of 8 books than when you select 4 books out of 6 books?
If 600 < n < 770, how many n are out there such that n is formed by either 6, or 7, or both?
40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. In how many ways can these DVDs be arranged?

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