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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?
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?
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

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


A and B are sorting out 160 books. It takes A 20 minutes to sort out a book, while it takes B 12 minutes to sort out a book. After negotiation, A and B decides to sort out all the books together. They start at the same time and finish the task also at the same time.

Quantity A

The number of books that A would sort out when they finished

Quantity B

60


If each interior angle of a regular polygon lies between 100° and 130°, inclusive,then the polygon could be?
Indicate all such integers.

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 line 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 at least one of 6 and 7?
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. How many ways can these DVDs be arranged?
What is the probability that a number comprised of at least one 6 on all digits is selected when selecting a number from 1 to 1,000 (inclusive)?
Give your answer as a fraction.
Let a be the greatest integer such that $$5^{a}$$ is a factor of 1,500, and let b be the greatest integer such that $$3^{b}$$ is a factor of 33,333,333. Which of the following statements are true?

Indicate all such statements.
How many positive factors does 1,575 have?
At most how many integers less than 25 could be the sum of the positive multiple of 4 and the positive multiple of 5?
How many integers from 1 to 603, inclusive, are multiples of 2 or 3?

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