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In an equilateral triangle ABC,three points P,Q and R are on the side AB,AC and BC, respectively.

Quantity A

The sum of any two interior angles in Δ ABC

Quantity B

The sum of any two interior angles in Δ PQR




Quantity A

a

Quantity B

b




Quantity A

x

Quantity B

90




△ABC is an isosceles triangle, BA=BC, DE is parallel to AC. If the perimeter of both triangle BDE and quadrilateral ADEC equals to 18 (the length of all the sides are integers), then what is the length of DE?
n is the number of three-digit positive integers in which at least two of the digits are equal to 1.

Quantity A

n

Quantity B

29




How many integers between 100 and 1,000 are multiples of 7?
How many of the multiples of 3 between 100 and 200 are odd integers?
In the xy-plane, the point (t, t-1) lies on the line with equation y = $$ - \frac{1}{2}$$ x +$$\frac{1}{3}$$ . What is the value of t?

Give your answer as a fraction.
If $$n$$, $$k$$, and $$r$$ are positive integers such that $$n^{k}=10r+3$$, which of the following could be the value of $$n$$?
Of the paperbacks in a private library, 5 percent are biographies. If 3 percent of all the books in the library are paperbacks that are biographies, what percecnt of all the books in the library are paperbacks?
List A contains a certain number of consecutive integers including 2. The sum of all the integers in List A is 11.

Quantity A

The number of integers in List A

Quantity B

10


What is the units digit of ($$4^{32}$$ - $$3^{32}$$)?
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?
Suppose there are 20 monkeys and they all have some number of chestnuts. If in average they have 88 chestnuts per monkey and only one of them has less than 60. If every monkey has an integer number of chestnuts and they all have different number of nuts. Then how many chestnuts does the monkey who has tenth most chestnuts have at least if given none of them has more than 100 chestnuts?
For which of the following can it be concluded that (0, 1)?
N=xyzwt-(x+y+z+w+t)

If N is an even integer and x, y, z, w,and t are integers, which of the following CANNOT be the number of the five integers x, y, z, w, and t that are even?
What is the remainder when $$8^{43}$$ is divided by 7?

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