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In the figure, the line l and the x-axis are tangent to the circle at points P and S, respectively, and the line segment QS passed through center R of the circle. What is the slope of l?
$$N=xyzwt-(x+y+z+w+t)$$

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?


The interior of the figure shown is divided into two squares and three triangles.

Quantity A

The measure of angle $$x$$

Quantity B

56




The shaded region in the xy-plane represents the surface of a pond. A length of 1 unit in the xy-plane represents 5 meters. The average depth of the water in the pond is 0.8 meter. Of the following, which is the best estimate of the total volume, in cubic meters, of the water in the pond?
$$j$$ and $$k$$ are integers such that $$51 \leq j \lt k \leq 99$$.

Quantity A

The number of combinations of $$100$$ objects taken $$j$$ at a time

Quantity B

The number of combinations of $$100$$ objects taken $$k$$ at a time




In the figure shown, AB is parallel to EC and the length of ED is $$\frac{1}{3}$$ of the length of AD.

Quantity A

The ratio of the area of triangle ECD to the area of quadrilateral ABCE

Quantity B

$$\frac{1}{8}$$


When the positive integer m is divided by 42, the remainder is 13. What is the remainder when m is divided by 6?

Quantity A

$$x$$

Quantity B

$$y$$


In a certain corporation,an employee council will consist of 3 employees who will be selected from 20 eligible employees. If each of the 3 positions on the council has a different role on the council,then there are 6,840 possible 3-employee selections from the 20 eligible employees. How many possible 3-employee selections are there if the 3 positions all have the same role?
A dinner menu offers 8 different entrees and 6 different vegetables. How many different combinations of 1 entrée and 2 different vegetables are possible?
List A consists of 25 positive integers $$a_1$$, $$a_2$$, $$a_3$$,...,$$a_{25}$$ that are ordered from least to greatest. The median and the mode of the integers in A are both equal to 10. List B consists of 25 positive integers $$b_1$$, $$b_2$$, $$b_3$$,...,$$b_{25}$$ that are ordered from least to greatest. The median and the mode of the integers in B are both equal to 15. List C consists of the 25 sums $$a_i$$ +$$b_i$$, for all integers $$i$$ such that 1 ≤ $$i$$ ≤ 25. The mode of the integers in C is $$m$$.

Quantity A

The median of the integers in C

Quantity B

$$m$$




According to the data in the graph, approximately what is the average (arithmetic mean) annual decrease from 1980 to 1995 in the list price of a Brand X microcomputer?
If the average (arithmetic mean) of w, x, and y is 3 more than the average of x, y, and z, then w is how much greater than z?


In the xy-plane, what is the area of the quadrilateral region ABCD?


Square GBDF is inscribed in the isosceles right triangle ACE.

Quantity A

The area of triangular region ABG

Quantity B

$$\frac{1}{4}$$ of the area of triangular region ACE


The integer $$n$$ is the product of four different prime numbers. If $$n$$ divided by 35 is a multiple of 13, which of the following could be equal to $$n$$ divided by 7?
While there is no evidence that Bigfoot is real, several well-known species were once thought to be________; the okapi, for instance, was known as the “African unicorn" until explorers obtained proof of its existence.
The author suggests that according to historical demographers, the birth rate in early-modern German cities
The prizes for a certain contest are in 5 sealed envelopes: 2 containing cash and the other 3 containing gift certificates. If 2 envelopes are to be randomly selected from the 5 envelopes, one at a time without replacement, what is the probability that at least one of the envelopes selected will contain a cash prize?

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