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If n = 2*3*5*7*11*13*17, then which of the following statements must be true?

I. $$n^{2}$$ is divisible by 600

II. n + 19 is divisible by 19

III. $$\frac{n+4}{2}$$is even
If n is a positive odd integer and $$k=n^{3}+2n$$, what is the value of $$ (-1)^{k}-(-1)^{k+1}$$?
A jar contains exactly 10 dimes and x quarters and no other coins. If a coin is randomly selected from the jar, the probability that a quarter is selected is 0.6. What is the value of x.
In a plane, points P and Q are 20 inches apart. If point R is randomly chosen from all the points in the plane that are 20 inches from P, what is the probability that R is closer to P than it is to Q ?
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?

Quantity A

$$(-87)^{8}$$

Quantity B

$$(\frac{1}{87})^{-8}$$


If an integer greater than 100 and less than 1,000 is to be selected at random, what is the probability that the integer selected will be a multiple of 7?


In rectangle ABCD, side DC is divided into five equal segments by points P,Q,R and S.

Quantity A

The area of ∆MCQ

Quantity B

The area of ∆NSP


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.
Set S = {2, 3, 4, 5, 6, 7, 8}

Quantity A

The total number of positive 4-digit integers that can be formed where each digit is in set T and the 4 digits in each 4-digit integer are different from each other

Quantity B

7·6·5·4


Set I consists of the integers from 11 through 100, inclusive.

Quantity A

4 times the number of integers in set T that are multiples of 4

Quantity B

5times the number of integers in set T that are multiples of 5


When the positive integer x is divided by 42, the remainder is 19. What is the remainder when x is divided by 7?
m and n are integers.

Quantity A

$$\sqrt{( 10^{2m} )}\sqrt{( 10^{2n} )}$$

Quantity B

$$10^{mn}$$


If x is a positive integer such that the units digit of $$x^{3}$$ is 3, what is the units digit of $$x^{15}$$?
$$\frac{60!-59!}{58!}=$$
n is an integer.

Quantity A

$$(-1)^{n}(-1)^{n+2}$$

Quantity B

1


The functions f and g are defined by f (x) = |2x +1| and g(x)=3 for all numbers x. What is the least value of c for which f (c) = g (c)?
Which of the following statements about the managers surveyed must be true?
The number of managers surveyed who identified work experience as an important characteristic to consider was approximately what percent greater than the number who identified appropriate attire and behavior as an important characteristic to consider?

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