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n and k are integers, n > k > 1

Quantity A

n!-k!

Quantity B

(n-k)!




What is the greatest prime divisor of $$3^{100}$$- $$3^{97}$$?
A family paid 12 percent of its annual after-tax income on food last year. This amount was equal to 10 percent of its annual before-tax income last year. Which of the following is closest to the percent of the family`s annual before-tax income that was paid for taxes last year?
The sequence $$a_{1},a_{2},a_{3}.....a_{n}$$....is defined by $$a_{1}=2$$, $$a_{2}$$=3, and $$a_{n}$$=$$(a_{n-1})(a_{n-2})$$ for all integers n greater than 2. What is the value of $$a_{8}$$?
Sample P: 0.8, 0.9, 0.9, 1.0

Sample Q: 1.0, 1.0, 1.0, 1.0

Sample R: 0.8, 0.8, 1.0, 1.0

Sample S: 0.7, 0.7, 0.9, 0.9

Sample T: 0.9, 1.0, 1.0, 1.1

Five samples of 4 washers each were taken from a production line. The inside diameter of each washer was recorded to the nearest 0.1 centimeter, as shown above. For which of the samples is the standard deviation of the measurements greater than the standard deviation of the measurements for sample P?

Indicate all such samples.
A box contains 6 cards, numbered 1, 2, 3, 4, 5, and 6, respectively. If one of the 6 cards is to be selected at random, what is the probability that the number on the card selected will be greater than 3, or even, or both?
Give your answer as a fraction.
k, m, and p are integers.

If k and m are negative integers, which of the following must be negative integers?

Indicate all such integers.
a is a positive integer.

x is the remainder when 15a is divided by 6

Quantity A

x

Quantity B

2


Quantity A

The remainder when 11,999,999 is divided by 12

Quantity B

11




The units digit of $$7^{34}$$ is x, and the units digit of $$6^{34}$$ is y. What is the value of the product xy?

Quantity A

The tens digit of

($$4^{100}$$)($$5^{99}$$)

Quantity B

The tens digit of

($$4^{100}$$)($$5^{101}$$)






m is an odd number and greater than 1

Quantity A

The greatest prime factor of 2m

Quantity B

The greatest prime factor of $$m^{2}$$




If a, b, and c are positive integers such that $$\frac{a}{c}$$=0.075, and $$\frac{b}{c}$$=0.09, What is the least possible value of c?
If k and n are each positive integers between 12 and 30, then $$\frac{5+k}{7+n}$$will be equal to $$\frac{5}{7}$$for how many pairs of (k, n)?
On May 5, 2004, the closing price of Stock A was $60.00, which was a decrease of 8 percent from the closing price of the stock on the previous day, May 4, 2004. On May 6, 2004, the closing price of the stock was exactly the same as the closing price on May 4, 2004. What was the percent increase in the closing price of the stock from May 5, 2004 to May 6, 2004?

Give your answer to the nearest whole percent.

_____%
y+5 > x

Quantity A

y+2

Quantity B

x-2




Which of the following is the best estimate of $$\frac{(16.8)(10^{3})}{(0.51)(10^{-11})}$$?
3x-2k=7

9x-6k=21

Quantity A

x

Quantity B

k




In plane P, point Q is on line l.

Quantity A

The number of points in plane P whose distance from line l is 2 and whose distance from point Q is 3

Quantity B

4






The three squares share a common vertex, as shown.

Quantity A

a+b

Quantity B

90°




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