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If a four-digit number is to be formed from the digits 1, 2, 3, and 4 by selecting each digit at random and using each digit only once, what is the probability that the number formed will be greater than 3,000?
n is an integer and $$(n-5)^{9-n}=1$$.

Quantity A

n

Quantity B

4


In the xy-plane, which of the following best represents the graph of $$y=(x-1)^2-8$$?

$$1 \lt x+y$$

Quantity A

$$x^2+y^2$$

Quantity B

$$1$$


Which of the following is closest to the fraction of the families with students in four-year public colleges who do not use income or savings as the main source to pay for college expenses?
Approximately how many of the families with students in four-year colleges use grants or scholarships as the main source to pay for college expenses?
S is the average (arithmetic mean) of n consecutive integers, beginning with the integer m. T is the average (arithmetic mean) of n consecutive integers beginning with the integer m+1.

Quantity A

S+1

Quantity B

T


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

$$m$$


The recorded heights, in inches, of 9 people are 58, 62, 62, 62, 63, 70, 71, 74, and 75. Which of the following lists the mean, the median, and the mode of the recorded heights in order, from least to greatest?
The average (arithmetic mean) of the six numbers $$y_1, y_2, y_3, y_4, y_5$$, and $$y_6$$ is $$k$$. The average of the six numbers $$y_1+k, y_2+k, y_3+k, y_4+k, y_5+k$$, and $$y_6+k$$ is $$m$$.

Quantity A

k

Quantity B

m


p is a positive prime number and a divisor of 40.

Quantity A

p

Quantity B

4


n > 4

Quantity A

The sum of the first n positive prime numbers

Quantity B

The sum of the first n positive integers


A certain list consists of 25 different positive integers, where each of the integers is a multiple of the positive integer m, The greatest integer in the list is 250.

Quantity A

m

Quantity B

5


$$n$$ is a positive integer.

Quantity A

The remainder when $$3^{4n+2}+5$$ is divided by 10

Quantity B

4


$$S$$ is the sum of 50 different numbers of the form $$1+\frac{1}{n}$$, where $$n$$ takes on positive integer values.

Quantity A

$$S$$

Quantity B

51


Quantity A

$$3^{120}$$

Quantity B

$$6^{60}$$


The average (arithmetic mean) of 5 consecutive even integers is 20.

Quantity A

The least of the 5 integers

Quantity B

16


A sequence of numbers $$p_1, p_2, p_3, .........., p_n,.........$$. is generated by the rules $$p_1=1$$ and $$p_n= 24p_{n-1}+8$$ for each integer $$n ≥ 2$$.

Quantity A

The remainder when $$p_{66}$$ is divided by 6

Quantity B

4


Each person who attended a seminar on politics was either a Democrat, a Republican, or an independent. If a person had been selected randomly from those attending the seminar, the probability would have been 0.52 of selecting a Republican and 0.35 of selecting a Democrat. What was the ratio of the number of independents to the number of Republicans at the seminar?
The common archaeological emphasis on changes in the shape of prehistoric stone implements should not _____________ the fact that other materials, such as wood, bone, and antler, were also used for tools throughout the Paleolithic era.

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