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Quantity A

The remainder when $$35^{12}+63^{17}$$ is divided by 14

Quantity B

3
What is the remainder when $$8^{43}$$ is divided by $$7$$?
If wooden logs are stacked in layers so that the bottom layer has n logs, the top layer has 1 log, and each layer except for the bottom layer has 1 log less than the layer immediately below it, then the total number of logs in the stack is equal to $$\frac{n(n+1)}{2}$$. If 62 logs are to be stacked in this manner, perhaps with some logs left over, what is the least number of logs that could be left over?
List $$S$$ consists of $$n$$ different positive values, where $$n$$ is greater than 1. List T consists of the squares of the $$n$$ values in $$S$$.

Quantity A

The square of the range of the values in $$S$$

Quantity B

The range of the values in $$T$$


A data set consists of 200 values, all of which are integers. The data set is summarized by the boxplot shown. Based on the boxplot, which of the following statements must be true?
Sets R, S, and T are nonempty, and each has the same number of elements. The sets R∩S, R∩T, and S∩T are nonempty, and each has the same number of elements. The set R∩S∩T is empty. Set V consists of all the elements in R that are not in S.

Quantity A

3 times the number of elements in V

Quantity B

The number of elements in the set R∪S∪T


In the survey of employees shown, none cited all three reasons for leaving, but 15 percent cited two of the three reasons. What percent of the employees surveyed cited none of the three reasons in the table?


Quantity A

The number of doctors surveyed who said that drug Q was effective and did not say that drug R was effective

Quantity B

210


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

Quantity A

The measure of angle $$x$$

Quantity B

56


In quadrilateral ABCD, AB=BC=BD and the measure of angle ABC is 60 degrees What is the measure of angle ADC?


The original two sides and hypotenuse of a triangle are x, y, and z, respectively.

Quantity A

The hypotenuse of the triangle after x and y are turned into x+1 and y+1

Quantity B

z+1


BC=DC

Quantity A

x

Quantity B

y


The relative frequency distributions of the values in data set A and the values in data set B are shown in the two histograms, respectively, where each interval contains values that are greater than or equal to the left endpoint and less than the right endpoint. The number of values in A is $$\frac{1}{2}$$ of the number of values in B. If data set C consists of the values in A and the values in B, which of the following histograms shows the relative frequency distribution of the values in C?
Of the 58 people who were accepted into a clinical trial to test the effectiveness of a new drug,17 people were over the age of 65 years. From the 58 people accepted, 10 will be selected to begin the first phase of the trial. Which of the following represents the number of combinations of the 10 people to be selected such that 3 of them are over the age of 65 years?


The figure shows a museum display illustrating the movement of a satellite around the Earth.The two circles shown are concentric, where the inner circle of radius 1 meter represents the Earth's equator and the outer circle of radius 2 meters represents the orbit of the satellite. The part of the equator in the range of the satellite is represented by the shorter arc AB. The satellite makes 6 revolutions around the equator per day. During one day,what is the total amount of time, in hours, that each point on the equator is in the range of the satellite?


From December 31, 1986, to December 31, 1995, approximately what was the average (arithmetic mean) annual increase, in square feet per year, of the total shopping area?
a, b, c, d, e, f, g, h, i, j

Let S be the set of all 10-letter sequences consisting of the 10 letters above.

Let T be the set of all 8-letter sequences consisting of the first 8 letters above.

Quantity A

The number of sequences in S in which f, b, h, and g appear consecutively in that order

Quantity B

The number of sequences in T in which f and b appear consecutively in that order
a, b, c, and d are numbers that are greater than 0 and less than 1.

Quantity A

(a+b)(c+d)

Quantity B

a+b(c+d)
A large number of people received a letter inviting them to subscribe to a certain magazine. Of the people who received the letter, 40 percent were already subscribers, and 60 percent of this group renewed their subscription.Of the people who received the letter and were not already subscribers, 25 percent subscribed.

Quantity A

The percent of people who received the letter and either subscribed or renewed their subscription

Quantity B

The percent of people who received the letter and neither subscribed nor renewed their subscription

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