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If y and z are integers, what is the value of $y+z$?

1. $y+z<8$ and $y+z>6$.
2. $\mathrm{<font\; color="\#FE8080">1</font>}<\frac{y}{2}<\frac{z}{2}<2.5$

What is the surface area of a certain rectangular solid?

1. Two adjacent faces of the solid have areas 30 and 45, respectively.
2. The volume of the solid is 270.

In the xy-plane, region R consists of all the points (x,y) such that $5x+6y\le 30$. Is the point (r,s) in region R?

1. $6r+5s=30$
2. $r\le 6$ and $s\le 5$.

If k is a positive integer, is ${\left(\frac{\mathrm{<font\; color="\#FE8080">1</font>}}{2}\right)}^k>0.125$?

1. $k>3$
2. ${\left(\frac{\mathrm{<font\; color="\#FE8080">1</font>}}{2}\right)}^{k-\mathrm{<font\; color="\#FE8080">1</font>}}<0.25$

If $\overrightarrow{z}$ denotes the greatest integer less than or equal to z, is $\overrightarrow{z}=\mathrm{<font\; color="\#FE8080">1</font>}$?

1. $8z-\mathrm{<font\; color="\#FE8080">1</font>}=-13+5z$
2. $\mathrm{<font\; color="\#FE8080">1</font>}<z<2$

In quadrilateral ABCD above, CD is parallel to and is longer than AB. What is the area of ABCD?

1. $EC=75$ meters
2. $BC=30\sqrt{10}$meters

What were the total wages of a person who worked last week for 40 hours, some of which were compensated at a normal hourly rate and the remainder of which were compensated at an overtime rate?

1. The number of hours worked at the normal rate was $\frac{3}{4}$ of the total number of hours the employee worked.
2. The overtime rate was $25 per hour.

In a game, blue chips are worth a certain amount of points each, and red chips are worth a certain amount of points each. What is the total point value of 5 red chips and 3 blue chips in the game?

1. The point value of 15 red chips and 9 blue chips is 732.
2. The point value of a red chip is 12 less than the point value of a blue chip.

What is the value of $x$?

1. $x=5$
2. $x=5 \text{or }x=6.$

If the sequence S has 100 terms, what is the 7th term of S?

1. The 93rd term of S is -100, and each term of S after the first is 7 less than the preceding term.
2. The first term of S is 544.

The value of an investment increased according to a variable annual rate such that its value in 2006 was 1.43 times its value in 1998. What was the value of the investment in 1998?

1. The value was $373.80 more in 2006 than in 1998.
2. The value of the investment was $1243.11 in 2006.

If a certain computer program scans a total of 5,760 files when it runs, how many minutes will it take to complete the scan?

1. The program scans 8 files per second.
2. It takes 3 times as long to run the scan as it takes to upload the output to a server, and it takes a total of 16 minutes to do both.

If $r_{\mathrm{<font\; color="\#FE8080">1</font>}}$ and $r_2$ are the roots of the equation $t^2+bt+c=0$, where b and c are constants, are both $r_{\mathrm{<font\; color="\#FE8080">1</font>}}$ and $r_2$ positive?

1. $b<0$
2. $c<0$

Can a circular manhole cover fit exactly into the circular recessed area of the street?

1. The recessed area of street measures 24 inches from one side to the other through its center point.
2. The area of the surface of the manhole cover is $144\pi$ inches squared.

In 2009, Marcos placed a total of $26,000 in 23 different investments. In 2010, he placed additional funds  into two new investments. For all 25 investments, is the average (arithmetic mean) amount of money per investment less than $1,200?

1. Each investment added in 2010 contained more than $1,000.
2. Each investment added in 2010 contained less than $1,500.

The cost of production of a certain item increases, though not proportionally, with the number of units produced. Is the cost of production of 4,800 units less than $40,000?

1. The cost of producing 4,600 units is more than $30,000.
2. The cost of producing 4,700 units is more than $50,000.

What is the area of the circle above with center O?

1. The area of $\Delta OAB$ is 50.
2. The length of arc ACB is $15\pi$.

What is the final digit of positive integer n?

1. n divided by 10 has a remainder of 1.
2. n divided by 11 has a remainder of 1.

The player of a certain game drew a number of cards from a deck in which each card was labeled with an integer from 1 to 10. Four more even than odd numbers were drawn. How many times were even numbers drawn?

1. The player drew 12 cards.
2. The player received 4 points for each even number and 2 points for each odd number drawn, for a total of 40 points.