If the set consists of six consecutive positive integers, then what is the sum of these six integers?

(1) The sum of the even integers is 42.

(2) The integer 17 is in , but 18 is not in .

A building has one- and two-bedroom apartments to rent, some with balconies and others without. If one of these apartments is to be selected at random, is the probability greater than that the apartment has two bedrooms and a balcony?

(1) Of the apartments, have two bedrooms.

(2) Of the apartments, have a balcony.

The rectangular picture shown in the figure above has a frame of uniform width. What is the area of the portion of the picture that excludes the frame?

(1) The perimeter of the framed picture is 56 inches.

(2) The width of the frame on all sides is 2 inches.

The rectangular quilt shown in the figure above has a border of uniform width. What is the area of the portion of the quilt that excludes the border?

(1) The width of the border on all sides is 4 inches.

(2) The perimeter of the entire quilt, including the border, is 220 inches. The length of the entire quilt is 20 inches longer than the width of the entire quilt.

If arc above is a semicircle, what is the length of diameter ?

(1)

(2)

The table above shows the cancellation fee schedule that a cruise company uses to determine the fee charged to a tourist who cancels a trip prior to departure. If a tourist canceled a trip with a package price of $3,800 and a departure date of August 5, on what day was the trip canceled?

(1) The cancellation fee was $950.

(2) If the trip had been canceled one day later, the cancellation fee would have been $570 more.

If the average (arithmetic mean) of four numbers is 150, how many of the numbers are equal to 150?

(1) None of the four numbers is less than 150.

(2) None of the four numbers is greater than 150.

If $u<v<w$ and$x<y<z$, is $v<y$?

1. $u<x$
2. $w<x$

A right triangle has two legs of equal length. What is the perimeter, in centimeters, of the triangle?

1. The area of the triangle is 4 square centimeters.
2. The hypotenuse of the triangle measures 4 cm.

In a school, 180 students study finance or accounting or both. If 60 of these students do not study finance, how many of these students study both finance and accounting?

1. Of the 180 students, 36 do not study accounting.
2. A total of 144 students study accounting.

What is the tenths digit in the decimal representation of a certain number?

1. The number is less than $\frac{5}{8}$
2. The number is greater than $\frac{5}{9}$

In the xy-coordinate plane, is point Q equidistant from points (4, 4) and (-2, 4)?

1. The x-coordinate of point Q is 1.
2. Point Q lies on the line $y=4$.

What is the value of x in the triangle above?

1. $y+z=130$
2. $x+z=100$

In a group of 60 integers, how many are divisible (with a remainder of 0) by neither 7 nor 13?

1. Of the 60 numbers, 20 are divisible by 7 but not by 13.
2. Of the 60 numbers, 30 are divisible by both 7 and 13.

If p and q are positive integers, can the fraction $\frac{p}{q}$ be expressed as a decimal with only a finite number of nonzero digits?

1. q is a factor of 12.
2. p is a factor of 12.

An exam was taken by a group of undergraduate students and graduate students. If the average (arithmetic mean) score for the entire group was 90, was the average score of the undergraduates greater than 95?

1. The average score for the graduate students was less than 85.
2. The group consisted of more graduate students than undergraduate students.

During a particular period, water enters a partially filled reservoir at a constant rate through a mountain stream. At the same time, water is pumped out of the reservoir at a constant rate through an outlet pipe. At what rate, in gallons per minute, is the amount of water in the reservoir increasing?

(1) The amount of water initially in the reservoir is 1800 gallons.

(2) Water enters the reservoir at a rate of 8 gallons per minute and is pumped out at a rate of 20 gallons every 3 minutes.

In the figure above, points A, B, C, D, E, and F lie on a line perpendicular to the square's sides. If point A lies on the square, point B lies on the circle, point C bisects AF, point D is the center of the circle, point E bisects DF, and point F lies on the circle and on the square, what is the difference in area between the square and the circle?

1. $AB=6$ and $BC=4$.
2. $AB=6$ and $EF=3.5$.

Pam has unopened packages of corn and of rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have?

(1) Pam has $282 worth of packages of corn and of rice.

(2) Pam has twice as many packages of corn as she has of rice.

l, 17.2, 12.2, 7.2, 22.2 What is the value of l in the list above?

1. $l>7.2$
2. The median of the numbers in the list is 14.7.