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What is the volume of the cube above?

(1) The surface area of the cube is 1014 square centimeters.

(2) The length of diagonal $\overline{VW}$ is $13\sqrt{3}$ centimeters.

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If 50 percent of people surveyed have at least one brother, what percent have at least one sister?

(1) 40 percent of people surveyed who have at least one brother also have at least one sister.

(2) 15 percent of people surveyed have no brother or sister.

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If the set $T$ 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 $T$ , but 18 is not in $T$ .

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A building has $48$ 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 $\frac{1}{2}$ that the apartment has two bedrooms and a balcony?

(1) Of the apartments, $40$ have two bedrooms.

(2) Of the apartments, $30$ have a balcony.

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A couple decides to have four children. If they succeed in having four children and each child is equally likely to be a boy or a girl, what is the probability that they will have at least two girls?

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On a certain day, a movie theater is playing all 3 parts of a trilogy. Part 1 plays every hour, beginning at 10:00 a.m., and lasts $2\frac{1}{4}$ hours. Part 2 plays every $1\frac{1}{2}$ hours, beginning at 10:00 a.m., and lasts 2 hours. Part 3 plays every $1\frac{1}{2}$ hours beginning at 12:15 p.m. What is the least total amount of time a person planning to watch all 3 parts of the trilogy in order must spend waiting between movies if all movies keep to their schedules?

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A passenger is planning a trip that involves three connecting trains that leave from Stations A, B, and C, respectively. The first train leaves Station A every hour, beginning at 6:30 a.m., and arrives at Station B $1\frac{1}{2}$ hours later. The second train leaves Station B every hour, beginning at 7:30 a.m., and arrives at Station C $2\frac{3}{4}$ hours later. The third train leaves Station C every 30 minutes, beginning at 9:00 a.m. What is the least total amount of time the passenger must spend waiting between trains if all trains keep to their schedules?

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At a seminar, Workshops A, B, and C take place throughout the day. Workshop A takes place every hour, beginning at 8:00 a.m., and lasts $\frac{3}{4}$ hour. Workshop B takes place every $\frac{1}{2}$ hour, beginning at 8:30 a.m., and lasts 1 hour. Workshop C takes place every hour, beginning at 8:45 a.m., and lasts $1\frac{1}{2}$ hours. What is the least total amount of time a person planning to attend all 3 workshops, in order, must spend waiting between workshops if all workshops keep to their schedules?

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If $a$ , $b$ , and $c$ are positive integers such that $a$ is a factor of $b$ , and $a$ is a multiple of $c$ , which of the following is NOT necessarily an integer?

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If $a, b$ and $c$ are positive integers such that $a$ is a multiple of $b$ , and $b$ is a factor of $c$ , which of the following is NOT necessarily an integer?

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If $p, q,$ $r$ are positive integers such that $p$ is a divisor of $q$ , and $r$ is a multiple of $p$ , which of the following is NOT necessarily an integer?

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If $n$ is a positive integer and $n^2$ is divisible by 98, then the largest positive integer that must divide $n$ is

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Kassi works $h$ hours a day for $d$ days and earns $x$ dollars per hour. If she puts $p$ percent of her earnings into savings, which of the following represents Kassi's earnings after savings?

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The function $h$ is defined for each positive three-digit integer $n$ by $h(n) = 2^{a}5^{b}7^{c}$ where $a, b$ and $c$ are the hundreds, tens, and units digits of $n$ respectively. If $p$ and $q$ are three-digit positive integers such that $h(p) = 25 \cdot h(q)$ , then what is the value of $p-q$ ?

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If $10 > \frac{3-x}{2}$ , which of the following must be true?

I. $17 < x$

II. $-(x+17)$ is negative.

III. $| x+5 | > 12$

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A bookstore that sells print books and ebooks reported that revenue from print book sales in 2016 was up 8 percent from 2015 and revenue from ebook sales in 2016 was down 7 percent from 2015. If total revenues from print book sales and ebook sales in 2016 were up 2 percent from 2015, what is the ratio of revenues from print book sales to ebook sales in 2015?

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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.

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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.

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If arc $XYZ$ above is a semicircle, what is the length of diameter $\overline{XZ}$ ?

(1) $XY=12$

(2) $YZ=5$

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Cruise Cancellation Fees
Days Prior to Departure	Percent of Package Price
61 or more	10%
46 − 60	25%
31 − 45	40%
6 − 30	60%
5 or fewer	100%

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.