Data Sufficiency

In each of the last five years, Company K donated p percent of its annual profits to a certain scholarship fund. Did Company K donate more than $10,000 to the scholarship fund last year? (1) Two years ago, Company K had annual profits of $3millionanddonated$15,000 to the scholarship fund (2) Last year, Company K had annual profits of $2.5 million

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? (1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. (2) The sum of the 3 numbers is equal to 3 times one of the numbers.

In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ? (1) The x-coordinate of point R is -1. (2) Point R lies on the line y = -3.

Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than π 100 π 100 square feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains ? (1) Jack's rug covers an area of 9π square feet. (2) The centers of the stains are less than 4 feet apart.

If a and b are positive integers, is a/b < 9/11 ? (1) a/b < 0.818 (2) b/a > 1.223

If q, s, and t are all different numbers, is q < s < t ? (1) t - q = |t - s| + |s - q| (2) t > q

If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? (1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z.

If x and y are positive integers, what is the value of x √ + y √ x + y ? (1) x + y = 15 (2) x y − − √ = 6 x y = 6

A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. If L 1 L 1 is the list consisting of the first n 1 n 1 numbers in L and L 2 L 2 is the list consisting of the last n 2 n 2 numbers in L, is 17 a mode for L ? (1) 17 is a mode for L 1 L 1 and 17 is a mode for L 2 L 2 . (2) n 1 + n 2 = n n 1 + n 2 = n

If y ≠2xz, what is the value of (2xz + yz)/(2xz – y)? (1) 2x + y = 3 (2) z = 2

If a and b are constants, is the expression x + b x + a − − − − √ x + b x + a defined for x = –2 ? (1) a = 5 (2) b = 6

Is the sum of two integers divisible by 10 ? (1) One of the integers is even. (2) One of the integers is a multiple of 5.

For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min (5, 2) = 2 and max(5, 2) = 5. For the integer w, what is the value of min(10, w) ? (1) w = max(20, z) for some integer z. (2) —

A, B, C, and D are points on a line. If C is the midpoint of line segment AB and if D is the midpoint of line segment CB, is the length of line segment DB greater than 5? (1) The length of line segment AC is greater than 8 (2) The length of line segment CD is greater than 6

The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth? (1) There are a total of 32 people in the line. (2) 23 people in the line are behind Adam.

What is the circumference of circle C ? (1) The radius of circle C is 2π. (2) The center of circle C is located at point (7,8) in the xy-plane.

In the xy-coordinate plane, what are the x-coordinates of the four vertices of square JKMN ? (1) J and M are on the x-axis, and K and N are on the y-axis. (2) The center of the square is at the origin.

If x is a positive integer, what is the value of x + 24 − − − − − √ − x √ x + 24 − x ? (1) x √ x is an integer (2) x + 24 − − − − − √ x + 24 is an integer

What is the value of x if x^3 < x^2? (1) –2< x < 2 (2) x is an integer greater than –2.

If u > 0 and v > 0, which is greater, u v u v or v u v u ? (1) u = 1 (2) v > 2