Data Sufficiency

Is (3x + 8)/(x + 2) an integer? (1) x is an integer (2) an integer? (1) x is an integer (2) x = 0

If x is an integer, what is the value of x? (1) –2(x + 5) < -1 (2) – 3x > 9

What is the value of k^2 - k? (1) The value of k - 1/k is 1. (2) The value of 2k –1 is 5 √ 5

If the Lincoln Library's total expenditure for books, periodicals, and newspapers last year was $44,000, how much of the expenditure was for books? (1) The expenditure for books was 20 percent greater than the total expenditure for periodicals and newspapers. (2) The total of the expenditure for books and newspapers was twice the expenditure for periodicals.

If x and y are positive integers and x y = x (2y–3) 𝑥 𝑦 = 𝑥 ( 2 𝑦 – 3 ) , what is the value of x y 𝑥 𝑦 ? (1) x=2 𝑥 = 2 (2) x 3 =8 𝑥 3 = 8

If R = 8x/3y and y ≠ 0, what is the value of R? (1) x = 2/3 (2) x = 2y

If xyz ≠ 0, what is the value of x y 2 𝑥 𝑦 2 ? (1) x= 3 4 y 𝑥 = 3 4 𝑦 (2) z= 2 3 x 𝑧 = 2 3 𝑥

What is the tens digit of positive integer x ? (1) x divided by 100 has a remainder of 30. (2) x divided by 110 has a remainder of 30.

If x, y, and z are numbers, is z = 18 ? (1) The average (arithmetic mean) of x, y, and z is 6. (2) x = -y

How much is 20 percent of a certain number a ? (1) 20 is 20 percent of the number a. (2) 80 percent of the number a is 80.

Last summer, as with every summer, Oshin and Reena made exactly one long trip together to a town neither of them had visited before. For their long summer trips, Oshin and Reena have always chosen to visit a town that Reena would have liked to visit—unless Oshin had been to that town before. Reena had visited Town F and Town G before—and Oshin had never visited Town J or Town K. Did Oshin and Reena visit one of these four towns last summer? (1) Reena had never visited Town J and Oshin had never visited Town F. (2) Oshin would have liked to visit either Town G or Town K.

How many people did Apex Company employ in 1990? (1) The company employed 538 more people in 1991 than in 1990. (2) The company employed 20 percent more people in 1991 than in 1990.

The table above gives the number of calories and grams of protein per kilogram of foods S and T. If a total of 7 kilograms of S and T are combined to make a certain food mixture, how many kilograms of food S are in the mixture? (1) The mixture has a total of 12,000 calories. (2) The mixture has a total of 810 grams of protein. Show Spoiler

In the figure above, what is the product of the lengths of AD and BC? (1) The product of the lengths of AC and BE is 60. (2) The length of BC is 8. Show Spoiler

The symbol ▽ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3 ▽ 2? (1) 0▽1 = 1 (2) 1▽0 = 1

If k and n are integers, is n divisible by 7 ? (1) n - 3= 2k (2) 2k - 4 is divisible by 7.

Is the positive integer n a multiple of 24? (1) n is a multiple of 4. (2) n is a multiple of 6.

Jane is in a certain ticket line in which each of the other people in the line is either behind her or ahead of her. In the line, the number of people ahead of Jane is 5 more than the number of people behind her. What is the total number of people in the line? (1) There are 11 people ahead of Jane in the line. (2) The total number of people in the line is 3 times the number of people behind Jane.

If x and y are positive, is the ratio of x to y greater than 3 ? (1) x is 2 more than 3 times y. (2) The ratio of 2x to 3y is greater than 2

The circular base of an above-ground swimming pool lies in a level yard and just touches two straight sides of a fence at points A and B, as shown in the figure above. Point C is on the ground where the two sides of the fence meet. How far from the center of the pool's base is point A? (1) The base has area 250 square feet. (2) The center of the base is 20 feet from point C. Show Spoiler