Data Sufficiency

The figure above shows the present position on a radar screen of a sweeping beam that is rotating at a constant rate in a clockwise direction. In which of the four quadrants will the beam lie 30 seconds from now ? (1) In each 30-second period, the beam sweeps through 3690° (2) r = 40 Show Spoiler

A certain mixture of paint requires blue, yellow, and red paints in ratios of 2:3:1, respectively, and no other ingredients. If there are ample quantities of the blue and red paints available, is there enough of the yellow paint to make the desired amount of the mixture? (1) Exactly 20 quarts of the mixture are needed. (2) Exactly 10 quarts of the yellow paint are available.

What is the average (arithmetic mean) of 3x and 6y? (1) x + 2y = 7 (2) x + y = 5

A certain company paid bonuses of $125toeachofitsexecutiveemployeesand$75 to each of its nonexecutive employees. If 100 of the employees were nonexecutives, how many were executives? (1) The company has a total of 120 employees. (2) The total amount that the company paid in bonuses to its employees was $10.000.

If x is a positive number, is x greater than 1? (1) 1> 1 x 1 > 1 𝑥 (2) − 1 x >−1 − 1 𝑥 > − 1

If a certain animated cartoon consists of a total of 17,280 frames on film, how many minutes will it take to run the cartoon? (1) The cartoon runs without interruption at the rate of 24 frames per second. (2) It takes 6 times as long to run the cartoon as it takes to rewind the film, and it takes a total of 14 minutes to do both.

If n is a positive integer, is n odd? (1) 3n is odd. (2) n + 3 is even.

The table above shows the distance, in kilometers, by the most direct route, between any two of the four cities, R, S, T, and U. For example, the distance between City R and City U is 62 kilometers. What is the value of x ? (1) By the most direct route, the distance between S and T is twice the distance between S and R. (2) By the most direct route, the distance between T and U is 1.5 times the distance between R and T. Show Spoiler

Are integers r and s consecutive ? (1) r is odd and s is even. (2) r - s = 1

What is the value of xy - yz? (1) y = 2 (2) x - z = 5

Committee X and Committee Y , which have no common members, will combine to form Committee Z . Does Committee X have more members than Committee Y ? (1) The average (arithmetic mean) age of the members of Committee X is 25.7 years and the average age of the members of Committee Y is 29.3 years. (2) The average (arithmetic mean) age of the members of Committee Z will be 26.6 years.

The number of seats in the first row of an auditorium is 18 and the number of seats in each row thereafter is 2 more than in the previous row. What is the total number of seats in the rows of the auditorium? (1) The number of rows of seats in the auditorium is 27. (2) The number of seats in the last row is 70.­ Show Spoiler

Is Sarah’s mathematics test score higher than the class average? (1) Sarah scored 90% on her mathematics test, answering 45 out of 50 questions correctly. (2) Sarah’s high percentage score indicates that she performed exceptionally well, with only a few questions answered incorrectly.

What is the capacity, in liters, of a certain aquarium? (1) Three liters is 1 2 1 2 of the capacity of the aquarium. (2) One-half liter is 1 12 1 12 of the capacity of the aquarium.

What fraction of his salary did Mr. Johnson put into savings last week? (1) Last week Mr Johnson put $17 into savings (2) Last week Mr Johnson put 5% of his salary into savings

The figure above shows four pieces of tile that have been glued together to form a square tile ABCD. Is PR=QS? (1) BQ = CR = DS = AP (2) The perimeter of ABCD is 16. Show Spoiler

What was the average number of miles per gallon of gasoline for a car during a certain trip? (1) The total cost of the gasoline used by the car for the 180 mile trip was $12.00 (2) The cost of the gasoline used by the car for the trip was $1.20 per gallon

Does 2m - 3n = 0 (1) m ≠ 0 (2) 6m = 9n Show Spoiler (1) m ≠ 0 (2) 6m = 9n Show Spoiler

Buckets X and Y contained only water and bucket Y was 1/2 full. If all of the water in bucket X was then poured into bucket Y, what fraction of the capacity of Y was then filled with water? (1) Before the water from X was poured, X was 1/3 full (2) X and Y have the same capacity.

There are exactly 6 teams in league x. What was the total number of games played by the 6 teams last season? (1) Each team in league x played each of the other teams at least once. (2) No team in league x played more than 7 games.