Data Sufficiency

Is 1 < x < 2? (1) 0 < x (2) x < 3

If a total of 84 students are enrolled in two sections of a calculus course, how many of the 84 students are female? (1) 2/3 of the students in Section 1 are female. (2) 1/2 of the students in Section 2 are male.

What is the remainder when the positive integer n is divided by 6? (1) n is multiple of 5 (2) n is a multiple of 12

In planning for a car trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hours of the actual time that the trip took? (1) Joan’s estimate for the distance was within 5 miles of the actual distance. (2) Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed.

Is n an integer? (1) 2n is an integer. (2) n 2 𝑛 2 is an integer

What is the average distance that automobile D travels on one full tank of gasoline? (1) Automobile D averages 8.5 kilometers per liter of gasoline. (2) The gasoline tank of automobile D holds exactly 40 liters of gasoline.

Did United States carriers use more than 10 billion gallons of jet fuel during 1983? (1) United States carriers paid a total of $9.4 billion for the jet fuel used in 1983. (2) United States carriers paid an average (arithmetic mean) of $0.90 per gallon for the jet fuel used in 1983.

John and David each received a salary increase. Which one received the greater salary increase? (1) John’s salary increased 8 percent. (2) David’s salary increased 5 percent.

If Jack’s and Kate’s annual salaries in 1985 were each 10 percent higher than their respective annual salaries in 1984, what was Jack’s annual salary in 1984 ? (1) The sum of Jack’s and Kate’s annual salaries in 1984 was $50,000. (2) The sum of Jack’s and Kate’s annual salaries in 1985 was $55,000.

Is x < y? (1) z < y (2) z < x

If x and y are integers, is x + y divisible by 6 ? (1) x is divisible by 6. (2) y is divisible by 6.

Water is pumped into a partially filled tank at a constant rate through an inlet pipe. At the same time, water is pumped out of the tank at a constant rate through an outlet pipe. At what rate, in gallons per minute, is the amount of water in the tank increasing? (1) The amount of water initially in the tank is 200 gallons. (2) Water is pumped into the tank at a rate of 10 gallons per minute and out of the tank at a rate of 10 gallons every 2 1 2 2 1 2 minutes.

What is the value of the greater of two numbers if one of the numbers is twice the other number? (1) One number is 5. (2) The sum of the two numbers is 15.

Three friends rented a car for a week and divided the cost equally. What was the total cost of renting the car ? (1) If the three friends had kept the car for a second week, they could have obtained the two-week rate, which was 1.5 times the cost of a one-week rental. (2) If a fourth friend had joined the three friends and the cost had been divided equally among the four friends, the cost to each of the original three would have been reduced by $15 ?

A telephone station has x processors, each of which can process a maximum of y calls at any particular time, where x and y are positive integers. If 500 calls are sent to the station at a particular time, can the station process all of the calls? (1) x = 600 (2) 100 < y < 200

Carlotta can drive from her home to her office by one of two possible routes. If she must also return by one of these routes, what is the distance of the shorter route? (1) When she drives from her home to her office by the shorter route and returns by the longer route, she drives a total of 42 kilometers. (2) When she drives both ways, from her home to her office and back, by the longer route, she drives a total of 46 kilometers.

What is the value of x ? (1) x +1 = 2 - 3x (2) 1/(2x) = 2

If a certain city is losing 12 percent of its daily water supply each day because of water-main breaks, what is the dollar cost to the city per day for this loss? (1) The city’s daily water supply is 350 million gallons. (2) The cost to the city for each 12,000 gallons of water lost is $2.

In the figure above, what is the length of segment BC ? (1) x = 90 (2) The perimeter of △ABC is 24. Show Spoiler

If P, Q, and R are three distinct points, do line segments PQ and PR have the same length ? (1) P is the midpoint of line segment QR. (2) Q and R lie on the same circle with center P.