Data Sufficiency

Is x y < 0 x y < 0 ? (1) x 2 * y 3 < 0 x 2 * y 3 < 0 (2) x y 2 > 0 x y 2 > 0

Is x > y? (1) 0 < x < 0.75 (2) 0.25 < y < 1.0

Two accountants, Rhodes and Smith, went to a business meeting together. Rhodes drove to the meeting, and Smith drove back from the meeting. If Rhodes and Smith each drove 140 kilometers, what was the average speed, in kilometers per hour, at which Rhodes drove? (1) The average speed at which Smith drove was 70 kilometers per hour. (2) Rhodes drove for exactly 2 hours.

In the figure above, R and Q are points on the x-axis. What is the area of equilateral triangle PQR ? (1) The coordinates of point Pare (6, 2 3 √ 2 3 ) . (2) The coordinates of point Q are (8, 0).

In parallelogram ABCD , what is the measure of ∠ADC? (1) The measure of ∠ABC is greater than 90 (2) The measure of ∠BCD is 70

If x = 2 y x = 2 y , what is the value of x y x y ? (1) x > y x > y (2) 3 x − 2 y = 14 3 x − 2 y = 14

Is n an integer greater than 14? (1) 3 n 3 n is a positive integer. (2) n 3 n 3 is a positive integer.

What is the value of x? (1) 5x - 3 = 7 (2) x/10 = 1/5

How much nitrogen is needed in the mixture used by a lawn maintenance company to fertilize the grass on a certain portion of a golf course? (1) The portion of the golf course to be fertilized is 30 meters by 50 meters. (2) The amount of fertilizer needed is 40 kilograms, and the fertilizer must be composed of nitrogen, phosphorus, and potash in the proportions 5:7:4, respectively.

If x is an integer, is x/2 an even integer (1) x is a multiple of 2 (2) x is a multiple of 4 (1) x is a multiple of 2 (2) x is a multiple of 4

When 200 gallons of oil were removed from a tank, the volume of oil left in the tank was 3 7 3 7 of the tank's capacity. What was the tank’s capacity? (1) Before the 200 gallons were removed, the volume of oil in the tank was 1 2 1 2 of the tank's capacity. (2) After the 200 gallons were removed, the volume of the oil left in the tank was 1,600 gallons less than the tank's capacity.

For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for each additional person. What is the charge for each additional person? (1) The daily cost per person for 4 people sharing the cost of a room equally is $45. (2) The daily cost per person for 2 people sharing the cost of a room equally is $25 more than the corresponding cost for 4 people.

Division R of Company Q has 1,000 employees. What is the average (arithmetic mean) annual salary of the employees at Company Q? (1) The average annual salary of the employees in Division R is $30,000. (2) The average annual salary of the employees at Company Q who are not in Division R is $35,000.

In June 1989, what was the ratio of the number of sales transactions made by Salesperson X to the number of sales transactions made by Salesperson Y ? (1) In June 1989, Salesperson X made 50 percent more sales transactions than Salesperson Y did in May 1989. (2) In June 1989, Salesperson Y made 25 percent more sales transactions than in May 1989.

If k, m, and t are positive integers and k/6 + m/4 = t/12, do t and 12 have a common factor greater than 1? (1) k is a multiple of 3. (2) m is a multiple of 3.

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105? (1) x is a multiple of 9. (2) y is a multiple of 25.

If r is a constant and a n = r n a n = r n for all positive integers n, for how many values of n is a n < 100 a n < 100 ? (1) a 50 = 500 a 50 = 500 (2) a 100 + a 105 = 2050 a 100 + a 105 = 2050

If line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k? (1) k is parallel to the line with equation y = ( 1 − m ) x + b + 1 y = ( 1 − m ) x + b + 1 . (2) k intersects the line with equation y = 2 x + 3 y = 2 x + 3 at the point (2, 7).

If m, p, and t are positive integers and m<p<t, is the product mpt an even integer? (1) t - p = p - m (2) t - m = 16

Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders? (1) The range of the seven remainders is 6. (2) The seven numbers selected are consecutive integers.