Data Sufficiency

If x is an integer, what is the value of x? (1) 1 5 < 1 x+1 < 1 2 1 5 < 1 𝑥 + 1 < 1 2 (2) (x−3)(x−4)=0 ( 𝑥 − 3 ) ( 𝑥 − 4 ) = 0 PS21277

Does x + y = 0 ? (1) xy < 0 (2) x^2 = y^2

If n is an integer, then n is divisible by how many positive integers? (1) n is the product of two different prime numbers. (2) n and 2^3 are each divisible by the same number of positive integers.

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

On Monday morning a certain machine ran continuously at a uniform rate to fill a production order. At what time did it completely fill the order that morning? (1) The machine began filling the order at 9:30 a.m. (2) The machine had filled 1/2 of the order by 10:30 a.m. and 5/6 to the order by 11:10 a.m.­ ID: 700115

What is the average (arithmetic mean) of x and y ? (1) x/2 + y/2 = 10 (2) x = 2y

If 2x + 3y = 5, what is the value of x ? (1) x + z = 3 + 2y + z (2) y = − 1 7 − 1 7 DS21227

The charge for a telephone call between City R and City S is $0.42foreachofthefirst3minutesand$0.18 for each additional minute. A certain call between these two cities lasted for x minutes, where x is an integer. How many minutes long was the call? (1) The charge for the first 3 minutes of the call was $0.36 less than the charge for the remainder of the call. (2) The total charge for the call was $2.88.

During a 6·day local trade show, the least number of people registered in a single day was 80. Was the average (arithmetic mean) number of people registered per day for the 6 days greater than 90 ? (1) For the 4 days with the greatest number of people registered, the average (arithmetic mean) number registered per day was 100. (2) For the 3 days with the smallest number of people registered, the average (arithmetic mean) number registered per day was 85.

In a survey of 200 college graduates, 30 percent said they had received student loans during their college careers, and 40 percent said they had received scholarships. What percent of those surveyed said that they had received neither student loans nor scholarships during their college careers? (1) 25 percent of those surveyed said that they had received scholarships but no loans. (2) 50 percent of those surveyed who said that they had received loans also said that they had received scholarships.

What is the perimeter of rectangle R ? (1) R is a square. (2) The area of R is 36.

At what speed was a train traveling on a trip when it had completed half of the total distance of the trip? (1) The trip was 460 miles long and took 4 hours to complete. (2) The train traveled at an average rate of 115 miles per hour on the trip.

Is quadrilateral Q a square? (1) The sides of Q have the same length. (2) The diagonals of Q have the same length

In the figure above, line AC represents a seesaw that is touching level ground at point A. If B is the midpoint of AC, how far above the ground is point C? (1) x = 30 (2) Point B is 5 feet above the ground. Show Spoiler

How many miles long is the route from Houghton to Callahan? (1) It will take 1 hour less time to travel the entire route at an average rate of 55 miles per hour than at an average rate of 50 miles per hour. (2) It will take 11 hours to travel the first half of the route at an average rate of 25 miles per hour

If @ represents one of the operations +, -, and x, is k@(l+m)=(k@l)+(k@m) for all numbers k, l,and m? (1) k@1 is not equal to 1@k for some numbers k. (2) @ represents subtraction.

If n + k = m, what is the value of k ? (1) n = 10 (2) m + 10 = n

How many bags of grass seed were used for rectangular lawn X ? (1) Lawn X has a perimeter of 240 feet. (2) One bag of grass seed was used for each 5,000 square feet of lawn X

If S is the sum of the first n positive integers, what is the value of n ? (1) S < 20 (2) S^2 > 220 DS84302.01

Is the integer P odd? (1) The sum of P, P + 4, and P+ 11 is even. (2) The sum of P – 3, P, and P+ 11 is odd.