Data Sufficiency

The length of the edging that surrounds circular garden K is 1/2 the length of the edging that surrounds circular garden G. What is the area of garden K (Assume that the edging has negligible width.) (1) The area of G is 25π 25 𝜋 square meters. (2) The edging around G is 10π 10 𝜋 meters long. (1) The area of G is 25π 25 𝜋 square meters. (2) The edging around G is 10π 10 𝜋 meters long.

What is the value of y ? (1) y^2 − 7y + 12 = 0 (2) y > 0

How many books did a librarian purchase ? (1) The librarian paid an average (arithmetic mean) of $15 per book for the books purchased. (2) The total sales tax on the books purchased was $7.

Jones has worked at Firm X twice as many years as Green, and Green has worked at Firm X four years longer than Smith. How many years has Green worked at Firm X ? (1) Jones has worked at Firm X 9 years longer than Smith. (2) Green has worked at Firm X 5 years less than Jones.

What is the value of n? (1) $\sqrt{n}=2$ (2) $\sqrt{4n}=4$

For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b? (1) a/b = 3/5 (2) a and b have no common factors greater than 1

How old is Jim? (1) Eight years ago Jim was half as old as he is now. (2) Four years from now Jim will be twice as old as he was six years ago.

If x and yare positive, is x/y greater than 1 ? (1) xy > 1 (2) x - y > 0

If xy < 3, is x < 1? (1) y > 3 (2) x < 3

If n is an integer, is n + 2 a prime number? (1) n is a prime number. (2) n + 1 is not a prime number.

Does x^2 = y ? (1) y √ =−x 𝑦 = − 𝑥 (2) x < y

If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ? (1) None of the six numbers is less than 75. (2) None of the six numbers is greater than 75.

If the list price of a new car was $12,300, what was the cost of the car to the dealer? (1) The cost to the dealer was equal to 80 percent of the list price. (2) The car was sold for $11,070, which was 12.5 percent more than the cost to the dealer.

Is the integer n a multiple of 15 ? (1) n is a multiple of 20 (2) n + 6 is a multiple of 3

In a gas sample, there are, rounded to the nearest order of magnitude (that is, to the nearest power of 10), approximately 10 21 10 21 molecules of H 2 H 2 and also 10 21 10 21 molecules of O 2 O 2 . What is the combined number of H 2 H 2 and O 2 O 2 molecules in the gas sample, rounded to the nearest order of magnitude? (1) The number of H 2 H 2 molecules and the number of O 2 O 2 molecules are each less than 3 × 10 21 3 × 10 21 . (2) The number of H 2 H 2 molecules is more than twice the number of O 2 O 2 molecules.

In ∆PQR, what is the measure of angle P? (1) Angle Q is a right angle. (2) The measure of R is 17 ̊

If the price of a magazine is to be doubled, by what percent will the number of magazines sold decrease? (1) The current price of the magazine is $1.00. (2) For every $0.25 of increase in price, the number of magazines sold will decrease by 10 percent of the number sold at the current price.

What is the value of x? (1) When x is multiplied by 8, the result is between 50 and 60. (2) When x is doubled, the result is between 10 and 15.

In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of triangle PQR has the greatest degree measure? (1) y = x+ 3 (2) x = 2

Each of the eggs in a bowl is dyed red, or green, or blue. If one egg is to be removed at random. what is the probability that the egg will be green? (1) There are 5 red eggs in the bowl. (2) The probability that the egg will be blue is 1/3