Is the positive integer n odd?

(1) n² + (n + 1)²+ (n + 2)² is even.

(2) n² − (n + 1)² − (n + 2)² is even.

What is the value of ~$r \over 2$~+~$s \over 2$~ ?

(1)~$r+s \over 2$~=5

(2) r + s = 10

What is the average (arithmetic mean) of x and y ?

(1) The average of x and 2y is 10.

(2) The average of 2x and 7y is 32.

If y is greater than 110 percent of x, is y greater than 75 ?

(1) x > 75

(2) y − x = 10

In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equal area, what are the coordinates of point R ?

(1) The coordinates of point P are (0,12).

(2) OP = OQ and QS = RS.

On the scale drawing of a certain house plan, if 1 centimeter represents x meters, what is the value of x ?

(1) A rectangular room that has a floor area of 12 square meters is represented by a region of area 48 square centimeters.

(2) The 15‐meter length of the house is represented by a segment 30 centimeters long.

Is zw positive?

(1) z + w³= 20

(2) z is positive.

What is the value of the integer N ?

(1) 101 < N < 103

(2) 202 < 2N < 206

How many hours would it take Pump A and Pump B working together, each at its own constant rate, to empty a tank that was initially full?

(1) Working alone at its constant rate, Pump A would empty the full tank in 4 hours 20 minutes.

(2) Working alone, Pump B would empty the full tank at its constant rate of 72 liters per minute.

Did Insurance Company K have more than $300 million in total net profits last year?

(1) Last year Company K paid out $0.95 in claims for every dollar of premiums collected.

(2) Last year Company K earned a total of $150 million in profits from the investment of accumulated surplus premiums from previous years.