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.

In the quilting pattern shown above, a small square has its vertices on the sides of a larger square. What is the side length, in centimeters, of the larger square?

(1) The side length of the smaller square is 10 cm.

(2) Each vertex of the small square cuts 1 side of the larger square into 2 segments with lengths in the ratio of 1:2.

If x > 0, what is the value of x⁵?

(1) ~$\sqrt{x}$~= 32

(2)~$x^2 = 2^{20}$~

In a certain factory, hours worked by each employee in excess of 40 hours per week are overtime hours and are paid for at 1~$1 \over 2$~ times the employee's regular hourly pay rate.

If an employee worked a total of 42 hours last week, how much was the employee's gross pay for the hours worked last week?

(1) The employee's gross pay for overtime hours worked last week was $30.

(2) The employee's gross pay for all hours worked last week was $30 more than for the previous week.

If p and q are positive, is~$p \over q$~ less than 1 ?

(1) p is less than 4.

(2) q is less than 4.

Is 2x > 2y ?

(1) x > y

(2) 3x > 3y