Problem Solving

I) If ab is not equal to zero, and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in this same quadrant?

(1) xy>0
(2) ax>0

correct answer:C

II)The numbers x and y are not integers. The value of x is closest to which integer?

(1) 4 is the integer that is closest to x+y.
(2) 1 is the integer that is closest to x-y.

correct answer:E

III) Is 2x-3y < x^2 ?



(1) 2x-3y = -2
(2) x>2 and y>0

Correct answer: D

IV) Working alone at its constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

a) 25%
b) 100/3 %
c) 50%
d) 200/3%
e) 75%

Correct answer : D

V) Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear p?

a) 6
b) 8
c) 10
d) 12
e) 15

VI) A certain roller coaster had 3 cars, and a passenger is equally to ride in any 1 od the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?

a) 0
b) 1/9
c) 2/9
d) 1/3
e) 1

Correct answer :C