Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?
(1) x^2+y^2<12
(2) Bonnie and Clyde complete the painting of the car at 10:30am
Statement 1: x² + y² < 12
It's possible that x=1 and y=1, in which case x=y.
It's possible that x=1 and y=3, in which case x≠y.
INSUFFICIENT.
Statement 2: Bonnie and Clyde complete the painting of the car at 10:30am
Thus, the total time = 10:30am - 9:45am = 3/4 hours.
Let the job = 3 units.
Case 1: x=1 and y=1
Bonnie's rate = w/t = 3/1 = 3 units per hour.
Clyde's rate = w/t = 3/1 = 3 units per hour.
Combined rate for Bonnie and Clyde = 3+3 = 6 units per hour.
Time for Bonnie and Clyde working together = w/r = 3/6 = 1/2 hour.
Doesn't work: the time here is LESS than 3/4 hours.
Case 2: x=3 and y=3
Bonnie's rate = w/t = 3/3 = 1 unit per hour.
Clyde's rate = w/t = 3/3 = 1 unit per hour.
Combined rate for Bonnie and Clyde = 1+1 = 2 units per hour.
Time for Bonnie and Clyde working together = w/r = 3/2 = 1.5 hours.
Doesn't work: the time here is MORE than 3/4 hours.
Notice the following:
In Case 1, the total time is less than 3/4 hours.
In Case 2, the total time is greater than 3/4 hours.
As x and y increase, the total time increases.
Implication:
If x=y, the job cannot be completed in exactly 3/4 hours.
Thus, x≠y.
SUFFICIENT.
The correct answer is
B.
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