1. 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
Ans-B
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Statement 1: x² + y² < 12Bonnie 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
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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Hi shibsriz,
This question is based on the Work Formula: (AxB)/(A+B)
In the prompt, we're told that the two variables are ODD INTEGERS, which is a significant restriction. We're asked if X=Y.
Fact 1: X^2 + Y^2 < 12
This is perfect for TESTing Values...
If X=1, Y=1 then the answer to the question is YES
If X=1, Y=3 then the answer to the question is NO
Fact 1 is INSUFFICIENT
Fact 2: We're told the job is done at 10:30am (and we're told in the prompt that it was started at 9:45am).
I'm going to run some "hypotheticals" to see what happens when the values of the two variables change...
If X=1, Y=1 then (1x1)/(1+1) = 1/2 hour to complete the job
If X=1, Y=3 then (1x3)/(1+3) = 3/4 hour to complete the job
If X=3, Y=3 then (3x3)/(3+3) = 9/6 hours to complete the job
Clearly, as the two variables change, the amount of time needed to complete the job changes.
Fact 2 tells us that the job takes 45 minutes (or 3/4 of an hour). Based on the above examples, the two variables MUST be 1 and 3 so the answer to the question is NO and it's ALWAYS going to be NO.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
This question is based on the Work Formula: (AxB)/(A+B)
In the prompt, we're told that the two variables are ODD INTEGERS, which is a significant restriction. We're asked if X=Y.
Fact 1: X^2 + Y^2 < 12
This is perfect for TESTing Values...
If X=1, Y=1 then the answer to the question is YES
If X=1, Y=3 then the answer to the question is NO
Fact 1 is INSUFFICIENT
Fact 2: We're told the job is done at 10:30am (and we're told in the prompt that it was started at 9:45am).
I'm going to run some "hypotheticals" to see what happens when the values of the two variables change...
If X=1, Y=1 then (1x1)/(1+1) = 1/2 hour to complete the job
If X=1, Y=3 then (1x3)/(1+3) = 3/4 hour to complete the job
If X=3, Y=3 then (3x3)/(3+3) = 9/6 hours to complete the job
Clearly, as the two variables change, the amount of time needed to complete the job changes.
Fact 2 tells us that the job takes 45 minutes (or 3/4 of an hour). Based on the above examples, the two variables MUST be 1 and 3 so the answer to the question is NO and it's ALWAYS going to be NO.
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
