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tough DS question !

by guerrero » Wed Feb 20, 2013 10:34 am
Hello All,

I am clueless on how to approach this kind of problems .. Please help!

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

OAB
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by GMATGuruNY » Wed Feb 20, 2013 10:56 am
guerrero wrote:Hello All,

I am clueless on how to approach this kind of problems .. Please help!

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

OAB
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.

If x=y and x and y increase in value -- implying that Bonnie and Clyde work more SLOWLY -- their total time will INCREASE.
Thus, it is not possible that x=y.
SUFFICIENT.

The correct answer is B.
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by Anurag@Gurome » Wed Feb 20, 2013 11:14 am
guerrero wrote: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
In one hour,
  • Bonnie paints 1/x of the car
    Clyde paints 1/y of the car

    Together, they pain (1/x + 1/y) = (x + y)/xy of the car
Hence, together they will take xy/(x + y) hour to finish painting the car

Statement 1: Consider the following two case,
x = 1 and y = 1 --> x = y
x = 1 and y = 3 --> x ≠ y

Not sufficient

Statement 2: Together they take (10:30 - 9:45) = 45 minutes = 3/4 hours to finish painting
Hence, xy/(x + y) = 3/4 ---> 4xy = 3(x + y)
Let us consider that x = y

So, 4x² = 3(x + x)
--> 4x² = 6x
--> 2x² - 3x = 0
--> x(2x - 3) = 0

Hence, x = 0 or x = 3/2
In either case neither x nor y is odd integer.

Hence, it is not possible that x = y

Sufficient

The correct answer is B.
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by Valentin » Tue Aug 13, 2013 1:34 pm
What I don't understand about this problem is the stem itself. It says:

"They start working simultaneously and independently at their respective constant rates at 9:45am..."

Here's what I understand from that:

-"They start working simultaneously..." = They start working at the same time

-"...and independently at their respective constant rates..." = Independently... mmm, then they start working on different cars, or in other words, they are not working together, but rather they are working on their own, independently.


What am I missing? What's wrong with my analysis? Please, any feedback will be appreciated.
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by [email protected] » Tue Aug 13, 2013 2:32 pm
Hi Valentin,

This is an example of a "work formula" question. In these types of questions, the phrase "work simultaneously and independently" means that the entities involved work on unique parts of the job (in this case, if one person paints the left side of the car, the other person WON'T ALSO paint the left side of the car). This is important to the math because the idea is that the entire car will be painted, but it will be done in the fastest way possible (with no duplicated work). It's the type of "legalese" that has to be included in the question, otherwise the correct answer could be debated.

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