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24 Sep 2009, 09:26
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24 Sep 2009, 20:33
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Set up the equation first like this, and see if the information provided in both statements are sufficient to solve for the equations.
Time = (Distance/Speed)
1) Time that Mary took to travel 40 miles is - [(y/x)]+[(40-y)/1.25x]
2) Time it would have taken her if she traveled at xmph for entire trip - 40/x
What we're looking for is equation 1 divided by equation 2, or:
3) [(y/x)+[(40-y)/1.25x]]/ (40/x)
Statement 1
Plugging in x=48 into the above equation 3, you get:
[(y/48)+[(40-y)/(1.25)(48)]]/ (40/48)
Even after simplifying this equation, y remains unknown as it does not cancel out. Hence, you cannot find the percentage of time.
Statement 1 is insufficient
Statement 2
Plugging in y=20 into the above equation 3, you get:
[(20/x)+[(40-20)/1.25x]]/ (40/x)
[(25+20)/1.25x]/(40/x)
You take (40/x) in denominator to the top by multiplying it by its reciprical (x/40)
The two x-es cancel each other as one x is now in the top and one at the bottom to get:
(45/50) or 90%.
Note that you do not actually need to find the percentage or to work out the entire thing as this is a data sufficiency question. Once you see that the x-es cancel each other out, you should know that the remaining number is a fraction which can be equated to a percentage, hence, statement 2 is sufficient.
Time = (Distance/Speed)
1) Time that Mary took to travel 40 miles is - [(y/x)]+[(40-y)/1.25x]
2) Time it would have taken her if she traveled at xmph for entire trip - 40/x
What we're looking for is equation 1 divided by equation 2, or:
3) [(y/x)+[(40-y)/1.25x]]/ (40/x)
Statement 1
Plugging in x=48 into the above equation 3, you get:
[(y/48)+[(40-y)/(1.25)(48)]]/ (40/48)
Even after simplifying this equation, y remains unknown as it does not cancel out. Hence, you cannot find the percentage of time.
Statement 1 is insufficient
Statement 2
Plugging in y=20 into the above equation 3, you get:
[(20/x)+[(40-20)/1.25x]]/ (40/x)
[(25+20)/1.25x]/(40/x)
You take (40/x) in denominator to the top by multiplying it by its reciprical (x/40)
The two x-es cancel each other as one x is now in the top and one at the bottom to get:
(45/50) or 90%.
Note that you do not actually need to find the percentage or to work out the entire thing as this is a data sufficiency question. Once you see that the x-es cancel each other out, you should know that the remaining number is a fraction which can be equated to a percentage, hence, statement 2 is sufficient.
25 Sep 2009, 10:53
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Thanks! :-D
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
