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logical gmat maths prob, plz help

Expert replies
by quantskillsgmat » Sat Dec 10, 2011 10:06 pm
three labelled boxes containing red and white balls are mislabeled.it is known that one of the boxes contain only white balls and one only red balls.Third contains mixture of red and white balls.you are required to correctly label the boxes with labels red,white and red and white by picking a sample of one ball from only one box.what is the label on the box you should pick.
a) white
b)red
c)red and white
d)more than one sample is required
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Source: — Problem Solving |

by chufus » Sat Dec 10, 2011 10:38 pm
Quite obviously the answer should be D.
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by Anurag@Gurome » Sat Dec 10, 2011 10:44 pm
If all of the boxes are mislabeled, then the following scenarios are possible...
  • (1) The box labeled with "Red & White" contains either all white or all red balls.
    (2) The box labeled with "Red" contains either all white or mixed balls.
    (3) The box labeled with "White" contains either all red or mixed balls.
Now picking a sample of one ball from the box labeled with "Red and White" will tell us whether the box has all red balls or all white balls.

If the box has all red balls then,
  • From (3) it follows that the box labeled with "White" has mixed balls. Hence, the box labeled with "Red" has all white balls.
If the box has all white balls then,
  • From (2) it follows that the box labeled with "Red" has mixed balls. Hence, the box labeled with "White" has all red balls.
The correct answer is C.

Note : If any two of the three boxes are mislabeled, in that case it is not always possible to correct the labeling by picking one sample.
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