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113) Tough PS

by ern5231 » Sun May 16, 2010 8:54 pm
A group of numbers has range 18 and mean 13. Distance of mean from large number is two times the distance from smallest number. What is the maximum number?

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by nikhilkatira » Sun May 16, 2010 10:32 pm
ern5231 wrote:A group of numbers has range 18 and mean 13. Distance of mean from large number is two times the distance from smallest number. What is the maximum number?

This question has no options. The question is taken from a higher secondary mathematics book.
Is the answer 25 ?
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Nikhil H. Katira

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by rajeshsources » Mon May 17, 2010 8:39 pm
ern5231 -----

Range means the difference of Maximum & Minimum. so,we can write as
Range = 18
Max - Min = 18

The given condition is Distance of mean from large number is two times the distance from smallest number. We can write this as,
Mean will always the number in between Largest(Maximum) number and Smallest(Minimum) number.
(Maximum - Mean) = 2 (Mean - Minimum)
Given Mean = 13,
Max - 13 = 2 (13 - Min)
Max - 13 = 26 - 2Min
Max + 2Min = 26+13
Max + 2Min = 39

We have two eqns,
Max - Min = 18
Max + 2Min = 39
By solving, Max = 25. -- CORRECT ANSWER.

HTH, GOOD LUCK,

Thanks,
Rajesh,
Loves GMAT....!!!