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formula required

by divya23 » Thu Jun 16, 2011 12:11 am
i did the below mentioned question by backsolving i want to know the formula to solve this type of question.

it says we have 5 no. have me an length of 124 and median of 140 what is the maximum posible length of the smallest number ....

options are
90
100
110
130
140

ans - 100
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by Geva@EconomistGMAT » Thu Jun 16, 2011 12:16 am
divya23 wrote:i did the below mentioned question by backsolving i want to know the formula to solve this type of question.

it says we have 5 no. have me an length of 124 and median of 140 what is the maximum posible length of the smallest number ....

options are
90
100
110
130
140

ans - 100
There's no such thing as "length" of a number, unless it's a made up function for the purposes of this question. Do you mean "range"?
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by divya23 » Thu Jun 16, 2011 12:21 am
okay like the question states 5 pieces of wood have mean length of 124..... and rest same we have to find the length of the smallest piece of the wood
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by Geva@EconomistGMAT » Thu Jun 16, 2011 12:42 am
divya23 wrote:okay like the question states 5 pieces of wood have mean length of 124..... and rest same we have to find the length of the smallest piece of the wood
oh, ok. If the mean of 5 terms is 124, their total is 124*5=620. So if we want the maximum length of the smallest term, all the other terms have to be at their minimum possible value. But what are the limitations on their values?

The median is 140, so the middle term needs to be 140, and the next two terms need to also be a minimum of 140 (greater thatn or equal to the median). That's already 3*140 = 420, leaving 620-420=200 for the smallest two terms. The second term needs to be smaller or equal to the smallest, so the maximum term for both is 200/2=100 each.
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