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range

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range [#permalink]

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New post 31 May 2009, 06:23
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X range=240, Y range=360, what is the least value of range of X+Y?

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Re: range [#permalink]

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New post 31 May 2009, 06:31
I am assuming the question is asking the least POSSIBLE value for range X+Y.

It would be 360.

For instance,

X ={0,1,2...240}
Y ={0,1,2...360}

Range would be 360.
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Re: range [#permalink]

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New post 31 May 2009, 16:01
X ={0,1,2...240}
Y ={0,1,2...360}
Adding elements of one set to another, only the union is intuitively suitable to be considered as the set addition. The empty set plays the role of zero.

However , for first 240 elements , X is not 0. For further values of Y(241-360) , X will be empty set.

So the Range would be X(240)+Y(240)=480.
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Re: range [#permalink]

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New post 01 Jun 2009, 01:19
I think, it depends on what the question is asking:
1. If we just combine the 2 sets, then the least possible range of X+Y will be 360 (if all the elements of X are from Y range).
2. If we add the 2 sets, then the least possible range will be 0: when sum of X = -sum of Y (e.g. X = {-240; -180; -60; 0} and Y = {0; 120; 360})
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Re: range [#permalink]

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New post 01 Jun 2009, 01:22
The least possible range is 360 for X + Y.

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Re: range   [#permalink] 01 Jun 2009, 01:22
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