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The range of the daily minimum temperatures in January is

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The range of the daily minimum temperatures in January is [#permalink]

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[GMAT math practice question]

The range of the daily minimum temperatures in January is \(10^o\), and the range of the daily minimum temperatures in February is \(15^o\). What is the smallest possible range of the daily minimum temperatures in January and February combined?

A. \(5^o\)
B. \(10^o\)
C. \(15^o\)
D. \(20^o\)
E. \(25^o\)
[Reveal] Spoiler: OA

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The range of the daily minimum temperatures in January is [#permalink]

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New post 05 Jan 2018, 09:11
MathRevolution wrote:
[GMAT math practice question]

The range of the daily minimum temperatures in January is \(10^o\), and the range of the daily minimum temperatures in February is \(15^o\). What is the smallest possible range of the daily minimum temperatures in January and February combined?

A. \(5^o\)
B. \(10^o\)
C. \(15^o\)
D. \(20^o\)
E. \(25^o\)


Given \(Jan_{max}-Jan_{min}=10\)

\(Feb_{max}-Feb_{min}=15\)

Now max and min temperatures during Jan & Feb combined are fixed. Let's assume max temperature occurred in Feb

So smallest range for these two months: \(Feb_{max}-Min=Range\)----------------(1). Here if Min value is low then range will be high and there are two min values possible, \(Jan_{min}\) & \(Feb_{min}\)

Now to make the range as small as possible \(Jan_{min}=Feb_{min}\) because if Min value of equation (1) is lower than \(Feb_{min}\) then the range of equation (1) will be higher than \(15\)

Hence smallest range possible is \(15\)

Option C

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Re: The range of the daily minimum temperatures in January is [#permalink]

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New post 07 Jan 2018, 17:18
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The smallest possible range of the daily minimum temperatures for the two months combined occurs when all daily minimum temperatures for one of the months lie inside the range of daily minimum temperatures for the other. As February has the largest range of minimum temperatures, the minimum temperatures for January must all fall inside the range of minimum temperatures for February. For example, if the data set for January is { \(0^o, 0^o, ………. , 10^o\)} and the data set for February is { \(0^o, 0^o, …….., 15^o\)}, the data set for both months combined is {\(0^o, 0^o, ………. , 10^o,……..,15^o\)}, which has the same range as the data set for February.
Thus 15 is the smallest possible range.

Therefore, the answer is C.

Answer : C
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Re: The range of the daily minimum temperatures in January is   [#permalink] 07 Jan 2018, 17:18
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The range of the daily minimum temperatures in January is

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