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  • Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

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Diffrentiation

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There are 4 positive integers whose sum is 4Q+3. S denotes the sum of the products of the four integers taken two at a time.. then what will be max/min value of S

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New post 09 Aug 2018, 07:16
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by taken two at a time, do you mean added?
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New post 09 Aug 2018, 07:37
Sum of the products of integers as : ab+ac+ad+bc+bd+cd

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Re: Diffrentiation  [#permalink]

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New post 09 Aug 2018, 08:03
Srishti97 wrote:
Sum of the products of integers as : ab+ac+ad+bc+bd+cd

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\((a+b+c+d)^2 = a^2+b^2+c^2+d^2 + 2(ab+ac+ad+bc+bd+cd)\)

\(ab+ac+ad+bc+bd+cd =\frac{(a+b+c+d)^2 - (a^2+b^2+c^2+d^2)}{2}\)

given \(a+b+c+d=4Q+3\)
\(a,b,c,d\) are positive integers, their minimum value is 1
When \((a^2+b^2+c^2+d^2)\) is maximum, then \(ab+ac+ad+bc+bd+cd\) will be minimum for a given \(a+b+c+d\).
\((a^2+b^2+c^2+d^2)\) will be maximum when \(a=1,b=1,c=1\) and \(d =4Q\)(any three of them can be 1 ,4th one have to be \(4Q\))

Minimum value of \(ab+ac+ad+bc+bd+cd =1+1+4Q+1+4Q+4Q = 12Q + 3\)
Is this correct?
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Re: Diffrentiation  [#permalink]

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New post 09 Aug 2018, 08:17
Srishti97 wrote:
There are 4 positive integers whose sum is 4Q+3. S denotes the sum of the products of the four integers taken two at a time.. then what will be max/min value of S

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Please read the link below before posting:

1. http://gmatclub.com/forum/11-rules-for- ... 33935.html

2. http://gmatclub.com/forum/rules-for-pos ... l#p1096628
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Re: Diffrentiation &nbs [#permalink] 09 Aug 2018, 08:17
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