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If a,b,c and d are positive integers and their sum is 63, then find th

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Director
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If a,b,c and d are positive integers and their sum is 63, then find th  [#permalink]

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New post 04 Jun 2019, 19:27
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If a,b,c and d are positive integers and their sum is 63, then find the maximum value of \(ab+bc+cd\)?

A. 552
B. 652
C. 752
D. 991
E. 1041
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Joined: 02 Aug 2009
Posts: 7763
Re: If a,b,c and d are positive integers and their sum is 63, then find th  [#permalink]

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New post 04 Jun 2019, 19:59
nick1816 wrote:
If a,b,c and d are positive integers and their sum is 63, then find the maximum value of \(ab+bc+cd\)?

A. 552
B. 652
C. 752
D. 991
E. 1041


We should get two of them the highest, so let us take other two as 1 each..
a=d=1, as a and d are used only once in the calculations.


max values of b and c will be 31 and 30 in any order.

so \(ab+bc+cd=1*31+31*30+30*1=31+930+30=991\)

D
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Re: If a,b,c and d are positive integers and their sum is 63, then find th  [#permalink]

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New post 07 Jun 2019, 14:23
chetan2u wrote:
nick1816 wrote:
If a,b,c and d are positive integers and their sum is 63, then find the maximum value of \(ab+bc+cd\)?

A. 552
B. 652
C. 752
D. 991
E. 1041


We should get two of them the highest, so let us take other two as 1 each..
a=d=1, as a and d are used only once in the calculations.


max values of b and c will be 31 and 30 in any order.

so \(ab+bc+cd=1*31+31*30+30*1=31+930+30=991\)

D


How do you come to the conclusion that we have to take 2 of them the highest?
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If a,b,c and d are positive integers and their sum is 63, then find th  [#permalink]

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New post 09 Jun 2019, 18:29
1
manpaslop wrote:
chetan2u wrote:
nick1816 wrote:
If a,b,c and d are positive integers and their sum is 63, then find the maximum value of \(ab+bc+cd\)?

A. 552
B. 652
C. 752
D. 991
E. 1041


We should get two of them the highest, so let us take other two as 1 each..
a=d=1, as a and d are used only once in the calculations.


max values of b and c will be 31 and 30 in any order.

so \(ab+bc+cd=1*31+31*30+30*1=31+930+30=991\)

D


How do you come to the conclusion that we have to take 2 of them the highest?


Exactly how do you get to know that we have to maximize two values out of four? I took 15,15,15 and 18 to solve it.
Director
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Re: If a,b,c and d are positive integers and their sum is 63, then find th  [#permalink]

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New post 10 Jun 2019, 11:40
We need to maximize the shaded portion area that is ab+bc+cd, hence we have to minimize the area of non-shaded part that is ad.
Area of Non-shaded part=ad
To minimize the ad, we have to assign minimum positive numbers to both a and d.

That's why he maximizes only 2 numbers (b and c).
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Intern
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Re: If a,b,c and d are positive integers and their sum is 63, then find th  [#permalink]

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New post 05 Jul 2019, 03:11
chetan2u wrote:
nick1816 wrote:
If a,b,c and d are positive integers and their sum is 63, then find the maximum value of \(ab+bc+cd\)?

A. 552
B. 652
C. 752
D. 991
E. 1041


We should get two of them the highest, so let us take other two as 1 each..
a=d=1, as a and d are used only once in the calculations.


max values of b and c will be 31 and 30 in any order.

so \(ab+bc+cd=1*31+31*30+30*1=31+930+30=991\)

D


chetan2u

i though that if we have a sum of three number for example a+b+c=25, then the maximum product of ab+bc will be when 25 is equally divided between three number plus the extra one to the most occurring number. So a=8,b=9,c=8 and will give ab+bc as 144 and if we take 1,23,1 it will just be 46.

Just put this example to show an approach, not sure its right or not.

So thinking this in mind, i took this as a=15,b=17,c=16,d=15 but you proved that is wrong.

Could you please help in providing a view to approach such problems in 3 variables and 4 variables.
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Re: If a,b,c and d are positive integers and their sum is 63, then find th   [#permalink] 05 Jul 2019, 03:11
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