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If a,b,c and d are positive integers and their sum is 63, then find th
[#permalink]
04 Jun 2019, 19:27
04 Jun 2019, 19:27
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Difficulty:
95%
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Question Stats:
51% (02:30) correct
49%
(02:30)
wrong
based on 227
sessions
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
A. 552
B. 652
C. 752
D. 991
E. 1041
Re: If a,b,c and d are positive integers and their sum is 63, then find th
[#permalink]
10 Jun 2019, 11:40
10 Jun 2019, 11:40
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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).
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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Re: If a,b,c and d are positive integers and their sum is 63, then find th
[#permalink]
04 Jun 2019, 19:59
04 Jun 2019, 19:59
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Expert Reply
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
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]
07 Jun 2019, 14:23
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
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?
If a,b,c and d are positive integers and their sum is 63, then find th
[#permalink]
09 Jun 2019, 18:29
09 Jun 2019, 18:29
1
Kudos
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
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.
Re: If a,b,c and d are positive integers and their sum is 63, then find th
[#permalink]
05 Jul 2019, 03:11
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
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.
If a,b,c and d are positive integers and their sum is 63, then find th
[#permalink]
27 Dec 2022, 03:53
27 Dec 2022, 03:53
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
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?
One hint could be to see that b and c are repeated twice in ab + bc + cd, whereas a and d are repeated only once.
Re: If a,b,c and d are positive integers and their sum is 63, then find th
[#permalink]
26 Mar 2024, 01:12
26 Mar 2024, 01:12
bad question - pls remove
Re: If a,b,c and d are positive integers and their sum is 63, then find th
[#permalink]
26 Mar 2024, 11:47
26 Mar 2024, 11:47
2
Kudos
ab+bc+cd=(a+c)(b+d)−ad
To maximize the objective, set ad=1 and make (a+c)×(b+d) as close to square as possible.
32×31−1=991
Posted from my mobile device
To maximize the objective, set ad=1 and make (a+c)×(b+d) as close to square as possible.
32×31−1=991
Posted from my mobile device
gmatclubot
Re: If a,b,c and d are positive integers and their sum is 63, then find th [#permalink]
26 Mar 2024, 11:47
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