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Question

If a+b+c+d=63, where a,b,c,dI+, then the maximum value of ab+bc+cd is
  1. 990
  2. 991
  3. 992
  4. 994


Solution

The correct option is B 991
ab+bc+cd=ab+bc+cd+adad
ab+bc+cd=(a+c)(b+d)ad 
Here, ad should be minimized, a=d=1
ab+bc+cd=(1+c)(1+b)1
Also a+b+c+d=63b+c=61
To maximization, b=31 and c=30
ab+bc+cd=(1+30)(1+31)1=991 
max(ab+bc+cd)=991

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