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Max/Min

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by kajcha » Fri Oct 05, 2007 4:03 am
IMO ans should be -74. What is the source of the question? How reliable are the answers?
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by samirpandeyit62 » Fri Oct 05, 2007 7:22 am
-4<= A <=8
-7<= B <=6
-3<= C <=2
then the least possible value of AB+ BC = ?

here to get the min value we need to ensure that AB & BC is negative

i.e B(A+C) is min

now is we take B as -ve so min possible val is -7

and max +ve value of A+B is 8 + 2 =10

so expr is -7*10 =-70

if we take B +ve & A+C -ve then we have 6(-7) = -42

so ans should be -70
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Samir
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by ldoolitt » Fri Oct 05, 2007 7:40 am
samirpandeyit62 wrote:-4<= A <=8
-7<= B <=6
-3<= C <=2
then the least possible value of AB+ BC = ?

here to get the min value we need to ensure that AB & BC is negative

i.e B(A+C) is min

now is we take B as -ve so min possible val is -7

and max +ve value of A+B is 8 + 2 =10

so expr is -7*10 =-70

if we take B +ve & A+C -ve then we have 6(-7) = -42

so ans should be -70
Exactly. I think what both of the above posters did is assume that the B in the first term did not have to be the same as the B in the second term. If that did not have to be true,you could get

A=8
B=-7

B=6
C=-3

8*-7+6*-3=-74

But in that case B would take on two values in the problem.
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by samirpandeyit62 » Fri Oct 05, 2007 8:09 am
Hi ldoolitt,
Thanks for posting, I was wondering how we can get -74 here
Regards
Samir
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by kajcha » Fri Oct 05, 2007 8:28 am
Yes, I assumed B not to be same in both terms. But, what should be the approach when we get such questions in the exam and the question does not mention anything.
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by samirpandeyit62 » Sat Oct 06, 2007 1:10 am
Hi Kajcha,
Since u got its as -74, so i was trying figure it out how we can get that value here, IMO since here each variable has a range of values so the best approach would be to segregate the variables i.e B(A+C), so as to avoid using two values.
Regards
Samir
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