Problem Solving

If
-4<= A <=8
-7<= B <=6
-3<= C <=2
then the least possible value of AB+ BC = ?

49
-42
-70
-72
-74

My Ans is -74 but ter ans is -70. PLs help..

IMO ans should be -74. What is the source of the question? How reliable are the answers?

-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

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.

Hi ldoolitt,
Thanks for posting, I was wondering how we can get -74 here

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.

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.