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You have got the right answer but the highlighted portions are wrong.

\(A = -|B|\). Notice that the negative sign is outside the mod function and mod is always positive. Hence \(A\) will be always negative irrespective of \(B\)

So if \(B=-5\), then \(A=-|-5| = -|5| =-5\) Hence \(A-B = -5-(-5) = 0\). Hence B cannot be \(-5\)

You have got the right answer but the highlighted portions are wrong.

\(A = -|B|\). Notice that the negative sign is outside the mod function and mod is always positive. Hence \(A\) will be always negative irrespective of \(B\)

So if \(B=-5\), then \(A=-|-5| = -|5| =-5\) Hence \(A-B = -5-(-5) = 0\). Hence B cannot be \(-5\)

Hey yah thanks for pointing it out. Totally agree with you. While solving question i made correct assumptions. while posting solution was in between 2 things so made mistake. Will update the solution.

Option: A Since the absolute value of both A and B is same, all we have to do is plug values from option in the equation A-B = -10. Only A suffices. Answer can be reached within a minute.