I need help on part B. how do you go about it? What I tried is to assume that the sources and the 4k and 3k resistors are fixed and set the 1k ohm as my unknown resistance then use kirch. law. I ended up having a R=5k ohm. that would make the voltage Va=6V. is my approach valid? TIA!
The question is wrong (or stupid). If the potential at Va is 6V, then the voltage across the top 7k is 20-6=14V and the voltage across the bottom 1k will be 10V. Calculate the currents and you will see that the same currents cannot flow through the series combination and part of the current will be sourced/sinked at Va.
You always have to source /sink currents if you want to fix the voltage across arbitrary resistors.
I could be wrong but I have a hunch this exercise is asking for the simplest possible type of event, such as, Which resistor went open (or short) so that these readings are the result?