Answer:
C
Explanation:
you need to follow the logic in the sequence of the switches.
we start with
1-off, 2-off, 3-on, 4-off
then we apply A and get
1-on, 2-off, 3-off, 4-off
then we apply B and get
1-on, 2-on, 3-on, 4-off
then we apply C and get
1-off, 2-off, 3-on, 4-off
but we get
1-on, 2-on, 3-on, 4-off
that is what we expect as result after B.
so, the first assumption is that C is malfunctioning.
but could it be that C actually works correctly, and a switch before C is feeding the wrong information leading to the faulty result ?
let's calculate backwards :
if C works and delivers
1-on, 2-on, 3-on, 4-off
then B must have delivered
1-off, 2-off, 3-on, 4-off
if B is working correctly, then A must have delivered
1-off, 2-on, 3-off, 4-off
if A is working correctly, this is only possible, if the input for A is
1-on, 2-on, 3-on, 4-off
but the input is
1-off, 2-off, 3-on, 4-off
now, we need to make the following assumption : each switch is only "touching" the 2 lines it is supposed to invert, and the other 2 lines cannot be changed, even if the switch is faulty.
otherwise we cannot determine which switch is faulty with the given information.
so, if A can only manipulate 1 and 3, then 2 and 4 would have the same setting after A as they have before A.
our backwards calculation has shown that for B and C to be working correctly, 2 must be on after A. but it is off as per the initial setting before A.
so, the assumption that B and C are working correctly (and therefore that A must be faulty) is false.
that means A is working correctly. and either B or C must be faulty.
now, is is possible that A and C are working correctly (and B is faulty) ?
if C is working correctly, we know already from the case before, that B must be delivering
1-off, 2-off, 3-on, 4-off
and if A is working correctly, it will be delivering to B
1-on, 2-off, 3-off, 4-off
but B can only change 2 or 3. and 1 is different before B and after B.
so, the assumption that A and C are working correctly (and therefore B must be faulty) is false.
and as we have proven at the beginning that the assumption of C being faulty is possible, and it is the last remaining possibility, C is the faulty switch.