If switch 1 and switch 3 are both off, then which one of the following could be two switches that are both on?

Ravi on July 10, 2019

@Lizzie-Annerino,

Happy to help. Let's take a look at (A).

Here are the main rules in this game:

1) 1 - >/3
1 - >/5

2) 4 - >/2
4 - >/5

3) circuit load corresponds to one of the switch numbers that's on

We're told that 1 and 3 are both off, and we're looking to figure out
which answer choice could be two switches that are both on.

Starting with (A), we have 2 and 7. Let's try it.

If 2 and 7 are both on, this means that 4 must be off (the
contrapositive of rule 2).

We have 2 and 7 on, and 1, 3, and 4 off with 5 and 6 not yet assigned.

Looking at our rules, we see that with 2 and 7, we already satisfy the
last rule (the switch whose number corresponds to the circuit load of
the panel is itself on). We can just put 5 and 6 in the out/off group,
so we have 2 and 7 in and all of the other switches out. This is why
(A) works and is the correct answer choice.

Does this make sense? Let us know if you have any other questions!