If no two lights are assigned light bulbs that are the same color as each other, then which one of the following coul...

Victoria on June 1, 2020

Hi @cholman,

Happy to help!

We know that there are exactly three light sockets.
1:
2:
3:

The worker has three of each colour of bulb for a total of nine bulbs - 3 G, 3 P, and 3 Y.

The placement of bulbs is governed by the conditions.

Condition 1: When 1 is purple, 2 must be yellow.

1P --> 2Y
Not 2Y --> Not 1P

Condition 2: When 2 is green, 1 must be green.

2G --> 1G
Not 1G --> Not 2G

Condition 3: When 3 is either purple or yellow, 2 must be purple.

3P or 3Y --> 2P
Not 2P --> Not 3P and Not 3Y

The question places an additional restriction on the placement of bulbs - no two lights are assigned light bulbs that are the same colour as each other.

Condition 1 is fine.

Condition 2 would require two green bulbs. Therefore, light 2 cannot be green. This eliminates answer choice (D).

Condition 3 would require two purple bulbs. Therefore, light 3 cannot be purple or yellow. This eliminates answer choices (C) and (E).

We are left with answer choices (A) and (B).

Answer choice (B) cannot be true because the condition imposed by the question requires that light 3 be purple. If light 3 is purple, then light 2 must also be purple. This is neither stated by the answer choice nor allowed by the additional condition. Therefore, answer choice (B) is incorrect.

Answer choice (A) means that light 3 must yellow.

1: G
2: P
3: Y

Neither conditions 1 nor 2 are relevant here. Condition 3 is met - whenever light 3 is yellow, then light 2 must be purple. The additional condition is also met as all three bulbs are different colours. Therefore, answer choice (A) is correct.

Hope this is helpful! Please let us know if you have any further questions.