Question

During a four-week period, each one of seven previously unadvertised products, G, H, J, K, L, M and O, will be advertised. A different pair of these products will be advertised during each of the four weeks. Exactly one of these seven products will be advertised during two of the four weeks; none of the other six products is repeated in any pair. The following conditions must hold.

1. J is not advertised during a given week unless H is advertised during the week immediately before it.
2. The product that is advertised twice is advertised during week 4 but is not advertised during week 3.
3. G is not advertised during a given week unless either J or O is also advertised during that same week.
4. K is advertised during one of the first two weeks.
5. O is one of the products advertised during week 3.

Which one of the following is a pair of products that could be advertised during the same week?

• A. G and H
• B. H and J
• C. H and O
• D. M and O

Hint:

Since three of the four pairs involve O, and O only ever sits in week 3, check which second product can safely join O there without starving week 4 of its required repeat.

Answer 1

The Correct Option is D

Three of the four candidate pairs involve O, and O only ever sits in week 3, so those three really boil down to whether the second product can also sit in week 3 with O. The fourth candidate, G and H, does not involve O, so it needs a separate check. Here is each one in turn.

1. G and H: G's rule (condition 3) always needs J or O in the very same week as G. A week only has two seats, so if G's seat-mate is H, there is no third seat left for J or O to also be there. G and H can never share a week, in week 3 or anywhere else.
2. H and J: J's rule (condition 1) needs H in the week right before J's week, a different week from J's own. Sharing a week does not satisfy that; it would additionally require H to repeat a second time in the prior week, meaning H shows up in two back-to-back weeks. The rule that fixes the repeated product's two weeks always spaces them out to week 4 plus week 1 or week 2, never two weeks that sit next to each other, so H repeating in consecutive weeks is never allowed. H and J cannot share a week.
3. H and O: This means H sits in week 3, O's only week. That immediately pushes J into week 4, since J can only follow a H-week, and week 4 is the only week after week 3. J being in week 4 then pulls G into week 4 as well, since G always needs J or O with it, and O is stuck in week 3. With G and J both single-use products sitting in week 4, there is no seat left for whichever product the puzzle requires to repeat there. That contradiction rules out H and O.
4. M and O: M carries no rule of its own, so nothing stops it from sitting in week 3 with O. Building outward from that: put H and K in week 1, put J (following H) and G (needing J) in week 2, keep O and M in week 3, and let L repeat into week 4 alongside a second copy of H or K. Every rule checks out in this arrangement, so M and O sharing week 3 is achievable in practice, not just in theory.

Three of the four candidates fail because week 3, O's week, cannot legally host a second linked product like G, H, or the H-J pair without starving week 4 of its required repeat. M and O works precisely because M is unlinked to any rule, so it slots into week 3 without disturbing the rest of the schedule.

Let's summarize:

• G and H, H and J, and H and O all break some rule the moment they are forced into the same week.
• M and O is the one pair that fits into a complete, rule-respecting schedule.

So the pair that could be advertised during the same week is M and O, option (EE).