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.

If L is the product that is advertised during two of the weeks, which one of the following is a product that MUST be advertised during one of the weeks in which L is advertised?

• A. G
• B. H
• C. J
• D. M

Hint:

Work out the only two ways a twice-advertised L can sit consistent with week 4 being one of its slots, then see which single product always ends up filling L's other week 4 seat.

Answer 1

The Correct Option is D

Step 1: Fix where a twice-advertised L must sit.
Since L is now the repeated product, condition 2 forces one of L's two appearances into week 4, and bans the other appearance from week 3. So L's second slot must be week 1 or week 2. That gives exactly two cases to check.

Step 2: Work out Case 1, L in week 1 and week 4.
The remaining five products, G, H, J, K, M, must fill week 1's other slot, both slots of week 2, and week 3's other slot next to O. G cannot stand alone with L in week 1 or week 4, since condition 3 needs J or O alongside G and neither is available in either of those weeks once L takes a seat. So G must sit in week 3 with O, which satisfies condition 3 on its own. That leaves H, J, K, M for week 1's open slot and both slots of week 2. J cannot be in week 1 (no week before it for H to occupy), so J must be in week 2, and H must fill week 1 alongside L to satisfy condition 1. That leaves K and M for week 2's second slot and week 4's second slot. Condition 4 needs K in week 1 or week 2, and week 1 is already full (H, L), so K takes week 2's open slot, leaving M for week 4. The schedule becomes week 1: H, L; week 2: J, K; week 3: G, O; week 4: L, M. Every condition holds, and M shares L's week 4 slot.

Step 3: Work out Case 2, L in week 2 and week 4.
By the same logic, G cannot sit in week 1 (no J or O there) or week 4 (paired only with L), so G again must sit in week 3 with O. J cannot be in week 1, and if J took the week 4 seat next to L, condition 1 would need H in week 3, which is full with G and O, so J cannot be in week 4 either. So J must be week 2's partner for L, and condition 1 then needs H in week 1. Condition 4 needs K in week 1 or week 2; week 2 is now full (L, J), so K must join H in week 1. That leaves M as the only product left over, which fills week 4 alongside L. The schedule becomes week 1: H, K; week 2: L, J; week 3: G, O; week 4: L, M. Again M shares L's week 4 slot.

Step 4: Compare both cases.
Every placement above was forced by a condition rather than chosen freely, so these are the only two schedules possible once L is fixed as the repeated product. In both, M sits with L in week 4. H only joins L in Case 1, J only joins L in Case 2, and G and K never share a week with L in either case, so none of G, H, J or K is forced to sit with L across both cases. Only M is guaranteed to share a week with L no matter which case actually holds.

Final Answer:
M must always share a week with L, so option (EE), M, is correct.