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 product that could be advertised in any of the four weeks?

• A. H
• B. J
• C. K
• D. L

Hint:

Look for the one product that is never named in any of the five given conditions, since that is the one free to move to any week.

Answer 1

The Correct Option is D

Step 1: Understanding the Approach.
Instead of building full schedules first, count how many of the five given rules mention each product by name. A product named in a rule can be pushed out of some week by that rule. A product never named cannot be directly blocked by any rule.

Step 2: Count the mentions.
Rule 1 names J and H. Rule 2 singles out whichever product repeats, without naming one product in particular. Rule 3 names G, J and O. Rule 4 names K. Rule 5 names O. Tallying this up across the seven products G, H, J, K, L, M, O: H, J, K, O and G are each named in at least one rule. L and M are the only two never named directly, so both deserve a closer look rather than picking L by name-count alone.

Step 3: Confirm H, J and K are genuinely blocked from some week, matching the count.
H is blocked from week 3, since putting H there forces J into week 4 (the only week right after a H-week), which then forces G into week 4 too to satisfy rule 3, filling week 4 with two single-appearance products and leaving no seat for the twice-advertised product rule 2 requires there. J is blocked from week 1, since rule 1 needs H the week before J, and week 1 has no earlier week. K is blocked from week 3, since rule 4 needs K in week 1 or week 2 at least once, and even a repeated K is sent to week 4 by rule 2, never week 3. The count correctly flagged all three as restricted.

Step 4: Confirm L is genuinely free, since it was one of the two unnamed products among the options.
With no rule naming L, the only way L could still be secretly restricted is if every valid full schedule happened to push it out of some week anyway. Checking concrete valid schedules for this set (one with L in weeks 1 and 4, one with L in weeks 2 and 4, one with L in week 3) confirms all four weeks are actually reachable for L, so the name-count shortcut holds up here.

Step 5: Final Answer.
Among the four options given, H, J and K are each ruled out by a specific condition, while L is confirmed to reach every week in real valid schedules, so option (DD), L, is the product that could be advertised in any of the four weeks.