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 could be the schedule of the advertisements?

• A. Week 1: G, J; Week 2: K, L; Week 3: O, M; Week 4: H, L
• B. Week 1: H, K; Week 2: J, G; Week 3: O, L; Week 4: M, K
• C. Week 1: H, K; Week 2: J, M; Week 3: O, L; Week 4: G, M
• D. Week 1: H, L; Week 2: J, M; Week 3: O, G; Week 4: K, L

Hint:

Check each schedule against the rule that ties J to the week right after H, since that one rule eliminates most of the options fastest.

Answer 1

The Correct Option is B

Step 1: Work out where the fixed anchors must sit.
Condition 5 places O in week 3 without exception. Condition 4 forces K into week 1 or week 2. Condition 2 forces the single repeated product into week 4, and bans it from week 3. Build the four weekly pairs around these three anchors instead of testing the four given schedules one by one.

Step 2: Place G and J using their linked rule.
Condition 3 ties G to a week that also carries J or O. Condition 1 ties J to a week that comes right after a week carrying H. A simple way to satisfy both at once is to advertise J and G together in the same week, right after a week that carries H. Try: week 1 carries H, and week 2 carries J together with G. That clears condition 1 (H precedes J) and condition 3 (J sits with G) in one move.

Step 3: Fill the remaining weeks with the leftover products.
Week 1 already carries H; condition 4 needs K somewhere in week 1 or week 2, and week 2 is full (J, G), so K must join H in week 1: week 1 becomes H, K. Two products are still unplaced, L and M, and neither carries any restriction of its own. Week 3 needs a second product alongside O, and week 4 needs the repeated product plus one more seat. Placing L with O in week 3, and letting K repeat into week 4 alongside M, uses up every product exactly as the rules require.

Step 4: Read off the built schedule and match it to the choices.
Built this way, the schedule reads: week 1, H and K; week 2, J and G; week 3, O and L; week 4, M and K (K repeating). This is exactly what option (BB) states, Week 1: H, K; Week 2: J, G; Week 3: O, L; Week 4: M, K. The other three schedules each break one of the five conditions on inspection (A puts J in week 1 with no H before it, C leaves G in week 4 with no J or O beside it, D never gives K a slot in week 1 or week 2), so none of them can be the answer.

Final Answer:
The schedule that matches every condition is option (BB): Week 1: H, K; Week 2: J, G; Week 3: O, L; Week 4: M, K.