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: Pin down the rule that breaks most wrong schedules.
Seven products fill eight weekly slots (four weeks, two products a week), so exactly one product repeats and the other six appear once each. Condition 2 says the repeated product sits in week 4 and never in week 3. Keep this rule ready, since it is what rules out two of the four schedules below.

Step 2: Test option (AA): Week 1: G, J; Week 2: K, L; Week 3: O, M; Week 4: H, L.
Condition 1 says J can only be advertised in a week if H was advertised the week right before it. J sits in week 1 here, and there is no week before week 1 for H to occupy. So J cannot legally open the schedule at all. Option A breaks condition 1 straight away and is rejected.

Step 3: Test option (BB): Week 1: H, K; Week 2: J, G; Week 3: O, L; Week 4: M, K.
J is in week 2, and H sits in week 1 right before it, so condition 1 holds. G is in week 2 along with J, so condition 3 (G needs J or O in its own week) also holds. K appears in week 1, which satisfies condition 4 (K in one of the first two weeks), and K repeats in week 4, which fits condition 2 since the repeat lands in week 4 and never touches week 3. O sits in week 3 as condition 5 demands. Every rule checks out, so option B is a fully valid schedule.

Step 4: Test option (CC): Week 1: H, K; Week 2: J, M; Week 3: O, L; Week 4: G, M.
G sits in week 4 here, paired only with M. Condition 3 needs J or O in the same week as G, but week 4 has neither. Option C breaks condition 3 and is rejected.

Step 5: Test option (DD): Week 1: H, L; Week 2: J, M; Week 3: O, G; Week 4: K, L.
Condition 4 says K must be advertised in one of the first two weeks. In this schedule K shows up only in week 4, never in week 1 or week 2. That breaks condition 4, so option D is rejected.

Final Answer:
Only option B, Week 1: H, K; Week 2: J, G; Week 3: O, L; Week 4: M, K, satisfies every condition, so option B is correct.