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Directions for questions 1 to 4: During a four-week period each one of seven products – P,Q,R,S,T,U and V will be advertised,. A different pair of these products will be advertised each week. Exactly one of the products will be a members of two of these four pairs. None of the other products gets repeated in any pair.
Further, the following constraints must be observed: R is not advertised during a given week unless Q is advertised during the immediately preceding week. The product that is advertised twice is advertised during week 4 but is not advertised during week 3. P is not advertised during a given week unless either R or V is also advertised that week. S is advertised during one of the first two weeks. V is one of the products advertised during week 3.

Question 1 : If T 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 T is advertised?
(a). P
(b). Q
(c). U
(d). S
(e). R

Question 2 : Which one of the following could be the schedule of the advertisements?
(a). Week 1: P, R; week 2 : S, T; week 3: V,U; week 4: Q, T
(b). Week 1: Q, S; week 2: R, P; week 3: V, T;week 4: U, S
(c). Week 1: Q, S; week 2: R, U; week 3: V, T;week 4: P, U
(d). Week 1: Q, T; week 2: R, U; week 3: V, P;week 4: S, T
(e). Week 1: S, U; week 2: Q, R; week 3: V, P;week 4: T, U

Question 3 : Which one of the following is a pair of products that could be advertisement during the same week?
(a). U and V
(b). P and Q
(c). Q and R
(d).  Q and V
(e). S and V

Question 4 : Which one of the following is a product that could be advertised in any of the four weeks?
(a). Q
(b). T
(c). S
(d). R
(e). V

Solution for questions 1 to 4: From the given mother data, we have

Q ⟵R

P             P

R    or    V

S = Week 1 or 2

Week 3 = V

Week 3 = Product that is  advertised twice.

The two possible cases can be

Week 1 = Q, S

Week 2 = T, R

Week 3 = V, P

Week 4 = T, U

Or

Week 1 = Q, T

Week 2 = S, R

Week 3 = V, P

Week 4 = T, U

So option (C) is correct.

R should come after Q so, (A) and (E) are eliminated. P cannot be with U, so (C) is also eliminated. (D) cannot be the correct choice as S is not present in the first 2 weeks. So option (B) is correct.

P and Q as well as Q and R can never be together, so (B) and (C) are eliminated.

S and V cannot be together otherwise Vis in the third week and it is not the repeated element, hence (E) is eliminated.

Q and V cannot be together otherwise R would have to come before Q, hence (D) is eliminated.

Hence U and V can be together.