**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

### Answers and Explanations

**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.

**Answer 1 : (c)**

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.

**Answer 2 : (b)**

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.

**Answer 3 : (a)**

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.

**Answer 4 : (b)**

R can occupy only 2th or 3th or 4^{th} weeks as it comes after Q.

Similarly, Q can occupy only 1^{st}, 2^{nd} or 3^{rd} week.

T is given to be in week 3.

S also can occupy only 1^{st} or 2^{nd} week.

Hence T becomes the suitable choice among the answer options.

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