**Direction for the questions: (1- 5:)** In a reality show, there are five contestants Ripal, Soniya ,Taniya , Usha , and Vaishali .

The contestants are awarded stars in the show. The winner will be selected on the bases of the number of stars won by a contestant.

• Five stars for the best performer, and four, three, two and one stars for the successive contestants.

• The stars are awarded for the following criteria: packs, acting and confidence

• The candidate who receives the highest total numbers of stars wins. If a tie occurs, the contestant with the maximum numbers of five stars will be the winner.

• Ripal gets the maximum stars in packs and acting.

• Taniya gets the minimum stars in packs and acting.

• Soniya gets 2 stars in packs and acting, and one star in confidence.

• Usha gets 5 stars in confidence

• Vaishali gets 4 stars in acting

**Question 1:** Any candidate can receive a maximum of how many stars?

(a) 30

(b) 20

(c) 15

(d) 25

**Question 2:** If no candidate gets the same number of stars in any two of the categories, the highest number of stars possible is

(a) 14

(b) 16

(c) 12

(d) 18

**Question 3:** If Soniya and Vaishali receive all the one and two star ratings between them and Ripal, Taniya and Usha each receive one five star rating, how many stars in addition to the 5 would Ripal need to win the contest without a tie?

(a) 5

(b) 6

(c) 4

(d) 8

**Question 4:** What is the maximum number of stars Ripal can get in all and still lose?

(a) 12

(b) 14

(c) 13

(d) 11

**Question 5:** For Usha to win under all conditions, Ripal can score a maximum of how many stars in confidence?

(a) 3

(b) 2

(c) 1

(d) 4

### Answers and Explanations

**Explanation for questions 4 and 5**:

**Answer 1 : (c)**

The maximum number of stars can be achieved when the person is the best performer in all categories. i.e packs , acting and confidence. Since the maximum are 5 stars in each category, the maximum total possible is 15.

**Answer 2 : (c)**

If no candidate gets the same number of stars in any two of the categories, that means a candidate can only get 5, 4 and 3 stars in three categories. These are the maximum possible number of stars that a contestant can get. Thus, the highest possible number of stars that any contestant can get is 12.

**Answer 3 : (d)**

Since all the one star, two star and five star ratings are gone, if we give three stars and four stars to one contestant, some else will also get the same combination. Thus, two 4 stars i.e 8 stars in total have to be given to Ripal to ensure she wins this competition.

**Answer 4 : (c)**

Ripal can get a maximum of 13 stars and still lose. This is shown below:

**Answer 5 : (b)**

For Usha to always win, Ripal cannot score more than 2 stars.