A five-storeyed building with floors from I to V is painted using four different colours and only one colour is used to paint a floor. Consider the following statements: 1. The middle three floors are painted in different colours. 2. The second (II) and the fourth (IV) floors are painted in different colours. 3. The first (I) and the fifth (V) floors are painted red. To ensure that any two consecutive floors have different colours:

Only statement 2 is sufficient.

Statement 1 is not sufficient, but statement 1 along with statement 2 is sufficient.

Statement 3 is not sufficient, but statement 3 along with statement 2 is sufficient.

QUESTION

CSAT

Medium

Reasoning

Prelims 2019

A five-storeyed building with floors from I to V is painted using four different colours and only one colour is used to paint a floor. Consider the following statements:

The middle three floors are painted in different colours.
The second (II) and the fourth (IV) floors are painted in different colours.
The first (I) and the fifth (V) floors are painted red.

To ensure that any two consecutive floors have different colours:

Select an option to attempt

Explanation

Statement 1 : The middle three floors are painted in different colours. Here, two conditions exist where consecutive floors can be of same colour. a) I and II floor can be of same colour. b) IV and V floor can be of same colour.

Statement 2 : The second (II) and the fourth (IV) floors are painted in different colours. Here, four conditions exist where consecutive floors can be of same colour. a) I and II floor can be of same colour. b) II and III floor can be of same colour. c) III and IV floor can be of same colour. d) IV and V can be of same colour.

Statement 3 : The first (I) and the fifth (V) floors are painted red. Here, it can be concluded that no two consecutive floors have same colour. There are four different colours and first and fifth floor are painted in red. So, three different colours are left for second, third and fourth. Therefore, from this statement it can be ensured that any two consecutive floors have different colours.

Thus, Statement 3 alone guarantees that no two consecutive floors will have the same colour, making Option B ("Only statement 3 is sufficient") the correct answer.

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