Read the following and answer the questions that follow
(i) There are three houses on each side of the road.
(ii) These six houses are labelled as P, Q, R, S, T and U.
(iii) The houses are of different colours, namely, Red, Blue, Green, Orange, Yellow and White.
(iv) The houses are of different heights.
(v) T, the tallest house, is exactly opposite to the Red coloured house.
(vi) The shortest house is exactly opposite to the Green coloured house.
(vii) U, the Orange coloured house, is located between P and S.
(viii) R, the Yellow coloured house, is exactly opposite to P.
(ix) Q, the Green coloured house, is exactly opposite to U.
(x) P, the White coloured house, is taller than R, but shorter than S and Q.
[CAT 2008]
13) What is the colour of the tallest house?
(1) Red
(2) Blue
(3) Green
(4) Yellow
(5) None of these
14) What is the colour of the house diagonally opposite to the Yellow coloured house?
(1) White
(2) Blue
(3) Green
(4) Red
(5) None of these
15) Which is the second tallest house?
(1) P
(2) S
(3) Q
(4) R
(5) Cannot be Determined
Solution
Case Solution:
Each house is of a different height than the other. Hence, let's rank them from 1 to 6, with 1 being the tallest and 6 being the shortest.
3 houses are on one side of the road and 3 houses are on the other side. Looking at the clues, there is no mention of North, South, East or West. Hence, it does not matter on which side of the road we start the case with.
U, the orange coloured house is in between two houses, P and S. So, U has to be the middle house on one side of the road.
From the above statement we can deduce that we have houses P, U and S on one side. Therefore, we have houses Q, R and T on the other side.
Q, the green coloured house is opposite to U. Hence, Q is the middle house on the other side of the row. Also, the house opposite to the green coloured house is the shortest house, so, U is rank 6 in terms of height.
Based on the position of P and S we can form two cases:
Case 1:
Case 2:
R, the yellow coloured house, is opposite to P and so, S and T are opposite to each other.
T the tallest house, ranked 1, is opposite to the red coloured house. Hence, S is the red coloured house.
P is the white coloured house which leaves us with only T which has to be the blue coloured house.
Case 1:
Case 2:
Q/S > P > R . With T and U taking rank 1 and rank 6 respectively there are only 4 ranks available.
Hence, R has to be the second shortest house taking the 5
th rank followed by P taking the 4
th rank.
Q and S can take either rank 2 or rank 3. There is no way of allotting them with unique ranks.
Case 1:
Case 2:
13) The tallest house is T and T is the blue coloured house.
Answer: (2) Blue
14) The yellow coloured house, R is the corner house and the house diagonally opposite to the corner house is also a corner house. S, the red coloured house is diagonally opposite to the yellow coloured house.
Answer: (4) Red
15) The second tallest house is the house that is ranked 2. Since ranks 2 and 3 cannot be uniquely allotted to P and Q, it is impossible to determine the second tallest house from this case. Hence, the answer cannot be determined.
Answer: (5) cannot be determined
Answer:
13) (2) Blue
14) (4) Red
15) (5) cannot be determined
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