Read the given information carefully and answer the questions based on it:
Six persons visit a place on two dates 11 and 22 in three different months i.e., September, October and November. They all like different colors viz. white, blue, pink, green, red and yellow but not necessarily in the same order as given.
The one who likes yellow visits three persons after L. L and S visit on same date and in the month of even numbered days. Two persons visit between S and R who likes green. Number of persons visit before R is same as the number of persons visit after V. The one who likes white visit just before H. No one visit between K and the one who likes blue. The one who likes red visits before the one who likes pink.
Which of the following statement(s) is/are true?
I. The one who likes green is the last one to visit
II. H likes pink
III. More than two persons visit before V
Correct Answer :
Only III
Solution :
To find the correct statement(s), let us systematically determine the schedule and color preferences of the six individuals based on the given clues.
The visiting schedule consists of three months with two dates each (11 and 22):
1. September 11 (30 days - even numbered days)
2. September 22 (30 days - even numbered days)
3. October 11 (31 days - odd numbered days)
4. October 22 (31 days - odd numbered days)
5. November 11 (30 days - even numbered days)
6. November 22 (30 days - even numbered days)
Step 1: Determine the positions of L, S, R, and V
- "L and S visit on same date and in the month of even numbered days."
The months with even numbered days are September and November. Since they visit on the same date, they must both visit on either the 11th or the 22nd. Thus, one of them visits in September and the other in November.
- "The one who likes yellow visits three persons after L."
This means L must visit in September, and the one who likes yellow visits in October or November. This leaves two main possibilities for L and S:
• Case 1: L visits on September 11 (Position 1) and S visits on November 11 (Position 5).
• Case 2: L visits on September 22 (Position 2) and S visits on November 22 (Position 6).
Let us analyze these two cases:
• In Case 1, the one who likes yellow visits 3 persons after L, which is October 22 (Position 4). "Two persons visit between S and R who likes green." Since S is at Position 5, R (Green) must be at Position 2 (September 22).
"Number of persons visiting before R is same as the number of persons visiting after V." Since 1 person visits before R, exactly 1 person must visit after V, placing V at Position 5. However, S is already at Position 5. Thus, Case 1 is invalid.
• In Case 2, the one who likes yellow visits 3 persons after L, which is November 11 (Position 5). "Two persons visit between S and R who likes green." Since S is at Position 6, R (Green) must be at Position 3 (October 11).
"Number of persons visiting before R is same as the number of persons visiting after V." Since 2 persons visit before R (Positions 1 and 2), exactly 2 persons must visit after V, placing V at Position 4 (October 22).
Step 2: Determine the positions of H and K
- "The one who likes white visits just before H."
Currently, the open positions for people are Position 1, Position 5, and Position 6 (held by S). Since the white color must be immediately before H, H cannot be at Position 1. If H is at Position 5, the person at Position 4 (V) must like white. This is a valid configuration, placing H at Position 5 (November 11) and K at Position 1 (September 11).
Step 3: Assign the remaining colors
- "No one visits between K and the one who likes blue."
This means K (Position 1) is adjacent to the one who likes blue. Therefore, L (Position 2) likes blue.
- "The one who likes red visits before the one who likes pink."
The remaining colors are Red and Pink, to be assigned to K (Position 1) and S (Position 6). Since K visits before S, K likes Red and S likes Pink.
The final arrangement is as follows:
1. September 11: K (Red)
2. September 22: L (Blue)
3. October 11: R (Green)
4. October 22: V (White)
5. November 11: H (Yellow)
6. November 22: S (Pink)
Step 4: Evaluate the statements
- I. The one who likes green is the last one to visit: False. The last to visit is S (Pink), while the one who likes green (R) visits third.
- II. H likes pink: False. H likes Yellow.
- III. More than two persons visit before V: True. V visits fourth (October 22), so three persons (K, L, and R) visit before V, which is indeed more than two.
Therefore, only statement III is true.
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