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 :
Based on the clues given, let us analyze the schedule step-by-step.
The six visits occur on the following six dates:
1. September 11
2. September 22
3. October 11
4. October 22
5. November 11
6. November 22
Step 1: Determine the positions of L, S, and R.
• The months with even number of days (30 days) are September and November.
• We are told that L and S visit on the same date and in a month with an even number of days. This means one of them visits in September and the other in November, both on either the 11th or the 22nd.
• "The one who likes yellow visits three persons after L." This means if L is at position x, the yellow-color liker is at position x + 3. Thus, L can only be at position 1, 2, or 3. Since L must be in September (even-day month), L can be on September 11 (position 1) or September 22 (position 2).
• If L is on September 11 (position 1):
S must be on November 11 (position 5).
Two persons visit between S and R, which places R at position 2 (September 22). R likes green.
• If L is on September 22 (position 2):
S must be on November 22 (position 6).
Two persons visit between S and R, which places R at position 3 (October 11). R likes green.
Step 2: Find the position of V.
• "Number of persons visiting before R is same as the number of persons visiting after V."
• Case A: R is at position 2.
Number of persons before R is 1. Thus, number of persons after V must be 1, placing V at position 5 (November 11). However, S is already at position 5, causing a contradiction.
• Case B: R is at position 3.
Number of persons before R is 2. Thus, number of persons after V must be 2, placing V at position 4 (October 22). This is a valid configuration.
Step 3: Determine the remaining positions.
Currently, we have:
1. September 11: (Vacant)
2. September 22: L
3. October 11: R (Green)
4. October 22: V
5. November 11: (Vacant - likes Yellow, since Yellow is 3 positions after L, i.e., 2 + 3 = 5)
6. November 22: S
Step 4: Place H, K, and assign colors.
• "The one who likes white visits just before H."
• Since positions 1 and 5 are the remaining vacant spots for the people K and H:
If H is at position 1, white must visit before H (at position 0), which is impossible.
Thus, H must be at position 5, and K must be at position 1.
Consequently, the person visiting just before H (position 4, V) likes White.
• "No one visits between K and the one who likes blue."
This means the person next to K (position 1) must like blue, so L (position 2) likes Blue.
• Now, the remaining colors are red and pink.
• "The one who likes red visits before the one who likes pink."
This means K (position 1) likes Red, and S (position 6) likes Pink.
Final Arrangement:
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)
Evaluating the Statements:
• I. The one who likes green is the last one to visit: False. R (Green) is at position 3, while S (Pink) is the last one at position 6.
• II. H likes pink: False. H likes Yellow.
• III. More than two persons visit before V: True. Three persons (K, L, R) visit before V.
Therefore, only statement III is true.
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