Read the following information carefully and answer the questions.
Six persons – A, B, C, D, E and F were born in six different months of the same year – January, March, May, July, September and November (not necessarily in the same order). Each of them also likes a different adventure activity – Trekking, Paragliding, Scuba Diving, Rafting, Skydiving and Bungee Jumping (not necessarily in the same order).
The one who likes skydiving was born four months after E. The number of persons born before E is one more than the number persons born after D. D was born immediate after the one who lives scuba diving. Two persons were born between the ones who like scuba diving and rafting A was born two months after the one who likes rafting. Three persons were born between A and the one who likes Paragliding. Two persons were born between C and the one who likes bungee Jumping. B was born after E.
How many persons were born between C and the one who likes trekking?
Correct Answer :
Three
Solution :
To find the number of persons born between C and the one who likes trekking, let's reconstruct the birth order and preferences of the six persons step-by-step.
We are given six months of the same year: January, March, May, July, September, and November.
Let us represent the positions of these months in chronological order:
1. January (1st month)
2. March (3rd month)
3. May (5th month)
4. July (7th month)
5. September (9th month)
6. November (11th month)
Step 1: Locate E and Skydiving
The clue states: "The one who likes skydiving was born four months after E."
Let's look at the gaps between the given months:
- March is 2 months after January.
- May is 2 months after March, 4 months after January.
- July is 2 months after May, 4 months after March.
- September is 2 months after July, 4 months after May.
- November is 2 months after September, 4 months after July.
Thus, the pairs of months that are exactly 4 months apart are:
- January (E) and May (Skydiving)
- March (E) and July (Skydiving)
- May (E) and September (Skydiving)
- July (E) and November (Skydiving)
Step 2: Use the clue about E and D
"The number of persons born before E is one more than the number of persons born after D."
Let's analyze the possibilities for E:
- If E is born in January (0 persons before E), then the number of persons born after D must be -1, which is impossible.
- If E is born in March (1 person before E), then the number of persons born after D is 0 (1 - 1 = 0). This means D is born in November (6th month).
- If E is born in May (2 persons before E), then the number of persons born after D is 1. This means D is born in September (5th month).
- If E is born in July (3 persons before E), then the number of persons born after D is 2. This means D is born in July (4th month). But E and D cannot be born in the same month.
- If E is born in September (4 persons before E), then the number of persons born after D is 3. This means D is born in May (3rd month).
- If E is born in November (5 persons before E), then the number of persons born after D is 4. This means D is born in March (2nd month).
Let's also consider: "D was born immediate after the one who likes scuba diving."
This means the person born in the month just before D likes Scuba Diving. Therefore, D cannot be born in January.
Let's test Case A: E is in March
- E is in March.
- Skydiving is in July (since Skydiving is 4 months after E, i.e., March + 4 months = July).
- D is in November (since 1 person is before E, so 0 persons must be after D).
- The one who likes Scuba Diving is born immediately before D, which means Scuba Diving is in September.
- "Two persons were born between the ones who like scuba diving and rafting."
If Scuba Diving is in September (5th position), then two persons born between means the other is at the 2nd position (March), which is E. So E likes Rafting.
- "A was born two months after the one who likes rafting."
The one who likes Rafting is E (March). Two months after March is May. Thus, A was born in May.
- "Three persons were born between A and the one who likes Paragliding."
A is in May (3rd position). The positions are 1st (Jan), 2nd (Mar), 3rd (May), 4th (July), 5th (Sept), 6th (Nov).
If A is in 3rd position, we cannot have 3 persons between A and another position (only 2 positions before, and 3 positions after, so the other would have to be in the 7th position, which doesn't exist). Thus, Case A is invalid.
Let's test Case B: E is in May
- E is in May (3rd position).
- Skydiving is in September (5th position) (since September is 4 months after May).
- Number of persons before E is 2 (Jan, Mar). So the number of persons after D is 2 - 1 = 1. Thus, D is in September (5th position).
But Skydiving is in September, and D is in September, which is consistent since D can like Skydiving. Let's check: "D was born immediate after the one who likes scuba diving."
Since D is in September (5th position), the one who likes Scuba Diving must be in July (4th position).
- "Two persons were born between the ones who like scuba diving and rafting."
Scuba Diving is in July (4th position). The one who likes Rafting must be in January (1st position), as 2 persons (born in March and May) are between them.
- "A was born two months after the one who likes rafting."
The one who likes Rafting is in January. Two months after January is March. Thus, A is born in March (2nd position).
- "Three persons were born between A and the one who likes Paragliding."
A is in March (2nd position). Three persons between A (2nd) and Paragliding means Paragliding must be in November (6th position) (with May, July, and September in between). So the person born in November likes Paragliding.
- "Two persons were born between C and the one who likes bungee Jumping."
Let's see the remaining months for the persons: January, March (A), May (E), July, September (D), November.
The remaining positions for persons are January, July, and November.
If C is in January:
The one who likes Bungee Jumping must be in July (2 persons between Jan and July: March and May). This is a valid configuration.
If C is in July:
The one who likes Bungee Jumping would have to be in January or November. But there is only 1 person between July and November, and 2 persons between January and July. So if C is in July, Bungee Jumping is in January.
Let's check the clue: "B was born after E."
E is in May (3rd position). The remaining spots for B are July (4th) or November (6th) (since A is in March, D is in September, E is in May).
If C is in January:
- January = C (likes Rafting)
- March = A
- May = E
- July = B (since B is born after E, and July is available. B likes Scuba Diving, and the one who likes Bungee Jumping is B, which is July)
- September = D (likes Skydiving)
- November = F (since F is the only remaining person. F likes Paragliding)
Let's check the activities:
- C (Jan) = Rafting
- A (Mar) = Bungee Jumping (since July is Bungee Jumping, wait. If C is in Jan, the person who likes Bungee Jumping is in July, so July is Bungee Jumping. But July was Scuba Diving. That's a conflict: July cannot be both Scuba Diving and Bungee Jumping).
Let's re-evaluate: "Two persons were born between C and the one who likes bungee Jumping."
If C is in July (4th position):
- The one who likes Bungee Jumping must be in January (1st position) (with March and May in between).
So January likes Bungee Jumping.
Let's check if this works:
- January = Bungee Jumping (Rafting was also in January, so this is a conflict, because January must like Rafting from the previous clue: "Two persons were born between Scuba Diving (July) and Rafting"). Thus, January must like Rafting. This is a contradiction.
Let's test Case C: E is in July
- E is in July (4th position).
- Skydiving is in November (6th position) (4 months after July).
- Number of persons before E is 3. Number of persons after D must be 2. So D is in July (4th position). But E is in July, contradiction.
Let's test Case D: E is in September
- E is in September (5th position).
- Skydiving is in January (1st position) - wait, "Skydiving was born four months after E", so E must be born before Skydiving. E (Sept) + 4 months = January (next year), which is not possible since they are born in the same year. So this is invalid.
Let's re-evaluate the month gaps. Let's list the months and their numerical values:
- Jan = 1
- Mar = 3
- May = 5
- July = 7
- Sept = 9
- Nov = 11
Let's re-test E and Skydiving: "The one who likes skydiving was born four months after E."
- If E = Jan (1), Skydiving = May (5)
- If E = Mar (3), Skydiving = July (7)
- If E = May (5), Skydiving = Sept (9)
- If E = July (7), Skydiving = Nov (11)
Let's check E = July (7) again:
- Persons before E (July) = 3 (Jan, Mar, May).
- Persons after D = 3 - 1 = 2.
- This means D is in July (4th position). But E is in July (4th position). That's a contradiction since they are different persons.
Let's check E = Jan (1):
- Persons before E = 0.
- Persons after D = 0 - 1 = -1 (impossible).
Let's check if the number of persons born before E is one more than the number of persons born after D:
Let be the number of persons before E, and be the number of persons after D.
Since there are 6 positions (0, 1, 2, 3, 4, 5 persons before/after):
- If E is 1st (Jan): (impossible)
- If E is 2nd (Mar): is 6th (Nov)
- If E is 3rd (May): is 5th (Sept)
- If E is 4th (July): is 4th (July) (contradiction: E and D cannot be same)
- If E is 5th (Sept): is 3rd (May)
- If E is 6th (Nov): is 2nd (Mar)
Let's test E is 5th (September):
- E is in September.
- Skydiving is 4 months after E: September (9) + 4 = 13 (not in the list). Wait, is Skydiving 4 months after E? If E is in July (7), Skydiving is in November (11).
But what if E is in May (5)? Then Skydiving is in September (9).
Wait, let's check: "B was born after E."
- If E is in September (5th), then B (born after E) must be in November (6th). This is possible!
Let's check: E is 5th (Sept).
- D is 3rd (May) (since is 3rd).
- "D was born immediate after the one who lives scuba diving." (Note: "lives" is a typo for "likes" in the source text).
So Scuba Diving is born immediate before D. Since D is 3rd (May), Scuba Diving must be 2nd (March).
- "Two persons were born between the ones who like scuba diving and rafting."
Scuba Diving is 2nd (March). Two persons between 2nd and rafting means rafting must be 5th (September) (which is E). So E likes Rafting.
- "A was born two months after the one who likes rafting."
Rafting is in September (9). Two months after September is November (11). Thus, A was born in November (6th position).
- "Three persons were born between A and the one who likes Paragliding."
A is in November (6th). Three persons between 6th and Paragliding means Paragliding must be in January (1st) (with Mar, May, July in between). So January likes Paragliding.
- "The one who likes skydiving was born four months after E."
E is in September (9). Four months after September is November (11) (actually 9 + 4 = 13, but November is 11, so 9 to 11 is 2 months). Wait, September is 9th month, November is 11th month. That is 2 months. Let's re-read: "The one who likes skydiving was born four months after E."
If E is in May (5), then 4 months after May is September (9). E is 3rd position (May), Skydiving is 5th position (Sept). Let's re-verify this case:
Wait, if E is in May (5), then D is in September (9, 5th position).
Scuba Diving is immediately before D, so July (4th position).
Rafting is 2 persons away from July, which is January (1st position).
A is born 2 months after Rafting (January + 2 months = March, 2nd position).
Three persons between A (2nd) and Paragliding (6th, November).
C and Bungee Jumping has 2 persons between them:
If C is in July (4th), Bungee Jumping is in January (1st). But January likes Rafting. Conflict.
What if C is in November (6th)? Then Bungee Jumping is in May (3rd). Let's check this:
- Jan (1st): Rafting (Person F or B)
- Mar (2nd): A (likes Bungee Jumping? No, Bungee Jumping is in May, let's see. If C is in Nov, Bungee Jumping is in May, so E likes Bungee Jumping. But E was born in May, so E likes Bungee Jumping. This works!)
Let's check the assignments:
- Jan (1st): B (likes Rafting) (since B is born after E? No, E is in May, B is born after E, so B cannot be in January).
Thus, the person in January must be F. So F likes Rafting.
- Mar (2nd): A
- May (3rd): E (likes Bungee Jumping)
- July (4th): C (likes Scuba Diving)
- Sept (5th): D (likes Skydiving)
- Nov (6th): B (likes Paragliding) (B is born after E (May), so B in November is correct).
Let's check the activities for each person:
- January: F (Rafting)
- March: A (Trekking)
- May: E (Bungee Jumping)
- July: C (Scuba Diving)
- September: D (Skydiving)
- November: B (Paragliding)
This satisfies all conditions!
Let's double check:
- "Two persons were born between C and the one who likes bungee Jumping."
C is in July (4th). Bungee Jumping is in May (3rd). The number of persons between July and May is 0 (immediate). Wait, the clue says: "Two persons were born between C and the one who likes bungee Jumping."
In our setup, C is in July (4th) and Bungee Jumping is in May (3rd). There are 0 persons between them. So this is a conflict.
Let's check if C is in November (6th):
- If C is in November (6th), the two persons between C and Bungee Jumping means Bungee Jumping must be in May (3rd) (since July and Sept are in between). This matches! E is in May, so E likes Bungee Jumping.
Let's assign the remaining persons:
- Jan (1st): F (likes Rafting)
- Mar (2nd): A (likes Trekking)
- May (3rd): E (likes Bungee Jumping)
- July (4th): B (likes Scuba Diving) (B is born after E, and July is after May, so this works!)
- Sept (5th): D (likes Skydiving)
- Nov (6th): C (likes Paragliding)
Let's check if all conditions are met:
1. E is born in May. Skydiving (Sept) is born four months after E (May to Sept is 4 months). (Correct)
2. Number of persons born before E (Jan, Mar = 2) is one more than number of persons born after D (Nov = 1). (Correct, 2 is one more than 1)
3. D (Sept) was born immediate after the one who likes Scuba Diving (July). (Correct)
4. Two persons were born between Scuba Diving (July) and Rafting (Jan). (Correct: Mar, May)
5. A (Mar) was born two months after Rafting (Jan). (Correct: Jan to Mar is 2 months)
6. Three persons were born between A (Mar) and Paragliding (Nov). (Correct: May, July, Sept)
7. Two persons were born between C (Nov) and Bungee Jumping (May). (Correct: July, Sept)
8. B (July) was born after E (May). (Correct)
9. The activities are: Rafting, Trekking (A), Bungee Jumping (E), Scuba Diving (B), Skydiving (D), Paragliding (C). (Correct, all 6 activities are uniquely distributed)
Therefore, the arrangement is:
- January: F (Rafting)
- March: A (Trekking)
- May: E (Bungee Jumping)
- July: B (Scuba Diving)
- September: D (Skydiving)
- November: C (Paragliding)
Step 3: Answer the Question
We need to find how many persons were born between C and the one who likes trekking:
- C was born in November.
- The one who likes trekking is A, who was born in March.
- The persons born between March (A) and November (C) are E (May), B (July), and D (September).
- Thus, there are exactly 3 persons born between C and the one who likes trekking.
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