Question Details

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.

Which of the following statements is/are true?
I. C likes Skydiving
II. D was born in July
III. A likes Trekking

Options

A

Only III

B

Only II

C

Only I and II

D

Only II and III

E

All are true

Show Answer

Correct Answer :

Option A

Only III

Solution :

To determine which statements are true, let's systematically analyze the information provided to find the birth month and adventure activity preference for each of the six persons: A, B, C, D, E, and F.

1. Identify the given months and their order:
The six birth months in chronological order are:
1. January (Month 1)
2. March (Month 3)
3. May (Month 5)
4. July (Month 7)
5. September (Month 9)
6. November (Month 11)

2. Analyze birth order and month gaps:
Let the order of persons born from first to last be positions 1 to 6.
- "The one who likes skydiving was born four months after E."
Looking at the months: January (1) + 4 months = May (5); March (3) + 4 months = July (7); May (5) + 4 months = September (9); July (7) + 4 months = November (11).
So, the possible pairs for (E, Skydiving) based on birth months are:
- (January, May)
- (March, July)
- (May, September)
- (July, November)

- "The number of persons born before E is one more than the number of persons born after D."
Let x be the number of persons born after D. The number of persons born before E is x+1.
Since there are 6 persons in total (positions 1 to 6):
- If D is at position 6 (0 born after), E must be at position 2 (1 born before).
- If D is at position 5 (1 born after), E must be at position 3 (2 born before).
- If D is at position 4 (2 born after), E must be at position 4 (3 born before) - Not possible as they are distinct persons.
- If D is at position 3 (3 born after), E must be at position 5 (4 born before).
- If D is at position 2 (4 born after), E must be at position 6 (5 born before).
Also, "B was born after E."

- "D was born immediate after the one who likes scuba diving."
This means the person immediately preceding D in the sequence of birth months likes Scuba Diving.

- "Two persons were born between the ones who like scuba diving and rafting."
This means there are two positions between Scuba Diving and Rafting.

- "A was born two months after the one who likes rafting."
Looking at the months, since the differences between consecutive months in the list are all exactly 2 months (January to March is 2, March to May is 2, etc.), "born two months after" means A is born in the month immediately following the one who likes Rafting in our sequence of six months.

- "Three persons were born between A and the one who likes Paragliding."
This means there are exactly three positions between A and the Paragliding lover.

3. Let's test the cases:

Case 1: D is at position 6 (November), E is at position 2 (March).
If E is in March, the one who likes Skydiving is born 4 months after E (March + 4 = July, which is position 4).
- D is at position 6 (November).
- The one who likes Scuba Diving is at position 5 (September), since D is born immediately after.
- Two persons were born between Scuba Diving (5) and Rafting. This places Rafting at position 2 (March), which is E.
- A was born two months after the one who likes Rafting (March). So A was born in May (position 3).
- Three persons were born between A (position 3) and Paragliding. The only possible position for Paragliding is 3 - 4 (not possible) or 3 + 4 = 7 (not possible since there are only 6 positions). Thus, Case 1 is invalid.

Case 2: D is at position 5 (September), E is at position 3 (May).
If E is in May, the one who likes Skydiving is born 4 months after E (May + 4 = September, which is position 5). But position 5 is D. So D likes Skydiving.
- D is at position 5 (September).
- The one who likes Scuba Diving is at position 4 (July).
- Two persons were born between Scuba Diving (4) and Rafting. This places Rafting at position 1 (January).
- A was born two months after Rafting (January). So A was born in March (position 2).
- Three persons were born between A (position 2) and Paragliding. This places Paragliding at position 6 (November) (since 2 + 4 = 6).
- We are told "B was born after E (position 3)". The available positions for B are 4 (July) or 6 (November).
- "Two persons were born between C and the one who likes bungee Jumping."
Let's look at the remaining positions for the people A (2), D (5), E (3). The remaining positions to assign to B, C, F are 1, 4, 6.
If C is at position 1 (January), the person who likes Bungee Jumping must be at position 4 (July) (since 1 + 3 = 4, leaving 2 positions in between, which are positions 2 and 3). This is valid.
Then B (who must be born after E) must be at position 6 (November), leaving F at position 4 (July).
Let's check the assignments:
1. January: C - Rafting
2. March: A - Trekking (remaining activity)
3. May: E - Bungee Jumping (if not at 4, let's check: Bungee Jumping is at position 4, which is F)
Wait, if C is at 1, the one who likes Bungee Jumping is at 4 (F). This works!
Let's list the full valid arrangement:
- January: C, likes Rafting
- March: A, likes Trekking
- May: E, likes Bungee Jumping (or Bungee Jumping is at 4)
Let's re-verify the Bungee Jumping clue: "Two persons were born between C (1) and the one who likes bungee Jumping (4)". So the person at position 4 (F) likes Bungee Jumping. Since position 4 is Scuba Diving, this is a contradiction because F cannot like both Scuba Diving and Bungee Jumping. Let's try placing C at position 6 (November). Then Bungee Jumping must be at position 3 (May) (since 6 - 3 = 3, leaving positions 4 and 5 in between). This works! So E (May) likes Bungee Jumping. Then B (who is born after E) must be at position 6 (November) since C is already at 6? No, B and C cannot both be at 6. If C is at 6, B cannot be at 6. Since B must be born after E (3), and the available positions left for B and F are 1 and 4, B cannot be after E because neither 1 nor 4 is after 3 (since 4 is Scuba Diving/F, and if B is at 4, it works!). Let's assign:
- 1 (January): F, likes Rafting
- 2 (March): A, likes Trekking
- 3 (May): E, likes Bungee Jumping
- 4 (July): B, likes Scuba Diving
- 5 (September): D, likes Skydiving
- 6 (November): C, likes Paragliding
Let's check all clues with this schedule:
- Skydiving (D, September) is 4 months after E (May). (True, May + 4 = September)
- Persons before E (2) is one more than persons after D (1). (True, 2 = 1 + 1)
- D (5) born immediate after Scuba Diving (B, 4). (True)
- Two persons between Scuba Diving (B, 4) and Rafting (F, 1). (True, 2 and 3 are in between)
- A (2, March) born two months after Rafting (F, 1, January). (True)
- Three persons between A (2) and Paragliding (C, 6). (True, 3, 4, 5 are in between)
- Two persons between C (6) and Bungee Jumping (E, 3). (True, 4 and 5 are in between)
- B (4) born after E (3). (True)
This schedule is completely consistent!

4. Evaluate the Statements:
- I. C likes Skydiving: False (C likes Paragliding; D likes Skydiving)
- II. D was born in July: False (D was born in September)
- III. A likes Trekking: True (A was born in March and likes Trekking)

Therefore, only statement III is true.

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