Question Details

Eight persons — A, B, C, D, E, F, G and H — were born on two different dates i.e. 5th and 12th of four different months viz. January, March, April and June of the same year. No two persons were born on the same day.

C was born on an odd date in the month having even number of days. Three persons were born between C and F. As many persons were born before F as after B. Four persons were born between D and B. G was born immediately before D. A was born on an odd date. E was born before H.

The number of persons born between C and F is ______ than the number of persons born between A and G.

Options

A

One more

B

One less

C

Two more

D

Equal

Show Answer

Correct Answer :

Option B

One less

One less

Solution :

The correct option is One less.

Let us write down the chronological order of the dates along with the number of days in each month:
1. January 5 (Odd date, 31 days)
2. January 12 (Even date, 31 days)
3. March 5 (Odd date, 31 days)
4. March 12 (Even date, 31 days)
5. April 5 (Odd date, 30 days)
6. April 12 (Even date, 30 days)
7. June 5 (Odd date, 30 days)
8. June 12 (Even date, 30 days)

Now, let us analyze the clues step-by-step to place each person:
Step 1: Determine C's position.
C was born on an odd date (5th) in a month having an even number of days (April or June). Therefore, C could be born on either April 5 (Position 5) or June 5 (Position 7).

Step 2: Case Analysis.
Case 1: C is born on April 5 (Position 5).
- Three persons were born between C and F. Since C is at Position 5, F must be at Position 1 (January 5).
- As many persons were born before F as after B. Since 0 persons were born before F, 0 persons must be born after B, placing B at Position 8 (June 12).
- Four persons were born between D and B. Since B is at Position 8, D must be at Position 3 (March 5).
- G was born immediately before D, which places G at Position 2 (January 12).
- A was born on an odd date. The remaining vacant positions are 4, 6, and 7. The only odd date position left is Position 7 (June 5). Thus, A is at Position 7 (June 5).
- E was born before H. The remaining positions are 4 (March 12) and 6 (April 12). Since E was born before H, E is at Position 4 and H is at Position 6.

This gives us the complete order for Case 1:
1. Jan 5 - F
2. Jan 12 - G
3. Mar 5 - D
4. Mar 12 - E
5. Apr 5 - C
6. Apr 12 - H
7. Jun 5 - A
8. Jun 12 - B

Let us check Case 2: C is born on June 5 (Position 7).
- Three persons between C and F places F at Position 3 (March 5).
- As many before F (2 persons) as after B places B at Position 6 (April 12).
- Four persons between D and B places D at Position 1 (January 5).
- G was born immediately before D. However, D is at Position 1, so no one can be born before D. Thus, Case 2 is invalid.

Step 3: Answer the question.
- The number of persons born between C (Position 5) and F (Position 1) is 3 (namely G, D, and E).
- The number of persons born between A (Position 7) and G (Position 2) is 4 (namely D, E, C, and H).
- Comparing the two, 3 is one less than 4.

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