Which among the following statement is not true? Study the following information carefully and answer the questions given below:
Ten persons- A, B, C, D, E, F, G, H, I and J have exam (but not necessarily in the same order) on two different dates either 8th or 11th of four different months - April, May, June, July and August of the same year.
Only three persons have exam between H and C who has exam in the month which has 31 days and on an odd numbered date. As many persons have exam after C as before I. C and E does not have exam in the same month. F has exam three persons after I. Only two persons have exam between E and A who has exam in the month which has 30 days. G has exam immediately after month of E but not in the same month as F. B has exam after G and both have exam on the same date. J has exam immediately before B.

Correct Option: More than five persons have exam before H

Step-by-Step Explanation:

Let's analyze the given clues step-by-step to determine the exact schedule of the exam for all 10 persons (A, B, C, D, E, F, G, H, I, J) across the 5 months (April, May, June, July, August) on two dates (8th and 11th).

1. Structure of Exam Dates:
- April 8 (30 days)
- April 11 (30 days)
- May 8 (31 days)
- May 11 (31 days)
- June 8 (30 days)
- June 11 (30 days)
- July 8 (31 days)
- July 11 (31 days)
- August 8 (31 days)
- August 11 (31 days)

2. Placing C, H, I, and F:
- C has an exam in a month with 31 days and on an odd-numbered date (11th). So, C can be on May 11, July 11, or August 11.
- "Only three persons have exam between H and C":
- If C is on August 11 (10th slot), H would be on June 8 (6th slot).
- If C is on May 11 (4th slot), H would be on July 8 (7th slot) or April 8 (1st slot).
- If C is on July 11 (8th slot), H would be on May 8 (3rd slot).
- "As many persons have exam after C as before I":
- If C is on August 11 (0 persons after C), I must be on April 8 (0 persons before I).
- "F has exam three persons after I" (meaning F is 3rd after I / 3 slots down from I, or 4th position):
- If I is on April 8 (slot 1), F is 3 persons after I, which means F is on May 11 (slot 4).
- Let's check this arrangement:
- Slot 1 (April 8): I
- Slot 2 (April 11):
- Slot 3 (May 8):
- Slot 4 (May 11): F
- Slot 5 (June 8): H
- Slot 6 (June 11):
- Slot 7 (July 8):
- Slot 8 (July 11):
- Slot 9 (August 8):
- Slot 10 (August 11): C

3. Placing E, A, G, B, J, and D:
- "C and E does not have exam in the same month": C is in August, so E cannot be in August.
- "Only two persons have exam between E and A who has exam in the month which has 30 days": A must be in April (30 days) or June (30 days).
- "G has exam immediately after month of E but not in the same month as F":
- F is in May. So G cannot be in May.
- If E is in April, G must be in May, which contradicts "not in the same month as F".
- Therefore, E must be in May (May 8 or May 11, but May 11 is F, so E = May 8).
- If E is on May 8 (slot 3), G has exam immediately after month of E (June), so G is in June.
- "Only two persons have exam between E and A":
- Since E is at slot 3 (May 8), A can be 2 persons away at slot 6 (June 11), which is a 30-day month.
- "G has exam immediately after month of E": G is in June. G can be June 8 or June 11. But June 8 is H and June 11 is A, so let's re-evaluate slot positions carefully:
- Slot 1 (Apr 8): I
- Slot 2 (Apr 11): J
- Slot 3 (May 8): E
- Slot 4 (May 11): F
- Slot 5 (Jun 8): H
- Slot 6 (Jun 11): A
- Slot 7 (Jul 8): G
- Slot 8 (Jul 11): D
- Slot 9 (Aug 8): B
- Slot 10 (Aug 11): C
- Let's check G and B on the same date:
- G = July 8 (8th date), B = August 8 (8th date). Both are on the 8th.
- J has exam immediately before B: J would be July 11, but let's check J before B on April 11 (8th date matches B on August 8).
- Let's verify all clues for the complete sequence:
1. April 8: I
2. April 11: D
3. May 8: E
4. May 11: F
5. June 8: H
6. June 11: A
7. July 8: G
8. July 11: J
9. August 8: B
10. August 11: C

4. Final Schedule Verification:
- Slot 1 (Apr 8): I
- Slot 2 (Apr 11): D
- Slot 3 (May 8): E
- Slot 4 (May 11): F
- Slot 5 (Jun 8): H
- Slot 6 (Jun 11): A
- Slot 7 (Jul 8): G
- Slot 8 (Jul 11): J
- Slot 9 (Aug 8): B
- Slot 10 (Aug 11): C

5. Checking the Options to find the NOT TRUE statement:
- No one has exam after C: True (C is on August 11, the last date).
- More than five persons have exam before H: H is at position 5 (June 8), so exactly 4 persons have their exam before H (I, D, E, F). Thus, "More than five persons have exam before H" is NOT TRUE.
- D has exam on an even numbered date: True (April 8th).
- J has exam after I: True (J is on July 11, I is on April 8).