Directions (28-32): Read the following information carefully and answer the given questions. Six persons: A, B, C, D, E, and F were born on different dates in March 2000, falling between the 20th and 28th, but not necessarily in the same order. There are three vacant dates, and these are not consecutive. A was born on an odd-numbered date. B was born on the 25th, but not before C. Three persons were born between A and F. F was born just next date of E. There are two vacant dates between C and F. D was born on an even-numbered date, and was born neither just before E nor just after A. Which of the following pairs of dates could be vacant, based on the given information?

### Concept & Logic This is a linear arrangement puzzle involving dates. The core strategy is to determine fixed positions first (like B on the 25th) and then use distance constraints ("three persons between", "two vacant dates") to narrow down possibilities for the remaining entities. ### Step-by-Step Solution * **Initial Setup:** We have 9 dates (20th to 28th) for 6 persons and 3 non-consecutive vacant dates. * **Fixed Clues:** * B is born on the 25th. * F is born the day immediately after E (E and F are consecutive). * **Positioning F and C:** * C is born before B (25th), so C is between 20th and 24th. * There are two vacant dates between C and F. Since E and F are consecutive, placing them early (e.g., 20, 21) doesn't allow room for C to be placed before 25th with two vacant dates between them. F must be late in the month. * F cannot be 26th because E would be 25th, clashing with B. * Let's test F = 28th. This makes E = 27th. * **Placing Remaining Persons:** * "Three persons were born between A and F(28)". Two of those persons are E(27) and B(25). The third must be C. * For C to be between A and B with two vacant dates between C and F(28), C must be on the 23rd. The vacant dates between 23rd and 28th are exactly the 24th and 26th (non-consecutive, which is valid). * So, we have: C(23), Vacant(24), B(25), Vacant(26), E(27), F(28). * A must be before C to ensure exactly three persons are between A and F. The only available odd date before 23 is 21. So, A = 21st. * Dates left for D and the final vacant slot: 20th and 22nd. * D must be on an even date (both are). However, D is "neither just before E nor just after A". Since A is 21st, 22nd is "just after A". Thus, D cannot be 22nd. * Therefore, D = 20th, making 22nd the third vacant date. * **Final Arrangement Table:** | Date | Person/Status | | :--- | :--- | | 20 | D | | 21 | A | | 22 | Vacant | | 23 | C | | 24 | Vacant | | 25 | B | | 26 | Vacant | | 27 | E | | 28 | F | ### Exam Strategy & Shortcut Always look for the most restrictive compound condition. Here, F being linked to E, having exactly 3 people between A and F, and exactly 2 vacant dates between C and F forms a rigid block that can only fit at the end of the timeline. ### Common Pitfall Misinterpreting "three persons were born between" as "three days between". The puzzle strictly separates chronological "dates" (which include vacants) from the sequence of actual "persons" born. ### Final Answer From our derived arrangement, the vacant dates are the 22nd, 24th, and 26th. The pair that matches is 24th and 26th. Therefore, the correct answer is **24th and 26th**.