Persons : P, Q, R, S, T, U
Months : May, September, November
Dates : 9, 16
1) Six persons P, Q, R, S, T and U were born in three different months May, September and November, on two different dates- 9 and 16 not necessarily in the same order.
⇒ We can draw following table according to the information given.
| Months (No of days) | Dates | Persons |
|---|
| May (31) | 9 | |
| May (31) | 16 | |
| September (30) | 9 | |
| September (30) | 16 | |
| November (30) | 9 | |
| November (30) | 16 | |
- Number of persons born before S is equal to the number of persons born after T. T was born in a month having even number of days.
⇒ T can be born in September or November. Thus we can have the following cases :
| Case 1: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | |
| May (31) | 16 | |
| September (30) | 9 | T |
| September (30) | 16 | S |
| November (30) | 9 | |
| November (30) | 16 | |
| Case 2: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | |
| May (31) | 16 | |
| September (30) | 9 | S |
| September (30) | 16 | T |
| November (30) | 9 | |
| November (30) | 16 | |
| Case 3: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | |
| May (31) | 16 | S |
| September (30) | 9 | |
| September (30) | 16 | |
| November (30) | 9 | T |
| November (30) | 16 | |
| Case 4: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | S |
| May (31) | 16 | |
| September (30) | 9 | |
| September (30) | 16 | |
| November (30) | 9 | |
| November (30) | 16 | T |
- Two persons were born between R and T.
⇒ We can place R according to the condition given. Case 3 will be eliminated as it is not possible to place R in case 3.
| Case 1: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | |
| May (31) | 16 | |
| September (30) | 9 | T |
| September (30) | 16 | S |
| November (30) | 9 | |
| November (30) | 16 | R |
| Case 2: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | R |
| May (31) | 16 | |
| September (30) | 9 | S |
| September (30) | 16 | T |
| November (30) | 9 | |
| November (30) | 16 | |
| Case 4: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | S |
| May (31) | 16 | |
| September (30) | 9 | R |
| September (30) | 16 | |
| November (30) | 9 | |
| November (30) | 16 | T |
- P was born after R but not on the same date as that of R.
⇒ We can place P according to the condition given. Case 1 is eliminated as there is no suitable place for P. From Case 2 we get one more case as shown below :
| Case 2A: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | R |
| May (31) | 16 | |
| September (30) | 9 | S |
| September (30) | 16 | T |
| November (30) | 9 | |
| November (30) | 16 | P |
| Case 2: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | R |
| May (31) | 16 | P |
| September (30) | 9 | S |
| September (30) | 16 | T |
| November (30) | 9 | |
| November (30) | 16 | |
| Case 4: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | S |
| May (31) | 16 | |
| September (30) | 9 | R |
| September (30) | 16 | P |
| November (30) | 9 | |
| November (30) | 16 | T |
- Q and U were born in the same month.
⇒ This is possible only in case 2.
| Case 2: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | R |
| May (31) | 16 | P |
| September (30) | 9 | S |
| September (30) | 16 | T |
| November (30) | 9 | |
| November (30) | 16 | |
No further information is given for Q and U, hence Q and U can be born on either 9th or 16th of November. Thus Case 2 will be our final solution.
| Case 2: | | |
|---|
| Months (No of days) | Dates | Persons |
| May (31) | 9 | R |
| May (31) | 16 | P |
| September (30) | 9 | S |
| September (30) | 16 | T |
| November (30) | 9 | Q/ U |
| November (30) | 16 | U/ Q |
Hence, we can see that among the given options, R was born in a month having odd number of days.