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X remembers that his mother's birthday falls after August 8th but before August 20th. His sister, Y, remembers that her mother's birthday is after 18th August but before August 28th. When is the mother's birthday?

X remembers that his mother's birthday falls after August 8th but before August 20th. His sister, Y, remembers that her mother's birthday is after 18th August but before August 28th. When is the mother's birthday? Correct Answer 19th August

1. X remembers that his mother's birthday falls after August 8th but before August 20th.

Therefore, possible birthday dates are : 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.

2.  His sister, Y, remembers that her mother's birthday is after 18th August but before August 28th.

Therefore, possible birthday dates are : 19, 20, 21, 22, 23, 24, 25, 26, 27

Clearly, X and Y's mother's birthday falls on 19th August as Y remembers that her mother's birthday is after 18th August and X remembers that his mother's birthday falls before August 20th.

Hence, ‘August 19th’ is the correct answer.

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