Cheryl gives her new friends - Albert and Bernard – ten possible dates to choose from when they inquire about her date of birth. She then tells Albert the month and Bernard the day of her birthday. give an essay

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this is a trick question Test-takers are then asked to use logic to deduce Cheryl's birthday using a short conversation between the two boys about the information given to them.
Answer: Cheryl celebrates her birthday on July 18. 
Ms McGourty explains that Albert knows which month, so he knows if it is May or June. Bernard knows the date but if it was 18 or 19, they only appear once, and he would know the answer. But he doesn't.
"You can rule out some of the options. For Albert to have known the answer, he would have to have May and June as that is when 19 or 18 occur [respectively]."
This means it is not May or June.
"So Albert must have a month where numbers are repeated, leaving us with July and August," Ms McGourty adds. Bernard knows Albert has either of those two months and the numbers left include 15 through to 17 and 14 is repeated.
The number 14 is the only one in both months but Bernard is now sure of the birth date.
This means Bernard knows it is July 16.

Answer: Cheryl celebrates her birthday on July 18. 

Ms McGourty explains that Albert knows which month, so he knows if it is May or June. Bernard knows the date but if it was 18 or 19, they only appear once, and he would know the answer. But he doesn't.

"You can rule out some of the options. For Albert to have known the answer, he would have to have May and June as that is when 19 or 18 occur [respectively]."

This means it is not May or June.

"So Albert must have a month where numbers are repeated, leaving us with July and August," Ms McGourty adds. Bernard knows Albert has either of those two months and the numbers left include 15 through to 17 and 14 is repeated.

The number 14 is the only one in both months but Bernard is now sure of the birth date.

This means Bernard knows it is July 16.