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Age Ascertainment (Posted on 2010-04-03) Difficulty: 3 of 5
Three friends Alan, Ben and Cal, the age of each of whom is a positive integer number of years, made the following statements in response to a query posited by Don, who is a mutual acquaintance. (It is known to Don that the age of each of the three friends exceeds 20 years.)

Alan: "If you take the two digits of my age and subtract 62, the result is 9 less than Ben's age."

Ben: "If you reverse the two digits of my age and subtract 12, the result is Cal's age with the digits reversed."

Cal: "If you reverse the two digits of my age and add 47, the result is Alan's age with the digits reversed."

Don was unable to determine their ages, and requested for additional clarification, when Alan replied, "If I tell you whether my age is prime or composite, you will be able to determine our ages."

Thereupon, Don accurately deduced their ages.

Determine the age of each of the three friends in conformity with the abovementioned statements.

Note: Don is a logician and math wizard.

  Submitted by K Sengupta    
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Solution: (Hide)
Alan is 97, Ben is 44, and Cal is 23.

For a detailed explanation, refer to the solution submitted by Dej Mar in this location.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutiona KISS solutionAdy TZIDON2010-04-04 03:24:13
SolutionSolutionDej Mar2010-04-03 21:04:51
Solutioncomputer solutionCharlie2010-04-03 13:43:26
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