Hi Roland2rule,
We're told that a number N is chosen at random from the set of two-digit integers whose digits are both PRIME numbers. We're asked for the probability that N is divisible by 3.
To start, we know that each of the two digits in each number must be 2, 3, 5 or 7. The number of two-digit numbers that fit this restriction is (4)(4) = 16, so the correct answer must be some fraction out of 16. If you had to guess at this point, then you could eliminate Answers A and C.
There's a quick way to determine whether a number is divisible by 3: "the rule of 3" - if the DIGITS of a number SUM to a total that is divisible by 3, then that number is divisible by 3... For example:
12 is divisible by 3 because 1+2 = 3 is divisible by 3
25 is NOT divisible by 3 because 2+5 = 7 and 7 is NOT divisible by 3
Given the possible digits of the two-digit number, the following 'pairs' of digits would give us a number that's divisible by 3:
2 & 7... giving us 27 and 72
3 & 3... giving us 33
5 & 7... giving us 57 and 75
5 out of the 16 numbers 'fit' what we're looking for, so the probability is 5/16.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
