jack0997 wrote:
In how many ways can a password of length 7 characters be created?
(1) The password only contains distinct vowels and distinct digits, in alternate positions.
(2) The password must begin with a digit.
Target question: In how many ways can a password of length 7 characters be created?
Statement 1: The password only contains distinct vowels and distinct digits, in alternate positions.
There are 10 digits (0,1,2,3,4,5,6,7,8,9) and there are 5 vowels (A,E,I,O,U)
We're told that we need to
alternate the vowels and digits, but we aren't told which we need to do first.
So, we have two possible cases:
case a: Vowel-Digit-Vowel-Digit-Vowel-Digit-Vowel
Since no repetitions are allowed,
the number of passwords = (5)(10)(4)(9)(3)(8)(2)
case b: Digit-Vowel-Digit-Vowel-Digit-Vowel-Digit
Since no repetitions are allowed,
the number of passwords = (10)(5)(9)(4)(8)(3)(7)
Since we cannot answer the
target question with certainty, statement 2 is SUFFICIENT
Statement 2: The password must begin with a digit.
There's no additional (and necessary) information explaining the composition of the password.
So there's no way to determine the number of passwords.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
From statement 1, we concluded that there are two possible cases:
case a: Vowel-Digit-Vowel-Digit-Vowel-Digit-Vowel
Since no repetitions allowed,
the number of passwords = (5)(10)(4)(9)(3)(8)(2)
case b: Digit-Vowel-Digit-Vowel-Digit-Vowel-Digit
Since no repetitions allowed,
the number of passwords = (10)(5)(9)(4)(8)(3)(7)
Statement 2 tells us that we are
specifically dealing with case b.
So,
the number of passwords = (10)(5)(9)(4)(8)(3)(7)
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
