Pl. help me with this.
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.
In my opinion, answer is A. We have to add ways for VDVDVDV (Vowel first) and for DVDVDVD (digits first) to get total number of ways.
Passwords of length 7 characters
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I believe that you are confusing digits (0,1,2,3,4,5,6,7,8 and 9) with consonants (B,C,D,F,G,H,J...)jack0997 wrote:Pl. help me with this.
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.
In my opinion, answer is A. We have to add ways for VDVDVDV (Vowel first) and for DVDVDVD (digits first) to get total number of ways.
Cheers,
Brent
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Target question: In how many ways can a password of length 7 characters be created?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.
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
Thank you Brent. But the total of (5)(10)(4)(9)(3)(8)(2) + (10)(5)(9)(4)(8)(3)(7) will give the final answer.Brent@GMATPrepNow wrote:Target question: In how many ways can a password of length 7 characters be created?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.
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
The question ask, "In how many ways can a password of length 7 characters be created?" so the answer is (5)(10)(4)(9)(3)(8)(2) + (10)(5)(9)(4)(8)(3)(7). Answer = A
Where am I wrong?
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I think you're correct.jack0997 wrote: Thank you Brent. But the total of (5)(10)(4)(9)(3)(8)(2) + (10)(5)(9)(4)(8)(3)(7) will give the final answer.
The question ask, "In how many ways can a password of length 7 characters be created?" so the answer is (5)(10)(4)(9)(3)(8)(2) + (10)(5)(9)(4)(8)(3)(7). Answer = A
Where am I wrong?
I read statement 1 as "The password only contains distinct vowels and distinct digits, in alternate positions...BUT I'M NOT TELLING YOU WHICH CHARACTER GOES FIRST"
What is the source of this question? And, according to this source, what is the correct answer?
Cheers,
Brent