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How many passwords of 7 characters can be designed?

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by stevecultt » Wed Sep 27, 2017 4:29 am
How many passwords of 7 characters can be designed?

(1) Passwords contain only distinct vowels and distinct digits, in alternate positions.
(2) Passwords must begin with a digit.

Experts, the correct answer is C. But I think (1) is also sufficient. 86400 + 302400 is what we get from (1). pl. help.
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Source: — Data Sufficiency |

by ErikaPrepScholar » Thu Sep 28, 2017 5:44 am
Hey Steve,

The key thing to recognize here is that we don't know whether the password starts with a vowel or a digit.

So we can have

vowel digit vowel digit vowel digit vowel (for 4 vowels and 3 digits)

or

digit vowel digit vowel digit vowel digit (for 4 digits and 3 vowels)

Since we have 10 digit options and 5 vowel options, changing the number of each gives us different numbers of passwords. We need to have both statements together to determine that the second statement is the correct option.
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