How many passwords of 7 characters can be designed?

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

stevecultt: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Nov 11, 2013 5:48 am; Thanked: 2 times

How many passwords of 7 characters can be designed?

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.

Quote

Source: Beat The GMAT — Data Sufficiency | Wed Sep 27, 2017 4:29 am

GMAT/MBA Expert

ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 am; Thanked: 86 times; Followed by:15 members; GMAT Score:770

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.