carcass wrote:
Researchers from a data analysis firm have found that the three most popular combinations—1234, 1111, and 0000—account for close to 20 percent of all four-digit passwords. The researchers also found that every four-digit combination that starts with 19, ranks above the 80th percentile in popularity, with those in the upper 1900s coming in the highest. Also quite common are combinations in which the first two digits are between 01 and 12 and the last two are between 01 and 31.
If the statements above are true, which of the following must be true?
(A) The password 1922 will most likely be less popular than 1981.
(B) The password 0123 will most probably be more common than 2331.
(C) If a password was to be selected from a random list of 100 four-digit passwords, there is a very high possibility that it will be 1234, 1111, or 0000.
(D) One out of three four-digit passwords will be 1234, 1111, or 0000.
(E) Passwords starting with 19 are more popular than those starting with 21.
Official Explanation
Since this is an inference question, let’s look at each option and eliminate.
(A) The correct answer. Since the numbers in the upper 1900s are more popular than the rest, 1981 has to be more popular than 1922.
(B) While you may think this is correct based on the last sentence of the argument, all that can be inferred from the last sentence is that the password 0123 will be a popular one. We cannot infer anything about how it would compare with the password 2331. There could be some other characteristic of 2331 that makes it more popular than 0123.
(C) Not necessarily. All that the argument states is that these three comprise close to 20% of all passwords, so there’s only a 20% chance that the chosen password will be one of these three.
(D) In fact, one out of five four digit passwords will be one of the three mentioned since the chances are 20%.
(E) We know that passwords starting with 19 are popular, but we don’t know anything about passwords starting with 21.
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