Researchers from a data analysis firm have found that the three most

fact 1. 1234, 1111, and 0000 -- account for close to 20 per cent of all four-digit passwords.

fact2. 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.

fact3. 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.

total distinct 4 digit passwords that could be formed are - 10000.....but may be all are not in use where as some are repeated.... eg 1234....

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...correct ......see fact 2..
(B) The password 0123 will most probably be more common than 2331 .....cannot be concluded..we could have said that for 0223 and 2331...... see fact 3
(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...its a 20 % possibility.... can't call it very high ... see fact 1
(D) One out of three four digit passwords will be 1234, 1111, or 0000 ....incorrect... one out of 05 will be.... that is 20%... see fact 1
(E) Passwords starting with 19 are more popular than those starting with 21..............can't say....nowhere inferred see fact 2.....

Researchers from a data analysis firm have found that the three most popular combinations -- 1234, 1111, and 0000 -- account for close to 20 per cent 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
This can definitely be proved by “with those in the upper 1900s coming in the highest”.

B) The password 0123 will most probably be more common than 2331
There is no information provided for the passwords starting with 21, so we cannot compare.

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
1234, 1111, and 0000 -- account for close to 20 per cent of ALL. 20% doesn’t mean VERY HIGH. Also the total number of passwords is not given. So scaling down to 100 and then speaking about VERY HIGH possibility cannot be proved.

D) One out of three four digit passwords will be 1234, 1111, or 0000
1/3 is 33%. But FACT says only 20%.

E) Passwords starting with 19 are more popular than those starting with 21
There is no information provided for the passwords starting with 21. Hence no comparison is possible.

Dear all ..
I have a small concern here . From the premises , it is given that the password starting with 19 have probability of 80% . That
means it has the highest probability when compared with 12 right ..
So how come the option E go wrong ... plz clarify this .. Thanks !!

E) Passwords starting with 19 are more popular than those starting with 21

This is a must be true question, in which correct answer choice should be proved with given information in the argument.

Choice E compares "Passwords starting with 19" with "Passwords starting with 21". But argument did not give any clue about "Passwords starting with 21". Hence the comparison cannot be proven. this is why E is wrong.

Because of the answer choices, I must assume that "popularity is not mutually exclusive, so 80% popularity, does not mean that other numbers are no more popular.

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.

What exactly we mean from the above statement. Could anybody please explain.

As per me, those in upper 1900s coming in the highest means number such as 1900, 1901, 1902 are more popular in comparison to numbers such as 1980 1981....
So how A is the answer.
I think A is the reverse of the above statement

Somebody, Please shed some light on the above mentioned issue.

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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