# Quantitative Reasoning – Passage Based – What is the ‘Security Rating’ of your ‘Password’!

PSA 2014_XI_Q23. Questions (57-60) : Read the following passage and answer the questions that follow :
Passwords : Literally words that had to be spoken to a guard in order to be allowed to pass -have been used since ancient times to keep people, areas and ideas secure. In the modern world, the passwords that we enter into computers protect our bank account and identities. A password that is easy for someone else to guess is said to be “weak”. Many Websites help us keep our information secure by advising us of our password’s strength rating (Weak, moderate, strong or very strong) as we enter it. This rating is determined by an automatic scoring system. A password’s security score depends on how many characters are used, the type of character, and the order in which the characters are arranged. Some of these aspects are considered favourable and attract points, while others attract penalties. Each of these aspects needs to be considered independently. The final score is calculated by subtracting the penalties from the points gained.

An Automatic scoring system for passwords is designed by noting that a typical password would be made up of a number (say C) of characters that can include :

Some upper case letters (say U)
and / or Some lower case letters (say Lc)
and / or Some digits (say D)
and / or Some punctuation marks.

The actual make-up of the password, from all, or some, of these, earns it both POINTS and PENALTIES. These
are awarded on the basis of the system given below :
The POINTS for a given password, are calculated as follows :
(a) The total number of characters, (including punctuation marks), in it, is multiplied by 4.
(b) The number of digits (say D), in it, is multiplied by 4.
(c) The number of upper case letters (say U) as well as the number of lower case letters (say Lc), in it, are each multiplied by 2.

(d) The number of digits (say M), between the first and the last character of the password, is multiplied by 2.
The sum total of all these products gives the total POINTS earned by the password. The PENALTIES, for a given password, are calculated as follows :
(a) A password, made up ONLY of letters, or ONLY of digits gets penalties equal to the number of characters used to make it.
(b) When a password uses the SAME character a number of times (say T times), it gets a penalty equal to 2 T.
(c) When a password uses consecutive upper case letters or consecutive lower case letters, it earns a penalties equal to two times the number of such consecutive upper case letters as well as two times the number of such consecutive lower case letters.
(d) When a password uses a number of sequential letters or sequential digits, it earns a penalty equal to two times the number of such sequential letters as well as such sequential digits present in it. The sum total of all such penalties gives the total PENALTIES earned by the password. The FINAL SCORE of the password equals the
difference between the sum total of its POINTS and the sum total of its PENALTIES.The value of the FINAL SCORE, of a password, determines its SECURITY RATING. The security rating is said to be :
WEAK when the final score is 29 or less
MODERATE when the final score is between (30 to 59)
STRONG when the final score is between (60 to 79)
VERY STRONG when the final score is 80 or more.
We now illustrate the use of this system for the password
DOG 123
* There are a total of 6 characters in it. It thus earns 6 × 4 = 24 points.
* This password has three upper case letters. It thus earns 3 × 2 = 6 points.
* This password has three digits in it. It thus earns 3 × 4 = 12 points.
* Again, this password has two digits (1 and 2) between the first character (D) and the last character (3). It thus earns 2 × 2 = 4 points.
The total number of points earned is thus (24 + 6+ 12 +4) = 46 points.
We now look at the PENALTIES earned by this password.
* It has 3 consecutive upper case letters. These give it 3 × 2 = 6 penalties.
* It has 3 sequential digits. These give it 3 × 2 = 6 penalties.
The total number of penalties given to it is thus 6 + 6 =12 penalties.
The final score of this password is thus (46 – 12) = 34.
The security rating of thus password would, therefore, be MODERATE.

(i) Supipi created a 6 character password made up of letters and numbers only. A week later, she recalls the first 5 characters but has forgotten the 6th character as shown :
A v 1 3 G ?
Supipi remembers that the last character is a repeat of one of the other characters and that the security score was 42. The last character would have been

(1) either A or G

(2) v

(3) G

(4) either 1 or 3
(ii) Rohith wants to use a 6-character password made up of identical characters. Which of the following passwords would give him the highest security score ?
(1) ??????

(2) 555555

(3) rrrrrr

(4) RRRRRR
(iii) A password is made up of 10 sequential, uppercase letters. e.g. A B C D E F G H I J
What is the highest security rating that this password can have ?
(1) very strong

(2) weak

(3) moderate

(4) strong
(iv) Veera wants to use veera2 as a password. What is the security score for this password ?
(1) 38

(2) 22

(3) 24

(4) 34

(i) The below table would give us the details regarding the final score in all scenarios:

 A v 1 3 G ? [?= A or G] A v 1 3 G ? [?= v] A v 1 3 G ? [?= 1 or 3] 1. Number of characters 6×4 6×4 6×4 2. Number of upper case letters 3×2 2×2 2×2 3. Number of lower case letters 1×2 2×2 1×2 4. Number of digits 2×4 2×4 3×4 5. Number of digits between first and last characters 2×2 2×2 2×2 6. Password has letters only 0 0 0 7. Password has digits only 0 0 0 8. Number of times the same character is used -2×2 -2×2 -2×2 9. Number of consecutive upper case letters -2×2 0 0 10. Number of consecutive lowercase letters 0 0 0 11. Number of sequential letters 0 0 0 12. Number of sequential digits 0 0 0 Final Score 36 40 42

Thus, option (4) is correct.

(ii) Looking at the rules we should notice that if all letters are either upper case or all are in only lower case, final score should be same (number of characters must be same). Thus, final score of “RRRRRR” and “rrrrrr”  would be identical; either of them can’t be the answer (as there could be only one option correct).

 ?????? 555555 1. Number of characters 6×4 6×4 2. Number of upper case letters 0 0 3. Number of lower case letters 0 0 4. Number of digits 0 6×4 5. Number of digits between first and last characters 0 4×2 6. Password has letters only 0 0 7. Password has digits only 0 -6 8. Number of times the same character is used -6X2 -6×2 9. Number of consecutive upper case letters 0 0 10. Number of consecutive lowercase letters 0 0 11. Number of sequential letters 0 0 12. Number of sequential digits 0 0

A quick look at the above table would tell us 555555 should be the answer. Option 2.

(iii) A password is made up of 10 sequential, uppercase letters.
1. Number of characters= 10, points= 10×4=40
2. Number of upper case letters=10; points= 10×2=20
3. Number of lower case letters=0;
4. Number of digits= 0;
5. Number of digits between first and last characters= 0
6. Password has letters only; true; penalty = 10
7. Password has digits only– not true here.
8. Number of times the same character is used= 0;
9. Number of consecutive upper case letters=10; penalty = 10×2=20
10. Number of consecutive lowercase letters=0;
11. Number of sequential letters=10; penalty= 10×2=20
12. Number of sequential digits=0

Final Score= 40 + 20 -10 – 20 – 20 =10
weak. Option 2.

(iv)

Final score calculation for the password “veera2”:

1. Number of characters= 6, points= 6×4=24
2. Number of upper case letters=0
3. Number of lower case letters=5; points = 5×2=10
4. Number of digits= 1; points = 1×4=4
5. Number of digits between first and last characters= 0
6. Password has letters only– not true here.
7. Password has digits only– not true here.
8. Number of times the same character is used= 2; penalty = 2×2=4
9. Number of consecutive upper case letters=0
10. Number of consecutive lowercase letters=5; penalty= 5×2=10
11. Number of sequential letters=0
12. Number of sequential digits=0

Final Score= 24 + 10 + 4 – 4 – 10 =24. Option 3. 