Set 1

Discover a pattern w.r.t the number of vowels in each of the words. The only exception is SOP, which has only one vowel as compared to other words, all of which have two vowels each. Thus, SOP becomes our starting point for analysis.

The password will not have any letter from the word SOP, because in that case the number of vowels in the password will be either 1 or 2, and therefore one cannot be sure about the exact number of vowels in that word.

For example, if we assume that the letter ‘S’ is present in the password, then there are two possibilities for the password – SOP and SUE, the former with 1 vowel and the latter with 2.

The only word with no letter from the word SOP is YAE.

-> YAE is the password.

7A+5B = 6C —– ❶ (as per P)

4A+9C = 5B —– ❷ (as per Q)

6C+3B = 4A —– ❸ (as per R)

From ❶ and ❷ 7A+4A+9C = 6C -> 11A+9C = 6C —– ❹

Equation ❹ is not feasible because LHS is definitely more than RHS, so they can’t be equal.

-> One out of P and Q is lying

From ❶ and ❸ 7A+5B+3B = 4A -> 7A+8B = 4A —– ❺

Equation ❺ is not possible because LHS is definitely more than RHS.

-> One out of P and R is lying

Now we know that one out of P and Q is lying, and one out of P and R is lying. Also, we know that exactly one of the three sales representatives is lying -> P is lying

Case I: P’s sister is R
In this case R’s legal husband is Q and from c, R argues with Q, which implies that both R and Q are not the ones to be murdered. Further, S has to be Q’s sister in this case and from d, S argues with the victim’s legal spouse. But this is not possible because if R, Q and S are not murdered, then it is P who is murdered and is therefore the victim. The only person who can be P’s spouse is S and S can not get into an argument with self. Hence case I is not possible.

Case II: P’s sister is S
In this case R’s legal husband is P and from c, S argues with P. So, both S and P can’t be the ones murdered. Further, Q’s sister will be R, and from d, R gets into an argument with the victim’s legal spouse. Since S, P and R are involved in post-murder arguments, Q is the victim. So, R gets into an argument with Q’s legal spouse, who has to be S.
Thus, we conclude the following:
• P is married to R
• Q is married to S
• P’s sister is S
• Q’s sister is R
• Q is the victim
Answer is Q