If M $ N means "M is the brother of N"; M # N means "M is the mother of N"; and M * N means "M is the daughter of N", then in the expression I # J $ K * L, who is the father?

Difficulty: Medium

Correct Answer: L

Explanation:


Introduction / Context:

This question introduces symbolic relationships and asks you to decode them to determine who plays the role of "father". Such coding problems combine blood-relations with a mini-logic language, commonly used in aptitude tests to measure symbol manipulation and inference skills.


Given Data / Assumptions:

  • M $ N means "M is the brother of N".
  • M # N means "M is the mother of N".
  • M * N means "M is the daughter of N".
  • The given expression is I # J $ K * L.
  • We must find who is the father among I, J, K and L.
  • We assume a standard heterosexual parental model where a child has a mother and a father, and gender is inferred from roles (mother, brother, daughter).


Concept / Approach:

We decode the composite expression piece by piece. Each symbol directly gives us a family relationship. From this, we infer the genders of I, J and K, and the parent–child relation connecting K and L. Once we know who is mother and who is brother or daughter, we can infer who must be the father to make the family structure consistent: the person whose child is K and J, while not already being assigned a female role.


Step-by-Step Solution:

Step 1: Decode I # J. The symbol # means "is the mother of". So I # J means I is the mother of J. Therefore, I is female and J is I's child. Step 2: Decode J $ K. The symbol $ means "is the brother of". So J $ K means J is the brother of K. Therefore, J is male, and J and K are siblings. Step 3: Decode K * L. The symbol * means "is the daughter of". So K * L means K is the daughter of L. Therefore, K is female and L is a parent of K. Step 4: Since J is the brother of K, and K is the daughter of L, it follows that J is also a child of L (siblings share parents in such puzzles). Thus, L is the parent of both J and K. Step 5: We already know that I is the mother of J. For J's parents, one is I (mother) and the other must be a father. Since J and K are children of L as well, L must be the other parent. Step 6: Therefore, L is the father of J and K, while I is their mother. Among I, J, K and L, the person who fits the role "father" is L.


Verification / Alternative check:

Summarize the family: I (mother) and L (father) are parents of J (son) and K (daughter). The symbols match perfectly: I # J (I mother of J), J $ K (J brother of K), and K * L (K daughter of L). No other assignment of roles satisfies all three symbolic statements while keeping genders consistent. Hence L must be the father.


Why Other Options Are Wrong:

I is explicitly the mother, so cannot be the father.

J is a brother (male child), not a parent.

K is a daughter (female child), also not a parent.


Common Pitfalls:

A common error is to read the expression from right to left and mix up who is the parent and who is the child for the * and # symbols. Always stick to the definitions given: "M * N" explicitly means M is the daughter, not the parent. Another pitfall is to forget that siblings share parents, which is crucial for identifying L as the common parent and thus the father.


Final Answer:

In the expression I # J $ K * L, L is the father.

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