In a certain code, P + Q means 'Q is the son of P'; P @ Q means 'Q is the daughter of P'; P $ Q means 'Q is the brother of P'; P % Q means 'P is the father of Q' and P # Q means 'P is the mother of Q'. Which of the following is true?
K + L $ M @ N means N is the granddaughter of K.
This question involves decoding relationships based on a given set of symbols. We need to analyze each option by breaking down the coded string and determining the relationships between the individuals mentioned.
Let's first understand what each symbol represents:
We can summarize these rules:
| Code | Relationship | P's Gender | Q's Gender |
|---|---|---|---|
| P + Q | Q is son of P | ? | Male |
| P @ Q | Q is daughter of P | ? | Female |
| P $ Q | Q is brother of P | ? | Male |
| P % Q | P is father of Q | Male | ? |
| P # Q | P is mother of Q | Female | ? |
We will now examine each option provided and trace the blood relations.
Based on this, C is the parent of F (since F is the brother of C's daughter). F is the father of G. So, C is the grandparent of G. For G to be the grandson of C, G must be male and the child of C's son. F is C's son, and G is F's child. We know F is male. However, the code F % G only tells us F is the father of G; it does not specify G's gender. G could be a grandson (male) or a granddaughter (female). Therefore, we cannot definitively say G is the grandson of C. This statement is not necessarily true.
Based on this, A is the parent of C (since C is the brother of A's son). C is the father of D. So, A is the grandfather of D. For A to be the *maternal* grandfather, A must be the mother of C. However, from A + B, we only know A is a parent of B and B is male; this does not specify A's gender. A could be male (paternal grandfather) or female (maternal grandmother). Therefore, we cannot definitively say A is the maternal grandfather of D. This statement is not necessarily true.
Based on this, K is the parent of M (since M is the brother of K's son). M is the father of N (as M @ N means N is daughter of M, so M is a parent). So, K is the grandparent of N. Specifically, M is the son of K, and N is the daughter of M. Therefore, N is the daughter of K's son. A daughter of a son is a granddaughter. N is female, which confirms she is a granddaughter. This statement, "N is the granddaughter of K," is true based on the decoded blood relations.
From G % H and H # K, we know G is the father of H, and H is the mother of K. This makes G the maternal grandfather of K.
Based on this, G is the father of H, and H is the mother of K and L. G is the maternal grandfather of both K and L. L is the brother of K, and L is male. For L to be the son-in-law of G, L would need to be married to G's daughter. G's only direct child mentioned is H, who is female. For L to be G's son-in-law, L would have to be married to H. However, L is the son of H. A son cannot be married to his mother. Therefore, L is not the son-in-law of G. L is G's grandson. This statement is false.
After analyzing each option and decoding the blood relation strings, we find that only the third statement, "N is the granddaughter of K" derived from "K + L $ M @ N", is definitively true based on the given coding rules.
| Coded String | Deduced Relationships | Stated Relationship | Is it True? |
|---|---|---|---|
| C @ D $ F % G | F is son of C, G is child of F. | G is grandson of C. | Cannot be confirmed (G's gender unknown) |
| A + B $ C % D | C is son of A, D is child of C. | A is maternal grandfather of D. | Cannot be confirmed (A's gender unknown) |
| K + L $ M @ N | M is son of K, N is daughter of M. | N is granddaughter of K. | True |
| G % H # K $ L | G is father of H, H is mother of K and L. | L is son-in-law of G. | False (L is grandson of G) |
Blood relation problems are common in reasoning sections of competitive exams. They test your ability to decode relationships from symbols or phrases and construct a family tree or diagram mentally or on paper. Key aspects to remember:
‘R+S’ means ‘R is the daughter of S’. ‘R−S’ means ‘R is the husband of S’.‘R × S’ means ‘R is the brother of S’. If ‘T × V + Z’, then which of the following options is true?
'P × Q' means 'P is the wife of Q'. 'P + Q' means 'P is the father of Q'. 'P ÷ Q' means 'P is the daughter of Q'. 'P - Q' means 'P is the son of Q'. How is E related to I in the expression 'E ÷ F + G - H ÷ I' ?
'K % L' means 'K is the brother of L', 'K $ L' means 'K is the husband of L', 'K @ L' means 'K is the sister of L', 'K # L' means 'K is the mother of L'.
How is H related to M in the expression ‘X @ P % T # M $ Y # J @ H’?
If ‘A % B’ means ‘A is the father of B’, ‘A # B’ means ‘A is the brother of B’, and ‘A $ B’ means ‘A is the wife of B’, then how is K related to R in the given expression?
K $ H % Y # M # R
If 'A + B' means 'A is the daughter of B ', 'A × B' means 'A is the sister of B', and 'A = B' means 'A is the wife of B', then how is G related to R in the expression 'C × G × U + M = R'?