# How to solve Family Tree, Relationships problems based on coded symbols

Thursday, October 8th, 2020 Relationships are an integral part of our life whether between or among living ones. Relationships provide definiteness between two objects or persons. Relationships among people are complicated and confusing especially when you are living in a big joint family with innumerable relatives! Blood Relations is a very important part of reasoning section in competitive exam. Every year questions are asked based on them in aptitude tests and entrance exams such as CAT, XAT, SNAP and Bank exams. One other topic of reasoning section is Coding-Decoding. And in this blog, we will understand and develop strategies to solve problems that are based on relationships that are coded.

As you all know, a code is a secret message encrypted using letters, numbers or symbols. And in coded-relationships, the problem involves interpreting a given relationship-string which is coded in a particular fashion and then matching it with the relationship given in the question. For example,

P/Q means P is the father of Q.

P+Q means P is the mother of Q.

P-Q means P is the brother of the Q.

P*Q means P is the sister of Q.

Now if A + B / C – D, then A is D’s?

Or, If A * B / C – D + E, then how A and E are related?

However, as you can notice in the above example that the process of decoding each and every relationship is burdensome and time-consuming. But if some intelligent and smart strategies could prove to be very handy in dealing with these kinds of problems. Before moving forth with the techniques and methods to simplify the job of decoding, the table given below defines some of the important blood relations for your understanding.

 Father of grandfather or grandmother Great grandfather Daughter of father or mother Sister Mother of grandfather or grandmother Great grandmother Son of second wife of father Step brother Father of father or mother Grandfather Daughter of second wife of father Step sister Mother of father or mother Grandmother Son/daughter of uncle/aunt Cousin Wife of grandfather Grandmother Brother of husband or wife Brother-in-law Husband of grandmother Grandfather Sister of husband or wife Sister-in-law Father-in-law of father/mother Grandfather Husband of sister/sister-in-law Brother-in-law Mother-in-law of father/mother Grandmother Son of father Oneself/Brother Father’s father/mother only Father Mother of son/daughter Oneself/Wife Only daughter-in-law of father’s father/father’s mother Mother Father of daughter/son Oneself/husband Husband of mother Father Son of son of grandmother/grandfather Brother/Oneself /Cousin Wife of father Mother Daughter of son of grandmother/grandfather Cousin/Oneself /Sister Second wife of father Step mother Son of brother or sister Nephew Brother of father Uncle Daughter of brother/sister Niece Brother of mother Maternal Uncle Grandson of father/mother Son/Nephew Sister of father Aunt Granddaughter of father/mother Daughter or Niece Sister of mother Maternal Aunt Husband of daughter Son-in-law Husband of aunt Uncle Wife of brother/brother-in-law Sister-in-law Wife of uncle Aunt Wife of son Daughter-in-law Son of grandfather/grandmother Father/Uncle Son of son/Daughter Grandson Daughter of father-in-law/mother-in-law of father Mother/Aunt Daughter of son/Daughter Granddaughter Father of wife/husband Father-in-law Son’s/Daughter’s grandson Great Grandson Mother of wife/husband Mother-in-law Son’s/Daughter’s granddaughter Great granddaughter Children of same parents Siblings Father’s/Mother’s only son/daughter Oneself Son of father or mother Brother

Now the approach that you should follow to solve the question is

1. Eliminate all wrong choices by the following methods.
• Check sex
• Check generation-gap
1. Draw a family tree diagram of the left-over choices and pick the correct answer.

## Check sex method

To quickly eliminate options what can be done is we can identify the sex of the person in consideration whether male/female and hence, can discard the wrong options accordingly i.e. If the person under consideration is a female then all the options such as father, son etc. can be ruled out and vice versa. Now there are two types of coding pattern one is Forward Type and the other one is the Backward type and the rule for checking sex is different. Given below is a table differentiating between the both.

 Forward Type Backward Type P + Q means P is the father of Q P \$ Q means Q is the father of P P – Q means P is the mother of Q P ₹ Q means Q is the mother of P P * Q means P is the brother of Q P > Q means Q is the brother of P P / Q means P is the sister of Q P < Q means Q is the sister of P P φ Q means P is the husband of Q P α Q means Q is the husband of P P Ω Q means P is the wife of Q P β Q means Q is the wife of P P ꓴ Q means P is the son of Q P @ Q means Q is the son of P P ꓵ Q means P is the daughter of Q P # Q means Q is the daughter of P

Now the rule is, in forward-type coding, reject an answer choice if the symbol immediately after the person in question indicates the wrong sex. Conversely, reject the choice if the symbol immediately before the person in question denotes the wrong sex, in case of backward-type coding. I know this rule sounds a bit puzzling though you will get a clear picture with the help of the example based on the relations defined above in the table.

Example 1: Which of the following means that “X is the grandson of Y”?

1. X / A + B – C * Y
2. X / A ꓴ B ꓴ C / Y
3. X ꓴ A / B / C ꓴ Y
4. X ꓵ A ꓵ B * C * Y

As you can notice, this is a forward-type code thus follow the column 1 of the table. Since, X is grandson of Y mean he is male and you can identify from the choices given above in the question that the symbol / and ꓵ after X means either X is a sister or a daughter thus all these options are wiped out because we need to find a male candidate to be a grandson and only option 3 points out that X is male. Hence 1, 2 and 4 choices are discarded on the basis of the symbol after X.

Example 2: Which of the following means that “B is the grandfather of E”?

1. A @ B @ C > D @ E
2. A # B # C > D # E
3. A < B < C > D < E
4. A < B < C @ D > E

In the above question you can easily make out it follows the backward-type code given in table the above. And in this type, our focus is on the symbol before the letter. And for B to be grandfather he should be male. Since, you can quickly eliminate the options 2, 3 and 4 by just looking the symbol before B and both < and # are used to represent female sex. Thus, option 1 is our choice.

I hope now you are clear with the rule to be followed in either of the cases i.e. Forward and Backward codes. Now we can move on to second technique of disposing of useless options by calculating generation Gap.

## Checking generation Gap

Generation Gap is the hierarchical structure of the particular family. And through generation Gap drawing tree diagrams would be a simpler task and also, we can easily rule out all the options that don’t have necessary generation gap asked in the question. Given below is explained the steps to calculate the generation gap with the help of examples

1. Take one of the people under consideration.
2. Move rightwards in case of Forward-type and for the backward pattern instead of starting from left we will begin from the right side and move leftwards. For each father/ mother relation put a + 1, for each brother/ sister/ husband/ wife relation put a 0 and for each son/ daughter relation put a -1.
3. Do a sum total.

Example: Consider the following: A – B * C ꓵ D ꓴ E Ω F * G. Find the generation gap between

• A and C
• G and A

Now the above code follows the forward-type code. In the case of A and C, A is on left and hence, we will start from A and move towards C. Since, – means mother thus between A and B we will write + 1 and here * means brother so we put 0 for B and C. Thus, the total is + 1 + 0 = 1. Therefore, A is of C’s father generation.

The second case is between G and A, where A is on the left in the above question so we begin from A and we have calculated till C now let’s move forth after C. Now ꓵ means daughter so we put -1 for C and D. After D the symbol is ꓴ which signify son relation and hence we again put -1 in between D and E. E Ω F means E is wife of F so we put a 0 here. Finally, * is for the brother so we put 0 for F and G too.

Thus, the total now becomes, 1 + 0 – 1 – 1 + 0 + 0 = -1. Hence, we conclude that A is a generation below G i.e. he belongs to G’s son’s generation.

Example: Consider the following: S > R β Q @ P # O > N \$ M. Find the generation gap between

• R and O
• O and Q

This is the backward-type coded relationship and in this case, we move from right to left. For R and O, O is on the right so we begin from O and proceed to R. # means daughter so we put -1 for O and P. @ is used for son thus, again we will use -1 in between P and Q. Since, β means wife, therefore, we put 0 for P and Q. Hence, the total is -1 -1 + 0 = -2. So, O is R’s grandson’s generation.

We can easily above formulation for O and Q as well. In this case, we begin from O and move towards Q and we get the sum as -2. Therefore, O is also 2 generation below than Q and is from Q’s grandson generation.

Since we have learned the two techniques of elimination we can easily proceed towards the final step of Decoding i.e. to draw family tree diagrams.

## Constructing Family tree diagrams

After being acquainted with the above methods we can quickly remove all the unviable options in the light of the relationship string given in the question. But we might still be left with few more options that stand in the competition of correct choice. And to rule them out we can use the final trick to find out the right answer. And the trick is a family tree. You can draw tree diagrams in the following fashion.

• Use vertical lines to represent parent-child relationships.
• Horizontal lines like <-> to denote marriages and diagonal lines to represent sibling relationships.
• You can also add gender differentiation to it by using a + sign for male and – sign for female.

Let’s do an example of it and understand how to draw a family tree.

Example: S * T means X is the wife of T.

S + Q means S is the son of T.

S – Q means S is the sister of T.

Which of the following means A is the daughter of B?

1. A + C – D * B
2. A * C + D – B
3. A – C * D + B
4. A – C + D * B
5. None of these

Sol: First of all, you can notice it is Forward-type code.

Step 1) Check sex: For A to be daughter of B, A should be female and in forward-type we check for symbols after the person in question. And, in this case * and – denote female relations. Thus, option 1 is ruled out as + means A is son of B.

Check generation gap: Since, A should be the daughter of B then the generation gap should be -1.

In option 2, A * C means A is the wife of C so we put 0. Now in between C and D we put -1 as C is the son of D and finally, D is the sister of T we get 0 here. So, total sum = -1. Thus, we can keep this option under consideration.

In option 3, between A and C we get, 0 and since C is the wife of D we get 0 here too. And for D and B, D is the son of B hence we put -1 here. Again, total sum is -1.

In a similar way, we will get generation gap on option 4 too as -1.

So, all three options are still in the race. Now we have to draw tree diagram to get the final answer.

Step 2) Family tree

Option 2) A * C means A is wife of C. Thus, Now C + D means C is son of D. Therefore, Finally, D – B means D is sister of B. Hence, A is niece of B. Thus, this is not the right option.

Option 3) A – C means A is sister of C. Now C is wife of D. And D is son of B. Therefore, Thus, A is the sister of B’s daughter in law.

Hence, this option is ruled out.

Option 4) Using the same technique like in the above options we will draw tree diagram for 4th option. We get, Thus, in this case, we get, A is the daughter of B. So, option 4 is correct.

I hope that now you have clearly understood the concept and formula to decipher the solutions to such problem!

### CAT Questions related to Logical Reasoning

All questions from CAT Exam Logical Reasoning
Logical Reasoning – Set 1: A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands.
Logical Reasoning – Set 2: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata
Logical Reasoning – Set 3: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row
Logical Reasoning – Set 4: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 5: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N).
Logical Reasoning – Set 6: A new airlines company is planning to start operations in a country.
Logical Reasoning – Set 7: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 8: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 9: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

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### One response to “How to solve Family Tree, Relationships problems based on coded symbols”

1. Divyani says:

Helpful..wud u post something forLR topic direction sense

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