Blood Relation

What the exam asks. A key defines four or five symbols, for example "A # B means A is the father of B". Then an expression such as P # Q * R @ S is given and you must say how P is related to S. In the second form a relation is given and you must pick, from four expressions, the one that shows it.

The logic. Each symbol is only a short way of writing a relation. Its meaning comes from the key of that very question and changes from one question to the next: "+" may mean father here and wife in the next. So read the key every time. Read each pair as "the first letter is the … of the second". In A $ B @ C, the symbol $ describes A and @ describes B. The person being described is always the first letter.

The step method. (1) Write every symbol as a relation in words and note the gender it fixes. (2) Collapse the chain from the left, two links at a time: if A is X of B and B is Y of C, then A is "X of Y" of C. (3) Read the final relation from the first letter to the last.

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In the picture, P # Q * R @ S with the key "# father, * sister, @ wife" collapses in two steps: P is the father of Q, and Q is the sister of R, so P is the father of R. Then R is the wife of S, so P is the father-in-law of S.

Only the symbols for father, mother, brother, sister, husband, wife, son and daughter tell you a gender. The second form ("which expression means X is the … of Y?") is not solved by building; it is solved by testing the four options, as Trick 3 shows. Digit codes such as "P 3 Q" work in exactly the same way.

What the exam asks. Four to seven short sentences such as "X is the son of Y" and "Z is the wife of W" are followed by one question, "How is A related to B?". Names or letters are used, and nothing is coded. The logic is simple: a family is made of couples and their children, each sentence adds one person or ties one more person to someone already drawn, and the only danger is losing track.

A statement chain introduces a family to you one sentence at a time. Nobody shows you the whole family at once. Each sentence adds one new person, or ties a new person to someone already on the page. If every person sits in the right generation row with the right gender, the final question is just reading the tree.

The method has three moves. First, draw a ladder of generations. Second, take one statement at a time, place the new person, and write M or F beside the person the moment a word such as brother, wife or father fixes the gender. Third, go to the two persons named in the question and read the relation from the first person to the second.

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Take this chain: P is the brother of Q. Q is the daughter of R. R is the wife of S. T is the father of S. How is T related to P? In the picture, R is S's wife and Q is R's daughter, so Q is also S's child. P is Q's brother, so P is a male child of the same parents. T is S's father, which makes T the father of P's father. So T is P's paternal grandfather.

Add one statement, fix one gender, move on. When a name repeats, do not draw a new person; attach the new fact to the person already drawn. In a big family, trace only the path between the two named persons, because the other branches are decoration. If no word ever fixes a gender, keep the diamond and give a neutral answer: parent, sibling or child.

Two facts do most of the work, and you can use them without drawing: the children of one couple are brothers and sisters of one another, and the spouse of a parent is the other parent (the standard exam convention). When a statement is not about the person you are chasing, it is usually only a bridge between two persons you do need.

What the exam asks. A speaker points to a person or a photograph and describes him or her through the speaker's own family, for example "He is the son of my grandfather's only child". You must say how the pointed person is related to the speaker. The sentences have become longer in recent papers, with "only", "wife" and "husband" packed in, but the logic below never changes.

In a pointing question one person speaks and describes someone else through his or her own family. Everything depends on one small word: "my". "My" always means the speaker.

Do three things in order. One, decide whether the speaker is a man or a woman. The question tells you through a word such as "a man said" or "a woman said". Two, replace every phrase like "my father's only son" by the person it must be. Three, walk outward from the speaker to the pointed person, and then give the relation in the direction the question asks.

Step two is where the gender of the speaker matters. A man is the son of his father. If he is the only son, then "my father's only son" is the man himself. But if the speaker is a woman, she is not a son, so "my father's only son" must be her brother.

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The last step is reversing. If the girl is the speaker's brother's daughter, the girl is the speaker's niece; but the speaker is the girl's uncle or aunt. The answer asked is "girl to speaker". Fix the speaker, build outward, and read the relation in the direction asked. When the speaker points to a "person", that person cannot be the speaker. When the speaker points to a "photograph", it can be his own photograph.

Phrases the paper-setters love. In the exam convention, "the only son my wife has" and "my wife's only son" are the speaker's own son, and "my husband's only daughter" is the speaker's own daughter. "My grandfather's only child" is the speaker's father or mother, because the speaker's parent must be one of the grandfather's children. So, when the speaker points to another person, "the son of my grandfather's only child" is the speaker's brother.

What the exam asks. One sentence packs three to five links, either as a direct question ("How is Sunita's mother's brother's son related to Sunita?") or inside a short story. The logic: every "'s" is one step on the family tree, and the word "only" often makes the sentence loop back to someone already known.

A long possessive sentence is a chain of "'s", such as "Arjun's mother's only brother's only son's sister". Do not try to see the last person at once. Collapse the sentence from left to right. Take the first two items, replace them by the single person they give, write the gender, and use that person as the new starting point.

Let us collapse the sentence above. Arjun's mother is a woman. Her only brother is Arjun's maternal uncle. That uncle's only son is Arjun's cousin, a boy. The boy's sister is the daughter of the same uncle, which makes her Arjun's cousin as well. So the last person is a cousin.

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The word only is the big shortcut. "Only son" closes the list of sons, "only daughter" closes the list of daughters, and the phrase very often loops back to a person you have already drawn. Learn these loops:

Resolve left to right, and write the gender of every person you meet. If the sentence starts with a name, first fix that person's gender from the question. Never drop a link: the phrase "Sunil's sister's son" has three persons, not two.

Pair cancelling. Some neighbouring pairs cancel and take you back to a known person: a spouse's spouse is the person himself or herself (Hari's wife's husband = Hari); a parent's only child of your own gender is you. After each cancelling, a five-link sentence often shrinks to two links.

What the exam asks. A paragraph describes six to eleven persons, sometimes with two couples across three generations, and the question asks for a relation between two members, for a count of males or females, or for the name of the person who fits a description. The clues are often not in order, so the logic is: build the family step by step and tick every clue.

A family puzzle gives you six to eleven persons and a paragraph of clues, and asks for a relation, a count of males or females, or who is who. The clues are often not in order, so the safe approach is to make the family step by step.

Step one: list every person once, using exactly the names or letters given. This also tells you how many members there are. Step two: write what is certain. A word like father, brother, husband or son makes a person male; mother, sister, wife or daughter makes a person female. Step three: draw the couples first, side by side with a double line, and hang the children below them. When there are two couples across three generations, the older couple is on top, the married children come next, and the grandchildren last. Step four: after drawing, read every clue once more and tick it.

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Here is a small example. In a family of seven, A is the husband of B. C is their son and D their daughter. E is C's wife, F is the son of C and E, and G is D's husband. The picture gives the count of males at once: A, C, F and G, so there are 4 males and 3 females.

For counting questions, ask of every person: which clue makes this person male (or female)? If no clue does, do not count that person. When a question allows two fillings, it will ask only about what both fillings agree on. If you find that your drawing breaks a clue, a person has been placed wrongly; go back and fix it.

Clues that fix a gender in disguise. A negative clue is a real clue. "B is the son of C, but C is not the mother of B" tells you that C is the father of B. "D does not have any brother-in-law" removes a whole group of persons from D's side of the family. Use such clues to fix a gender or to cross out a possibility, and do it early, before the couples are drawn.

What the exam asks. Some recent questions look like an ordinary statement chain, but the last option reads "Cannot be determined", and it is often the right answer. The paper-setters hide the trap in one place: the gender of a person that no sentence has fixed. The link can be found, but the name of the relation cannot.

The logic. A relation name needs two things: a link (who is joined to whom) and a gender at the right end. Words like father, mother, brother, sister, husband, wife, son and daughter fix a gender. Words like child, sibling, cousin, parent and spouse do not, and neither do names or letters. Read every sentence as fixing only the first person named: "R is the sister of S" makes R a woman and says nothing about S.

The step method. (1) Build the chain as usual and find the level and the link. (2) Do the gender check last: look at the person asked about, the first one in "How is X related to Y?", and ask "which sentence fixes his or her gender?". (3) If one does, answer. If none does, and the name of the relation changes with gender (uncle or aunt, nephew or niece, grandfather or grandmother, brother or sister), the answer is "Cannot be determined". If the two persons are not joined by any chain at all, the answer is the same.

Do not overuse it: when the gender of the answer person is fixed, even a long chain is solvable. "A is the sister of B and B is the father of C" makes A the paternal aunt of C, because the word "sister" fixes A. The option is right only when a gender is missing at the answer end.

The older sub-case: two statements. Some papers give a question with Statement I and Statement II and ask which is sufficient. The same two ideas decide it: a link needs a shared person, and a relation name needs a gender. In the picture (N = Nisha, R = Ravi, M = Mohan), the question is "Is Nisha the granddaughter of Mohan?". Statement I links Nisha to her father Ravi, and statement II links Ravi to Mohan. Neither alone joins Nisha to Mohan; together they share Ravi, and "daughter" gives the gender, so the answer is "both together". Work in the same order every time: draw I alone, II alone, then both.

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