# Coded Relationship

This type of problems is also a relatively new feature but nowadays it is appearing quite frequently. The problem involves interpreting a given relationship-string which is coded in a particular fashion and then matching it with the relationship mentioned in the question. The process of decoding each and every relation and then interpreting from the given relationship-string the final relationship is a cumbersome process and doing all of it for all the choices makes it very time taking.

However, some clever short-cut techniques may make the solution miraculously quick. Let us see how. But before that, let us have a look at a sample problem.

## A sample problem

A + B means A is the father of B
A - B means A is the sister of B
A x B means A is the husband of B
A ÷ B means A is the wife of B

Q. 1 Which of the following means 'T is the nephew of Q' ?

(a) Q x R - S + T     (b) Q + R ÷ S + T     (c) Q - R ÷ S + T

(d) Q ÷ R + S - T    (e) None of these

Q. 2 Which of the following means 'S has a blood-relationship with T' ?

(a) S ÷ R + T x Q     (b) S ÷ Q + R x T     (c) S - R x T - Q

(d) S x Q - R - T       (e) None of these

## Our standard code

In order to explain many of the points that I am going to make later in the chapter, I will be referring to some of these codes again and again. In order to avoid confusion and also to avoid repetition, I am going to follow one standard set of codes for the rest of this chapter. (Later, of course, when we face the actual problems we will follow the coding pattern as given in that problem.)

So, our standard coding system for the rest of the chapter will be as follows.

Type I (Forward Type)

A + B means A is the father of B
A - B means A is the mother of B
A x B means A is the brother of B
A ÷ B means A is the sister of B
A @ B means A is the husband of B
A Δ B means A is the wife of B
A α B means A is the son of B
A β B means A is the daughter of B

Type II (Backward Type)

A ^ B means B is the father of A
A ~ B means B is the mother of A
A # B means B is the brother of A
A \$ B means B is the sister of A
A γ B means B is the husband of A
A δ B means B is the wife of A
A > B means B is the son of A
A < B means B is the daughter of A

Note : Difference between Forward type and Backward type Codes

The difference is obvious by its very appearance.

Forward Type : In the forward type codes, the first person is the given relation of the second person.

For example, in A + B, the relationship is of father. Now, in A + B, A appears first and B later. So, A is the father of B means it is a forward-type code.

Backward Type : In the backward type code, the second person is the given relation of the first person.

For example, in A ^ B, the relationship is again that of father. But, here, the second man is the father. So, here, the meaning is that B is the father of A and hence it is a backward-type coding.

As another example compare, A - B and A ~ B. In both these cases, the relationship is that of mother. But in first case, A is the mother of B and in the second, B is the mother of A. Therefore, the first is a forward-type code while the second is a backward-type code.

## Some Quick Techniques for Eliminating Wrong Answers

We will now discuss some quick methods to eliminate the wrong answers:

Rule #1:
Check Sex

Sometimes the person under consideration must be a male (or a female) if the given answer choice were to true. But the choices start with information's that the person is a mother- sister.. (or a father, brother.) etc, which means that this choice can be easily eliminated.

Consider the following examples to understands this.

Ex. 1:  Which of the following means that "A is the grandmother of B" ?

1) A + B x C - D ÷ F     2) A x C - D + B x F     3) A - B - C + D + E

4) A - C x B + D ÷ F     5) None of these

Here, in the question, since A is to be the grandmother of B. A must be a female. But the very first word in (1) and (2) mean that A is a male. Because in (1), A + B means A is father (a male) of B and in (2), A x C means A is the brother (a male) of C. Therefore, in these two choices we don't need to look any further and straightaway eliminate them.

Ex. 2 : Which of the following means that "X is the grandson of Y" ?

1) X ÷ A + B - C x Y     2) X ÷ A α B α C ÷ Y     3) X α A ÷ B ÷ C α Y

4) X β A β B x C x Y     5) None of these

Here, in this question, if X is to be the grandson of Y, X must be a male. But the very first words in choices (1), (2) and (4) make X out to be a female. For example, in (1), X ÷ A means X is a sister (hence a female) of A. Same is true of (2). In (4), X β A means X is a daughter (hence a female) of A. Therefore, we can straightaway eliminate choice (1), (2) and (4).

Ex. 3:  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     5) None of these

Here, in this question, since B is to be the grandfather of E; B must be a male. But choice (2), (3) and (4) are quickly rejected as these B turns out to be a female in the first glance. For example, in (2): A < B means B is the daughter (hence, a female) of A; in (3) A \$ B means is the sister (hence a female) of A and same in (4). Hence, (2), (3) and (4) are quickly eliminated.

MIND IT !

Note that Ex. 3 was a case where the relationships were coded in the backward type format. And in this case we rejected the wrong choices (2), (3) and (4) because there the code that indicated the wrong sex of B appeared before B.

[See, A < B in (2), A \$ B in (3) and (4)].

On the other hand, in Ex. 1 and Ex. 2, the relationships were coded in the forward type format. And in that case we rejected the wrong choices because there the codes that indicated the wrong sex of A and X appeared after A and x.

For example, [ See, a + B in (1) and A x C in (2) of Ex. 1, X ÷ A in (1) and (2) and X β A in (4) of Ex. 2].

This give us our brief and quick short-cut technique.

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 indicates the wrong sex, in case of backward-type coding.

To understand the above rule consider Ex.1, Ex. 2, Ex. 3 once again:

Ex.1 : Person in question is A (because the question wants us to find if A is the grandmother). All coding's are forward-type. Now, immediately after A, we have + and x sign in choices (1) and (2) respectively and these indicate the wrong sex because + and x mean father and brother respectively which is a male-sex. So, (1) and (2) are eliminated.

Ex. 2: Person in question in X (because the question wants us to find if X is a grandson). Coding's are forward-type. Now, immediately after X, we have ÷ in (1) and (2) and β in (4). They indicate wrong (female) sex as + stands for sister and β stands for daughter. So, choices 1, 2 and 4 are quickly eliminated.

Ex. 3: Person in question is B (because the question wants us to find if B is a grandfather). Here, the coding's are backward-type and hence we analyse the symbols immediately before B. The symbols immediately before B are <, \$ and \$ in choice 2, 3 and 4. They indicate the wrong sex (female) as < stands for daughter and \$ stands for sister. So, 2, 3 and 4 are quickly eliminated.

Rule #2:
Check Generation-gap

It may be time-consuming to actually draw the family-tree (using the method I am going to describe later) and see if A is indeed a, say, grandfather of say, B. But we can easily and quickly check by giving mere cursory glances that A is indeed two generations over B. So, all choices that are possibly correct must have a generation gap of 2 between A and B.
Using this tip we can eliminate all the choices that don't have this necessary generation gap.

Consider the following statements, for example:

1) A + B + C         2) A x B x C

3) A x B + C         4) A - B Δ C α D

In (1), we have, A is the father of B and B is the father of C. Clearly, A is the grandfather of C. The generation gap is two, between A and C. The gap between A and B is 1 (because A is father of B). Similarly, gap between B and C is 1. So, gap between A and C is 1 + 1 = 2.

In (2), we have A is brother of B who is brother of C. Clearly, A is brother of C. So, there is no i.e. zero generation-gap. The gap between A and B is 0 (as A and B are of the same generation, i.e. brothers) and that between B and C is 0. So, gap between A and C is 0 + 0 = 0.

In (3), we have A is brother of B who is father of C. Clearly, A is uncle of C. So, there is a gap of one generation between A and C. Here, gap between A and B is zero (as A and B are brothers and, therefore, of the same generation) and that between B and C is 1 (as B is father of C). So, gap between A and C is 0 + 1 = 1.

In (4), we have: A is mother of B, who is wife of C who is son of D. Clearly, A is the Samdhan of D and the generation-gap between them is zero. Here, gap between A and B is 1 (because A is a mother of B), that between B and C is zero (as they are husband and wife and hence, no generation gap), that between C and D is minus one or -1 * (as C is a son of D). So, the total gap between A and D is 1 + 0 + (-1) = 0.

• Since a son is a generation below the father's generation, we take the gap as negative. So, in cases of sons or daughters, the generation gap is taken as 1.

By the foregoing analysis it is clear that:

for father/mother: gap is taken as +1
for brother/sister/husband/wife: gap is taken as 0
for son/daughter: gap is taken as -1

Now for each choice, calculate the generation-gap between two persons.

If it is proper we don't reject the choice but if it is not we reject it. For example if A is to be the grandfather of B, the gap between A and B must be 2. Similarly if X is to be the grandniece of Y, the gap between X and Y must be -2.

How to calculate the generation-gap between two persons

We give below an easy, step-by-step approach to calculate the generation gap:

Step #1: Take one of the persons under consideration

Step #2: Move rightwards. For each father/mother relation put a +1, for each brother/sister/husband/wife relation put a 0, for each son/daughter relation put a -1.

Step #3: Do the sum total

MIND IT !

The above is applicable only for forward-type coding. In the backward-type coding, the process remains the same but there is one minor change.
Here, instead of moving to the right, we start from the right side and move to the left. Rest of the method remains the same.

Ex. 4:  Consider the following: A - B x C β D α E Δ F x G
Find the generation gap between

(i) A and C   (ii) C and E   (iii) E and B   (iv) G and A

Soln: (i) A and C

Since A is on left we start from A and move towards C. - means mother so we write +1, x means brother so we write 0.
gap: +1 + 0 = +1.

Conclusion: A is of C's father's generation.

(ii) C and E

Since C is to the left of E, we start from C and move rightwards to E. We have a β and an α between C and E. Since both are son/daughter relations we write -1 for both.
gap: (-1) + (-1) = (-2)

Conclusion: C is of E's grandson's generation

(iii) E and B

Since E is to the right of B, we don't start from E. We start from left i.e. we start from B and move right. x means brother so we write 0, β means daughter so we write -1 and α means son so we write -1.
gap: 0 + (-1) + (-1) = -2

Conclusion: B is E's grandson's generation

Note: If gap between B and E is -2, gap between E and B is +2. In other words, E is B's grandfather's generation.

(iv) G and A

We start from A as A is on the left of G. - means mother so we write +1, for x we write 0, for β we write -1, for α we write -1, for Δ we write 0, for x we write 0.
gap: +1 + 0 + (-1) + 0 + 0 = -1

Conclusion: A is G's son's generation

Note: If gap between A and G is -1, gap between G and A is +1. In other words, G is A's father's generation.

Ex. 5:  Consider the following: S # R δ Q > P < O # N ^ M
Find the generation gap between

(i) S and Q   (ii) R and O   (iii) O and Q   (iv) M and S

Soln: (i) S and Q

This is a backward-coding case. So, we will always take the right letter and move to the left.

Here, we take Q and move to the left. δ means wife so we write 0, # means brother so we write 0.
gap: 0 + 0 = 0

Conclusion: S and Q are of the same generation.

(ii) R and O

We take O and proceed to left. < means daughter so we write -1, > means son so we write -1, δ means wife so we write 0.
gap: (-1) + (-1) + 0 = (-2)

Conclusion: O is R's grandson's generation.

Note: If gap between O and R is -2, gap between R and O is +2. In other words, R is O's grandfather's generation.

(iii) O and Q

We take O and proceed to the left. For < we write -1 and for > we write -1.
gap: (-1) + (-1) = -2.

Conclusion: O is Q's grandson's generation.

(iv) M and S

We take M and proceed to the left. For ^ we write +1; for # we write 0, for < we write -1, for > we write -1, for δ we write 0, for # we write 0.
gap: +1 + 0 + (-1) + (-1) + 0 + 0 = -1

Conclusion: M is S's son's generation.

Tip !

In our examples, we are considering more than six relations in a single expression. We are also considering backward-type coding. In the examinations, you'll generally get only forward-type coding and there too, not more than three-four relations in a single expression.

In this case, finding generation-gap is still easier and fast. Just take the two persons under consideration and consider the symbols between them. Ignore all brother/sister/husband/wife/relations. Put +1 for mother-father and -1 for son-daughter and; add. Usually we have forward-coding, so start from left to right.

## Drawing a family tree

The tips given in above are techniques for quickly eliminating the obviously wrong answers. But even after employing that technique, we may not be able to eliminate all the wrong choices. In that case, two or more choices may still be left for consideration. If that be case, we will have to actually analyse each of these remaining choices and see which one is correct.

The best way to draw quick conclusions about relationships in these type of questions is by drawing family tree.

Here we give a brief method:

Drawing a family tree

(a) Vertical or diagonal lines should be used to represent parent-child relationships.
(b) A double horizontal line (like <=>) should be used to represent marriages.
(c) A dashed line should be used to represent brother or sister relationships.

Note: Apart from dashed lines, brother or sister relationships are also easily established if two persons have the same root (i.e. parents depicted by vertical or diagonal lines).

(d) Put a + sign before someone who is a male and a - sign before someone who is a female.
(e) Whenever something is not known put a ? mark or some such symbol (x, y, z etc., for example) before it.

For example, consider the following diagram:

The above diagram tell us that:

(i) F and A are a couple; F is the husband while A is the wife.
(ii) F has a sister K.
(iii) The couple, F and A, has three children: M, C and another son, whose name is not known. C is also a son while the sex of M is not known.
(iv) M and the other unknown son are unmarried while C is married to D.
(v) The couple, C and D, has daughter S and a son whose name is not known.

Suggested Method for Solution !

We are now in a position to lay down our integrated approach towards our solution. That is:

Step I: Eliminate all wrong choices by the quick method discussed in above

(a) check sex and (b) check generation-gap

Step II: Draw family-tree for the remaining choices and pick the correct answer.