In a certain code language, ‘A + B’ means ‘A is the mother of B’; ‘A − B’ means ‘A is the brother of B’; ‘A × B’ means ‘A is the wife of B’ and ‘A ÷ B’ means ‘A is the father of B’. Based on the above, how is 5 related to 2 if ‘5 ÷ 1 × 3 ÷ 4 − 2’?
- (a)Mother’s mother
- (b)Father’s father
- (c)Mother’s father
- (d)Father’s mother
Answer
Why
Correct — C. Read the chain left to right and mark each person's sex the moment a symbol fixes it.
Rule: + is mother of, − is brother of, × is wife of, ÷ is father of.
5 ÷ 1 → 5 is the father of 1.
1 × 3 → 1 is the wife of 3, so 1 is female.
3 ÷ 4 → 3 is the father of 4, and 1 is his wife, so 1 is the mother of 4.
4 − 2 → 4 is the brother of 2, so 2 is 1's child too.
So 2's mother is 1 and 1's father is 5: 5 is 2's mother's father → option (c).
Why the others are wrong
- (a)Mother’s mother — Mother's mother needs 5 to be female. But 5 ÷ 1 makes 5 the father of 1, and no symbol in the chain ever puts 5 on the female side.
- (b)Father’s father — Father's father would be the father of 3, who is 2's father. The chain never names 3's parents, and 5 is attached to 1, not to 3.
- (d)Father’s mother — Father's mother fails twice: 5 is male, and the parent 5 is linked to is 1, who is 2's mother rather than 2's father.
Concept
Coded blood relations give you four symbols and a chain, and the work is a diagram, not a memory feat.
Two of the four symbols also fix a person's sex. × (wife of) makes the left person female and the right person male, and ÷ (father of) makes the left person male.
Once 1 is female and married to 3, every child of 3 is also 1's child, which is the bridge that connects 5 at the top to 2 at the bottom. Draw two levels, put 5 alone on the first, 1 and 3 on the second, and 4 and 2 on the third.
The relation always runs from the term on the left of the symbol to the term on the right. Reading 5 ÷ 1 as 1 is the father of 5 inverts the whole family and still produces a plausible-looking option.
Key facts
- A ÷ B means A is the father of B, so ÷ fixes the left term as male.
- A × B means A is the wife of B, so × fixes the left term as female and the right term as male.
- In 5 ÷ 1 × 3 ÷ 4 − 2 the people are 5 (1's father), 1 and 3 (a married couple) and 4 and 2 (their children).
Study next
Common traps
- Reading the chain right to left. The relation runs from the left term to the right term.
- Trying to fix 2's sex. The symbol − (brother of) tells you about 4, not about 2, and the answer never needs it.
- Forgetting that being 3's wife makes 1 the mother of 3's children, which is the only step joining 5 to 2.
The four definitions used here are reused word for word with a different chain on 10 Sep 2024, 16:00, Reasoning Q.2, where 5 − 2 × 4 ÷ 3 makes 5 the mother's brother of 3.
So the symbol table is worth learning as a shape rather than as a fact, because the chain changes and the reading procedure does not.
Related PYQs
No directly related past PYQ was found.