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 4 related to 2 if ‘4 + 3 ÷ 2 ÷ 1 − 5’?
- (a)Mother’s father
- (b)Father’s father
- (c)Mother’s mother
- (d)Father’s mother
Answer
Why
Correct — D. Read the chain left to right, one symbol at a time.
Rule: each symbol binds only the two names on either side of it.
4 + 3: 4 is the mother of 3.
3 ÷ 2: 3 is the father of 2.
2 ÷ 1: 2 is the father of 1.
1 − 5: 1 is the brother of 5.
The last two links sit below 2 and say nothing about 4, so drop them.
That leaves 3 as 2's father and 4 as 3's mother. Climbing from 2: first the father, then his mother.
So 4 is 2's father's mother — option (d).
Why the others are wrong
- (a)Mother’s father — This needs 3 to be 2's mother, but the symbol joining them is ÷, which this question defines as 'is the father of'. It also asks 4 to be male, and 4 + 3 has already made 4 a mother.
- (b)Father’s father — The route up through 2's father is right, but 4 is female: 4 + 3 reads as 4 is the mother of 3, so 4 cannot be anybody's father.
- (c)Mother’s mother — ÷ means 'is the father of', so 3 is 2's father and not 2's mother. The second half of this option is sound — 4 is indeed a mother — but the first half breaks the code.
Concept
Symbol-coded relation chains are read strictly left to right, and each symbol joins only its two neighbours. '4 + 3 ÷ 2' is two separate statements — 4 is the mother of 3, and 3 is the father of 2 — not one compound claim about 4 and 2.
Draw the family as you read. Put each parent above the child, and mark sex from the relation word itself: mother and wife fix a woman, father and brother fix a man.
Then answer only what was asked. Links beyond the two people named in the question can be ignored.
The question asks how 4 is related to 2, so '2 ÷ 1' and '1 − 5' are decoration. Working them out costs time and changes nothing.
Key facts
- In this question's dictionary + is 'is the mother of', − is 'is the brother of', x is 'is the wife of' and ÷ is 'is the father of'.
- '4 + 3 ÷ 2' makes 4 the mother of 3 and 3 the father of 2.
- A person reached by going up to the father and then to his mother is the paternal grandmother.
Study next
Common traps
- Carrying a symbol dictionary over from another question instead of reading this one's.
- Answering from 2's side and giving the granddaughter relation rather than the one asked.
- Forgetting that + has already fixed 4 as female before you choose between the grandparents.
10 Sep 2024, 16:00, Reasoning Q.2 uses this exact dictionary — mother, brother, wife, father — on the chain '5 − 2 × 4 ÷ 3'. 12 Sep 2024, 16:00, Reasoning Q.20 keeps the four symbols and redefines them, with − reading 'is the husband of', so never carry a dictionary across.
Related PYQs
No directly related past PYQ was found.