Four people P, Q, R, and S, of different ages, make the following observations.
P – I am younger than S.
Q – I am neither the youngest nor the oldest.
R – P is older than me.
Based on these observations, the youngest person is ______.
P
Q
R
S
ANSWER
The youngest person is R, option (C).
Official answer: CSource: Official answer key, GATE 2026 IN (IIT Guwahati)
Write each statement as an inequality of ages. From P: . From R: , that is, .
Chain the two inequalities (the order is transitive): .
From Q: Q is neither the youngest nor the oldest, so Q holds position 2 or 3 in the order from youngest to oldest.
The only orders that satisfy all three statements are and .
R comes first in both, so R is the youngest whichever middle position Q takes (S is the oldest in both).
Check the options: P is older than R, S is older than P, and Q cannot be the youngest by its own statement, which leaves only R.
KEY IDEA
Turn each statement into an age inequality and chain them. and give , so neither P nor S can be the youngest. Q rules itself out, which leaves R. You do not need the full order to answer.
WATCH OUT FOR
Misreading R's statement "P is older than me" as . It means , so R is younger than P. Some candidates also think Q's statement makes the order ambiguous. Q can sit second or third, but R is youngest either way, so the question still has one answer.
From the GATE 2026 IN paper. Every question of this paper · Download the full paper · All 41 Reasoning questions, with notes
