Read the given statement and conclusions carefully. Decide which of the given conclusions is/are definitely TRUE from the statement. Statement: P > Q < S > T = R ≥ U > V Conclusion I: V < S Conclusion II: P > T
- (a)Only Conclusion II is True
- (b)Both Conclusion I and Conclusion II are True
- (c)Only Conclusion I is True
- (d)Neither Conclusion I nor Conclusion II is True
Answer
Why
Correct — C.
Rule: two letters compare only if every sign between them points the same way.
Conclusion I: S > T = R ≥ U > V.
The signs all point one way and include a strict >, so S > V. I is true.
Conclusion II: P > Q < S > T.
The direction flips at Q, so P and T cannot be compared. II is not definite.
Only Conclusion I is true → option (c).
Why the others are wrong
- (a)Only Conclusion II is True — P > T cannot be proved. P and S are both larger than Q, but nothing in the chain says which of them is larger, so P is not linked to T.
- (b)Both Conclusion I and Conclusion II are True — Conclusion II fails, so 'both' fails with it. P = 10, Q = 1, S = 20, T = R = 15, U = 12, V = 5 fits the chain and gives P < T.
- (d)Neither Conclusion I nor Conclusion II is True — Conclusion I is definite. From S down to V the signs are >, =, ≥, > — one direction throughout — so S > V always holds.
Concept
In an inequality chain, compare two letters along the stretch between them. If every sign on that stretch points one way (only >, ≥ and =, or only <, ≤ and =), the comparison holds, and one strict sign makes it strict.
If the direction flips anywhere between them, as it does at Q with > on one side and < on the other, the two letters cannot be compared.
Q is smaller than both P and S, which is exactly why it cannot link them. Two numbers that each exceed a third can stand in either order.
Key facts
- Two letters compare only if every sign between them points the same way.
- One strict sign (> or <) in an unbroken chain makes the result strict.
- A dip like P > Q < S blocks any comparison across Q.
Study next
Common traps
- Reading P > Q and Q < S as if they chained into P > S
- Treating the ≥ in R ≥ U as a break, which wrongly throws out Conclusion I
Here the chain has seven letters with a dip at Q, and one conclusion reaches across it.
19 Sep 2025, 09:00, Reasoning Q.7 uses almost the same chain, P > Q < S ≤ T = R ≥ U > V, and keys Only Conclusion I: Q < R is definite, U > T is not.
Related PYQs
No directly related past PYQ was found.