A statement is given followed by two conclusions. Find which conclusion is TRUE based on the given statement. Statement: C= A ≤ T < D ≥ O; G ≥ D < S; T ≥ A Conclusions: I: A < O II: C < G

Correct — A.
Rule: a conclusion is definite only if every sign between its two letters points the same way.

II: C = A ≤ T < D, and G ≥ D means D ≤ G.
So C ≤ T < D ≤ G: one direction, one strict sign, and C < G holds.

I: A ≤ T < D rises, then D ≥ O turns the chain round. A and O have no fixed order, so I fails.

Only II is true → option (a).

Why the others are wrong

• (b)
  Only I — A < O needs one direction from A to O, but the chain rises A ≤ T < D and then falls at D ≥ O. O could sit above or below A.
• (c)
  Either I or II — Either I or II applies only when neither conclusion holds alone and the two, on the same pair of letters, cover every case. Here II holds by itself.
• (d)
  Neither I nor II — Neither misses conclusion II. C = A ≤ T < D ≤ G runs one way from C to G with a strict sign on the path, so C < G is definite.

Coded inequalities are solved by joining the clauses into one chain and reading the path between the two letters of each conclusion. A conclusion is definite only when every sign on that path points the same way.

One strict sign (< or >) on the path makes the result strict. A reversal anywhere, as at T < D ≥ O here, leaves the two end letters with no fixed order.

Key facts

• G ≥ D is the same statement as D ≤ G.
• One strict sign on a one-way path makes the conclusion strict: C ≤ T < D ≤ G gives C < G.
• A reversal on the path, such as T < D ≥ O, leaves the end letters unrelated.

Common traps

• Reading D ≥ O as if the chain kept rising, and accepting A < O
• Leaving G ≥ D unflipped, so C seems to have no path to G

No directly related past PYQ was found.