Statements: L < K, N ≤ M < R, K = N Conclusion: I. N < R II. R > L
Statements: L < K, N ≤ M < R, K = N
Conclusion:
I. N < R
II. R > L
Answer: E. If both conclusions I and II follow — Concept: In a chain of inequalities that are all oriented the same way (e.g. all '≤'/'<' signs pointing left-to-right, as here), the relation between the two…
- A.
If only conclusion I follows
- B.
If only conclusion II follows.
- C.
If either conclusion I or II follows.
- D.
If neither conclusion I nor II follows.
- E.
If both conclusions I and II follow
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Correct answer: E
Concept: In a chain of inequalities that are all oriented the same way (e.g. all '≤'/'<' signs pointing left-to-right, as here), the relation between the two end variables is strict '<' as soon as at least one link in the chain is strict — a '≤' next to a '<' still collapses to '<' overall (e.g. X ≤ Y < Z always gives X < Z, whether X = Y or X < Y).
Application: Combine the three statements into one chain.
Substitute K = N into L < K to get L < N.
From N ≤ M < R, the chain rule above gives N < R directly — so Conclusion I (N < R) follows.
Chain L < N and N < R together: L < N < R, so L < R, i.e. R > L — so Conclusion II (R > L) also follows.
Cross-check: Pick values satisfying every statement, e.g. L = 1, K = 2, N = 2, M = 3, R = 4. Check: L < K (1 < 2 ✓), K = N (2 = 2 ✓), N ≤ M < R (2 ≤ 3 < 4 ✓). Then N < R gives 2 < 4 (✓, Conclusion I holds) and R > L gives 4 > 1 (✓, Conclusion II holds).
Result: Both Conclusion I and Conclusion II follow necessarily from the statements, so the correct choice is 'If both conclusions I and II follow'.