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A test paper puts these five symbols in place of the usual signs: '◆' means 'is greater than', '▲' means 'is greater than or equal to', '■' means 'is equal to', '●' means 'is less than', and '▼' means 'is less than or equal to'.
Given that 'J ◆ K', 'K ■ L' and 'L ▲ M' are all true, which of the following is definitely true?

Competition practiceInequalities
  • AM ▲ J
  • BJ ◆ M
  • CJ ▼ M
  • DJ ■ M

Step-by-Step Solution

Decode first: J > K, K = L, L ≥ M. Substituting through the equality gives J > K = L ≥ M, that is J > L ≥ M, and a strict link followed by a non-strict one is strict, so J > M. In code that is 'J ◆ M'. 'M ▲ J' (M ≥ J) reverses the whole chain and is the option a solver picks who reads the statements from right to left. 'J ▼ M' (J ≤ M) is the plain reversal of the correct relation. 'J ■ M' (J = M) is what you get by treating every link as an equality because the middle link happens to be one.
Answer: B) J ◆ M

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