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Read the key carefully — it is not the same as in other questions. In a certain code: '◆' means 'is less than or equal to', '▲' means 'is less than', '■' means 'is equal to', '●' means 'is greater than or equal to', and '▼' means 'is greater than'.
Given that 'N ▼ O', 'O ● Q' and 'Q ■ R' are all true, which of the following is definitely true?

Competition practiceInequalities
  • AN ◆ R
  • BN ▼ R
  • CR ● N
  • DN ■ R

Step-by-Step Solution

Decode against this key: '▼' is >, '●' is ≥ and '■' is =, so the statements read N > O, O ≥ Q and Q = R. Composing, N > O ≥ Q = R, that is N > Q = R, and a strict link followed by a non-strict one stays strict, so N > R. In this key that is written 'N ▼ R'. 'N ◆ R' means N ≤ R, the exact reverse, and it is the option a solver picks who carries over a key from elsewhere in which '◆' stood for 'greater than' — the reason the key must be re-read every time. 'R ● N' means R ≥ N, again a reversal. 'N ■ R' means N = R, which the strict first link rules out.
Answer: B) N ▼ R

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