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Data Sufficiency — decode meanings of digits ‘‘9’’ and ‘‘5’’ Given base codes: '13' = 'stop smoking'; '59' = 'injurious habit'. Statements: I. '157' = 'stop bad habit'. II. '839' = 'smoking is injurious'. Find what '9' and '5' mean respectively. Choose the correct sufficiency option.

Difficulty: Easy

Correct Answer: II alone is sufficient while I alone is not sufficient

Explanation:

From Statement II with the base '839' = 'smoking is injurious' and base '13' = 'stop smoking' ⇒ common digit 3 = 'smoking'. Thus in '839', digit 9 = 'injurious'. From base '59' = 'injurious habit', if 9 = 'injurious', then 5 = 'habit'. II alone suffices.

Statement I '157' = 'stop bad habit'. With base, we get 1 = 'stop', but cannot split 5 between 'habit' and 'bad' without Statement II. I alone is insufficient.

Therefore II alone is sufficient while I alone is not sufficient. (Digit 9 = injurious; digit 5 = habit.)

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