Two Limbs of the Shorthand Test
The recruitment board conducts a shorthand test under these printed rules: dictation of 10 minutes at 80 words per minute; transcription within 50 minutes; a candidate is declared qualified only if transcription is completed inside the limit and errors do not exceed 5 per cent of the dictated words. Three candidates are in the final batch. P types at 15 words per minute and leaves 30 uncorrected errors. Q types at 20 words per minute with 38 uncorrected errors. R types at 25 words per minute with 44 uncorrected errors. All three heard the same 800-word passage. The board has one vacancy, no re-test, and a rule that a candidate failing either limb is not considered at all. A member suggests relaxing the error limit to fill the post, since 'the work is only typing'. The chairman asks for the arithmetic first, then a recommendation with reasons that would survive an audit or a court challenge.
1. Work out each candidate's transcription time and error percentage against both limbs.
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Dictated words = 80 × 10 = 800; the error ceiling is 5 per cent of 800, that is 40 errors. P: 800 ÷ 15 = 53.3 minutes, beyond the 50-minute limit, so P fails the time limb; the 30 errors would have been within the ceiling but are irrelevant once a limb fails. Q: 800 ÷ 20 = 40 minutes, within the limit; 38 errors against a ceiling of 40 is within, so Q qualifies, with a margin of 10 minutes and 2 errors. R: 800 ÷ 25 = 32 minutes, comfortably within the limit; 44 errors exceeds 40, so R fails accuracy by 4 errors. Only Q clears both limbs. The test is conjunctive - fast but inaccurate, or accurate but slow, both fail - and the arithmetic shows each candidate failing for a different reason.
2. Which candidate should the board select, and what safeguards should accompany the decision?
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Select Q, the only candidate who satisfies both limbs on the record. But the margin is thin: 2 errors against a hard ceiling and 10 minutes against the clock, so the board should preserve Q's transcript and the examiner's error sheet, and re-check disputed errors before publishing the result, since one reclassified error changes nothing and two change everything. The error limit should not be relaxed for this vacancy. It is part of the advertised terms, and changing it after the test invites challenge from candidates already failed under it, who were denied a relaxation they were never told about. If the post must be filled and a fresh test is lawful, R can be invited to a re-test with a target of 40 errors or fewer, which is realistic given R's 18-minute buffer. All of this reasoning belongs in the minutes, not in memory.
3. Suppose the board tightens the transcription limit to 35 minutes before the test. Who then qualifies, and what does that reveal about the rule?
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P still fails at 53.3 minutes. Q now fails at 40 minutes, even though 38 errors would have been within the accuracy ceiling. R passes the time limb at 32 minutes but still fails accuracy at 44 errors. Nobody qualifies, and the vacancy cannot be filled without re-advertising or reconsidering the limit. The episode shows that the binding constraint must be identified before a rule is tightened: here accuracy, not speed, is the marginal failure for the fastest candidate, so shortening the clock removes the wrong person and leaves the real problem untouched. A board should model any proposed change against the actual batch - time, errors and their spread - before adopting it, and should state in the advertisement which limb is expected to bite, so that candidates and reviewers can see the rule was designed rather than improvised.