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06 Sep 2026, 22:44
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rashminuligonda
Other languages are irrelevant here because the question considers only English, German, and Spanish.
So we are not assuming that no other languages are spoken. We are simply classifying the 200 members according to these three languages.
07 Sep 2026, 04:41
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Hi rashminuligonda,
This is a sharp instinct, and you're right that in general you shouldn't invent categories the problem never mentions. But here the question itself takes care of the "other languages" worry, so let me show you where.
Look at the phrase in Statement (2): "20 of the members do not speak any of the three languages." That bucket isn't "people who speak nothing at all" - it's "people who speak none of English, German, or Spanish." So a Mandarin-only speaker, or someone who speaks Mandarin and French, or someone who speaks nothing - every single one of them lands in that same group of 20.
So the whole population of 200 splits cleanly into just these boxes:
- Only Spanish = 70
- Only English = 60 (from Statement 1)
- English + German, and English + Spanish = the two-language people we want
- None of the three languages = 20 (from Statement 2)
Mandarin never gets its own slot because it's already swept into that last box. That's why the equation 60 + 70 + (two-language) + 20 = 200 is complete - nothing is left uncounted.
The key idea: the question is only ever asking about the three named languages. Any other language a member speaks is irrelevant unless it changes which of these boxes they fall into - and it doesn't. A Mandarin speaker either also speaks one of the three (then they're counted there) or doesn't (then they're in the 20).
So your rule - "don't assume things not stated" - actually still holds. We're not assuming Mandarin doesn't exist; we're noting the problem's wording already accounts for anyone who speaks it. That's what makes the two statements together sufficient, giving C.
Answer: C
This is a sharp instinct, and you're right that in general you shouldn't invent categories the problem never mentions. But here the question itself takes care of the "other languages" worry, so let me show you where.
Look at the phrase in Statement (2): "20 of the members do not speak any of the three languages." That bucket isn't "people who speak nothing at all" - it's "people who speak none of English, German, or Spanish." So a Mandarin-only speaker, or someone who speaks Mandarin and French, or someone who speaks nothing - every single one of them lands in that same group of 20.
So the whole population of 200 splits cleanly into just these boxes:
- Only Spanish = 70
- Only English = 60 (from Statement 1)
- English + German, and English + Spanish = the two-language people we want
- None of the three languages = 20 (from Statement 2)
Mandarin never gets its own slot because it's already swept into that last box. That's why the equation 60 + 70 + (two-language) + 20 = 200 is complete - nothing is left uncounted.
The key idea: the question is only ever asking about the three named languages. Any other language a member speaks is irrelevant unless it changes which of these boxes they fall into - and it doesn't. A Mandarin speaker either also speaks one of the three (then they're counted there) or doesn't (then they're in the 20).
So your rule - "don't assume things not stated" - actually still holds. We're not assuming Mandarin doesn't exist; we're noting the problem's wording already accounts for anyone who speaks it. That's what makes the two statements together sufficient, giving C.
Answer: C
rashminuligonda
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