You'd never need to know this on the GMAT, but the standard deviation won't ever be more than half the range. That's quite easy to prove if you have a symmetric set, and not at all easy to prove if you have an asymmetric set. It's also not a widely known or reported property of standard deviation, so there's no way any GMAT test taker could be expected to know it, nor could anyone reasonably be expected to prove it in anything close to 2 minutes.
So that's why the answer is A here, but you absolutely don't need to be even remotely concerned about this for the GMAT. Where is this question from?
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