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Bunuel
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ok, so 10 people paid 420. 20 people, paid 840. 21 people -> 882.
we can see that 21 or more doesn't work. 20 is fine though, so 20 must be the answer.
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CounterSniper
Divide the total sum by 42 and we get 20.xxx
thus the max has to be 20

I believe your method is way more lengthy and time consuming.
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Bunuel
A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 867.50. If each member of the club paid at least $ 42, then what is the greatest possible number of members in the club?

A. 19
B. 20
C. 21
D. 23
E. 25

This problem tests your logic more that it tests your math.

Given: Each person spends $42.
By looking at the options, we see that if there were 20 members, each person will spend atleast $42.
If there were 21 members, each person will spend $41.3

Hence the greatest number of members = 20. Option B
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