Bunuel wrote:
A group of friends contributed to the cost of a party where each person had to contribute the same integer amount. Since three people did not participate, the remaining people had to pay Rs. 10 more. If the total amount contributed is the minimum value possible, what would be the per person contribution had 10 people contributed to the party?
(A) Rs. 2
(B) Rs. 5
(C) Rs. 6
(D) Rs. 8
(E) Rs. 10
poorvi125We are asked to find a minimum. Okay, let’s just start trying some numbers to see if we can wrap our heads around what’s happening.
Can the original number of people be 0, 1, 2, or 3? No, because 3 people didn’t participate and there was still at least one person to cover the shortfall.
Can the original number of people be 4? Well, if there were 4 and 3 didn’t participate, that would leave 1. We are told that the remaining person(s) would need to add $10 to their contribution. But there’s no way for the 3 missing people to have totaled to $10. So, the original number of people can’t be 4.
Can the original number of people be 5? Well, if there were 5 and 3 didn’t participate, that would leave 2. Those 2 would combine for an extra $20, but there’s no way for the 3 missing people to have totaled $20. So, the original number of people can’t be 5.
Can the original number of people be 6? If there were 6 and 3 didn’t participate, that would leave 3. Those 3 would combine for an extra $30. Aha, the 3 missing people can total $30 if everyone had been expected to pay $10. So, 6 people were each expected to pay $10, for a total of $60.
We are asked what the payment would be if 10 people split that $60. So, $6.
Answer choice C.
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