A group of friends contributed to the cost of a party where each pers

Question

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

(A) Rs. 2 
(B) Rs. 5
(C) Rs. 6 
(D) Rs. 8
(E) Rs. 10

TestPrepUnlimited · Answer

If we know there are X people that were to originally pay Y each, we have  X*Y = (X - 3)(Y + 10) . Then we can try to simplify this, although we will have infinitely many paired solutions of (X, Y), it is possible to find the smallest one.

X*Y = (X - 3)(Y + 10)

0 = 10X - 3Y - 30

10X - 3Y = 30  or  10X = 3Y + 30

Without making Y = 0, we need the right side to be a multiple of 10. The smallest possible Y to achieve that is Y = 10. Then we get X = 6, so the total would be XY = 60. The question is asking whats the per person contribution if 10 ppl were to pay, so the answer would be 60/10 = 6.

Ans: C

poorvi125 · Answer

ThatDudeKnows

Can you please help with a straightforward solution for this question?
Thanks!!

ThatDudeKnows · Answer

poorvi125

We 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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Kinshook · Answer

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?

Let the integer amount each person had to contribute be Rs x and number of friends be n.

nx = (n-3)(x+10) = nx -3x + 10n - 30

x = 10(n-3)/3

Since nx is minimum, n = 6; x = 10

The per person contribution had 10 people contributed to the party = nx/10 = 60/10 = Rs 6

IMO C

A group of friends contributed to the cost of a party where each pers

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A group of friends contributed to the cost of a party where each pers

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