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A recent lunch meeting at a certain club was attended by members and

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A recent lunch meeting at a certain club was attended by members and  [#permalink]

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New post Updated on: 06 Oct 2018, 03:51
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A recent lunch meeting at a certain club was attended by members and guests. Each member paid $4 for the lunch and each guest paid $8 for the lunch. How many of the people attending the meeting were members


(1) A total of 20 people attended the meeting.

(2) A total of $92 was paid for the lunch

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Originally posted by gmat1393 on 06 Oct 2018, 03:47.
Last edited by Bunuel on 06 Oct 2018, 03:51, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A recent lunch meeting at a certain club was attended by members and  [#permalink]

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New post 06 Oct 2018, 04:18
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gmat1393 wrote:
A recent lunch meeting at a certain club was attended by members and guests. Each member paid $4 for the lunch and each guest paid $8 for the lunch. How many of the people attending the meeting were members


(1) A total of 20 people attended the meeting.

(2) A total of $92 was paid for the lunch


The given question translates into 4m+8g = total. To find the value for m we need to know the value for 'g' and that for 'total' or to see that there is exactly one solution.
We'll look for this information, a Logical approach.

(1) this gives m+g=20. Without information on the total we cannot solve these equations.
Insufficient.

(2) This gives 4m+8g=92 which simplifies to m+2g=23. This has many solutions, for example m = 1,g=11 and m=3,g=10.
Insufficient.

Together, we have two equations with two variables which has only one solution (m=17,g=3)
Sufficient.

(C) is our answer.
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Re: A recent lunch meeting at a certain club was attended by members and  [#permalink]

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New post 11 Dec 2018, 08:43
gmat1393 wrote:
A recent lunch meeting at a certain club was attended by members and guests. Each member paid $4 for the lunch and each guest paid $8 for the lunch. How many of the people attending the meeting were members


(1) A total of 20 people attended the meeting.

(2) A total of $92 was paid for the lunch


In this kind of question, where the integer value restriction exists, we can easily know whether there is one possible integer value or more than one possible integer value.

let M is the number of members and G is the number of guest. we have to find the value of M. now

statement (1) tells us, M+G=20. from this we can have multiple values of M. for example, if M=2, then G=18; if M=5, then G=15. Not Sufficient.

Statement (2) tells us 4M+8G=$92. from the prompt question we know M and G have to be integer. Because the number of people can not be fraction or negative. NOW here is the RULES,
the LCM of 4 and 8 is 32 which is smaller than 92. so we can say, there will be multiple values of M and G for this equation. if the LCM would be greater than the Left hand side value(92), then there will be only one possible value for M and G. so this is also NOT Sufficient.

together, we have 2 distinct equation and 2 variables. so we can find the values of M.
both statements together are sufficient.
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Re: A recent lunch meeting at a certain club was attended by members and   [#permalink] 11 Dec 2018, 08:43
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