gmat1393
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.