A Recent Lunch Meeting at a Certain Club was Attended by Members GMAT Data Sufficiency

Question: 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

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: C

Solution and Explanation:
Approach Solution 1:
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.

Approach Solution 2:
Let M is the number of members and G is the number of guests. 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 integers. Because the number of people can not be fraction or negative.

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 equations and 2 variables. So we can find the values of M.
Both statements together are sufficient.

“A recent lunch meeting at a certain club was attended by members and”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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