Arithmetic mean

[Winner2013]

Committee X and Committee Y , which have no common members, will combine to form Committee
Z . Does Committee X have more members than Committee Y ?

(1) The average (arithmetic mean) age of the members of Committee X is 25.7 years and the
average age of the members of Committee Y is 29.3 years.

(2) The average (arithmetic mean) age of the members of Committee Z will be 26.6 years.

Answer is C

[theCodeToGMAT]

Please use spoiler for Hiding the Answers

N1 = X
N2 = Y

N1/N2 = (M2-M)/(M-M1) [weighted average formula]

To find: N1/N2 > 0

Statement 1:
M1 = 25.7
M2 = 29.3
We don't have "M"
INSUFFICIENT

Statement 2:
M = 26.6
INSUFFICIENT

Combining..
We have M,M1 & M2.
SUFFICIENT

Answer [spoiler]{C}[/spoiler]

[mevicks]

Let the Nos. of members be x, y, z
We know that x + y = z

Q: Is x > y ?

St1: Just gives the average ages of x and y. INSUFFICIENT.
St2: Only average age of Z is known. INSUFFICIENT

St1 + St2: Becomes a Weighted Average Problem.

If the proportion of x and y was equal this would be the scenario:
x_____________Mid___________y
25.7_________27.5___________29.3

Since the final average is 26.6 (avg of z) we can answer that x > y
x_____________Mid___________y
25.7___26.6___27.5__________29.3

[spoiler]Answer : C[/spoiler]

Here x pulls the average down (for more info) and is less than 27.5


Regards,
Vivek

p.s: Please hide your answers using the "spoiler" tag

[Brent@GMATPrepNow]

Committee X and Committee Y , which have no common members, will combine to form Committee Z. Does Committee X have more members than Committee Y?

(1) The average (arithmetic mean) age of the members of Committee X is 25.7 years and the
average age of the members of Committee Y is 29.3 years.

(2) The average (arithmetic mean) age of the members of Committee Z will be 26.6 years.

Target question: Does Committee X have more members than Committee Y?

Statement 1: The average (arithmetic mean) age of the members of Committee X is 25.7 years and the average age of the members of Committee Y is 29.3 years.
No way to determine which committee has more people.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The average (arithmetic mean) age of the members of Committee Z will be 26.6 years.
No way to determine which committee has more people.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT CONCEPT: If there are 2 populations (A and B) and A's population is greater than B's population, then the average for the COMBINED population will be closer to A's average than to B's average.

Committee X has an average age of 25.7 years
Committee Y has an average age of 29.3 years
If the two committees had the same population, then the combined committee (Z) would have an average age of 27.5 [since (25.7 + 29.3)/2 = 27.5]

In actuality, the COMBINED committee has an average age of 26.6 years. Since 26.6 is closer to 25.7 (committee X's average) than to 29.3 (committee Y's average), we can conclude that committee X must have more people
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Aside: for more information on weighted averages, you can watch this free GMAT Prep Now video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Answer = C

Cheers,
Brent

[Winner2013]

Thank you all.

Brent, thank you for helping me understand the concept as well. Your inputs are always very helpful !