BTGmoderatorDC wrote:The average weight of the women in a room is 120 lbs, and the average weight of the men in the room is 150 lbs. What is the average weight of the people in the room?

(1) There are twice as many men as women in the room.

(2) There are a total of 120 people in the room.

OA A

Source: Manhattan Prep

Say there are x numbers of men and y numbers of women in the room. Thus, there are a total of x + y numbers of people in the room.

Average weight of x + y people = (150x + 120y)/(x + y)

Let's take each statement one by one.

(1) There are twice as many men as women in the room.

=> x = 2y

Thus,

Average weight of x + y people = (150x + 120y)/(x + y) = (150*2y + 120y)/(2y + y) = (420y)/(3y) = 140 lbs. Sufficient.

(2) There are a total of 120 people in the room.

Insufficient since we do not know the unique values of x and y.

The correct answer: A

Hope this helps!

-Jay
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