VeritasPrepKarishma wrote:
Responding to a pm:
Question:
A group of men and women gathered to compete in a marathon. Before the competition, each competitor was weighed and the average weight of the female competitors was found to be 120 lbs. What percentage of the competitors were women?
(1) The average weight of the men was 150 lb.
(2) The average weight of the entire group was twice as close to the average weight of the men as it was to the average weight of the women.
Solution:
Avg weight of women = 120 lbs
Stmnt 1: Avg weight of men = 150 lbs
This statement doesn't tell us the average weight of the entire group. The avg weight of men is not helpful till we know the avg weight of the entire group. Not sufficient
Stmnt 2: Avg weight of group was twice as close to the average weight of the men as it was to the average weight of the women.
Since avg weight is twice as close to avg weight of men, the number of men must be twice of the number of women So women must be 1/3 of the total group. Think of the scale method we use. Ratio of the distances is 1:2 (avg is closer to men's avg than women's avg) so number of men: number of women = 2:1.
Sufficient.
Check out this link for scale method:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... -averages/Answer (B)
Hi, thanks in advance.
Stmnt 2: Avg weight of group was twice as close to the average weight of the men as it was to the average weight of the women.
I couldn't really understand the second statement & how you arrived at this conclusion from the second statement:
Since avg weight is twice as close to avg weight of men, the number of men must be twice of the number of women
What I could gather from this statement is that the difference between the avg wt of the group & avg wt of men is twice the difference between avg wt of group and avg wt. of women
i.e. |avg wt. of group - avg wt. of men| = 2 x |avg wt. of group - avg wt. of women| where || represent mod
Could you please help me understand the language of the statement?