Multiple choice

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 150lb. (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.

  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 (1) and (2) TOGETHER are sufficient to answer

  4. EACH statement ALONE is sufficient to answer the question asked

  5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

Statement (1) only provides the average weight of the men, which is insufficient to find the ratio of men to women without knowing the overall group average. Statement (2) states the overall average is twice as close to the men's average as it is to the women's average, meaning the ratio of the distances from the group average to the men's and women's averages is 1:2. Using the method of alligation, this distance ratio is the inverse of the ratio of the number of men to women, so the ratio of men to women is 2:1, proving women make up 1/3 or 33.33% of the competitors; statement (2) alone is sufficient.

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