Multiple choice

Directions: The following question has two statements, (1) and (2). Answer the question using the following instructions: In a certain group of people, the average (arithmetic mean) weight of the males is 180 pounds and that of the females, 120 pounds. What is the average weight of the people in the group? (1) The group contains twice as many females as males. (2) The group contains 10 more females than males.

  1. Statement (1) alone is sufficient but statement (2) alone is not

  2. Statement (2) alone is sufficient but statement (1) alone is not

  3. Both (1) and (2) together are sufficient but none of them alone is sufficient

  4. Both independently are sufficient

  5. Both statements (1) and (2) together are not sufficient
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A Correct answer
Explanation

Let M be the number of males and F be the number of females. Average weight = (180M + 120F) / (M + F). Statement (1) says F = 2M. Substituting gives (180M + 120(2M)) / (M + 2M) = (180 + 240) / 3 = 140. This is sufficient. Statement (2) says F = M + 10, which leaves M unknown, so it is not sufficient.

AI explanation

Using statement (1), we can set the number of males as x and females as 2x, making the weighted average (180x + 120(2x)) divided by (x + 2x) equal to 140 pounds, which is sufficient to solve. Using statement (2), the average depends on the exact total population, which is not fixed by just knowing the difference is 10, making it insufficient. Statement (1) alone is sufficient, while statement (2) alone is not.

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