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Choose the correct statement.

In a certain group, the average (arithmetic mean) age of the males is 28, and the average age of the females is 30. If there are 100 people in the group, how many of them are males?

(1) The average age of all 100 people is 28.9

(2) There are 10 more males than there are females.

Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. Each statement ALONE is sufficient to answer the question. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

Title

Average age of men and women

Your Result

Correct

Difficulty

Hard

Your Pace

0:24

Others' Pace

1:50

Video Explanation

Text Explanation

The total number of people in the group is 100, so:

Next, we know the average ages, and we can use the rule that the sum of a set of numbers is the mean times how many numbers there are:

We have expressions for the total number of people and the sum of their ages, so let's go to the statements. Statement 1 tells us that the average age of all of the people is 28.9. We can use this plus the information we got from the prompt to set up the following equation:

To find the average, we add up all of the ages and divide by 100. We know the average is 28.9, we know the sum of the ages is 28M + 30F, so plug them in. Multiply both sides by 100 and we get 28M + 30F = 2890. That's one equation with both M and F. Combine that with M + F = 100, and we have two equations for two variables. We could absolutely solve this for M, so the statement is sufficient.

Statement 2 is even more direct. Translate it into math. If there are 10 more males then females, then we have M = 10 + F. Combine that with M + F = 100, and we have two questions with two variables. Absolutely solvable:

Each statement is sufficient on its own, so the answer is (D).

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