Multiple choice

Directions: The following question has two statements, (1) and (2). Answer the question using the following instructions: If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75? (1) None of the six numbers is less than 75. (2) None of the six numbers is greater than 75.

  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 neither of them alone is sufficient

  4. Both independently are sufficient

  5. Both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If the average of 6 numbers is 75, their sum is 450. If no number is less than 75 (Statement 1), the only way the sum can be 450 is if all are 75. Similarly, if no number is greater than 75 (Statement 2), all must be 75. Both statements independently force all numbers to be 75.

AI explanation

The sum of the six numbers is 6 times 75, which equals 450. Statement 1 states none of the numbers is less than 75, meaning every number is at least 75; if any number were greater than 75, the sum would exceed 450, so all six numbers must equal 75. Statement 2 states none of the numbers is greater than 75, meaning every number is at most 75; if any were less than 75, the sum would fall short of 450, so again all six numbers must be exactly 75. Thus, both statements independently prove that all six numbers are equal to 75.

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