If the average (arithmetic mean) of g and 100 is 75, what is the value of g + 100?

Rationale

g + 100 equals 150.

To find the value of g + 100, we start with the average of g and 100 being 75. By solving the equation for g, we determine that g + 100 must equal 150.

A (50) YOUR ANSWER

If g + 100 were 50, this would imply that g equals -50. Plugging this back into the average calculation gives an average much less than 75, as the average would be (-50 + 100) / 2 = 25, which does not satisfy the initial condition.

B (125) YOUR ANSWER

If g + 100 were 125, then g would equal 25. The average of 25 and 100 would be (25 + 100) / 2 = 62.5, which is also less than 75, thus failing to meet the requirement set by the problem.

C (150) CORRECT

If g + 100 equals 150, then g would be 50. The average of 50 and 100 is (50 + 100) / 2 = 75, which perfectly aligns with the condition given in the question.

D (175) YOUR ANSWER

If g + 100 were 175, this would imply that g equals 75. The average of 75 and 100 would be (75 + 100) / 2 = 87.5, which exceeds 75, thereby contradicting the problem's stipulation.

Conclusion

The correct value of g + 100 is 150, derived from the condition that the average of g and 100 is 75. By isolating g, we confirm that only choice C satisfies the average condition, while the other options lead to values of g that do not align with the specified average. Thus, the arithmetic mean condition uniquely identifies the correct answer.

If the average (arithmetic mean) of g and 100 is 75, what is the value of g + 100?

g + 100 equals 150.

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