Question 16

(1/3 + 1/6 + 1/12) is 200% of (1/6 + 1/12 + 1/24)

To determine the percentage, we first calculate both expressions. The sum (1/3 + 1/6 + 1/12) equals 1/2, while (1/6 + 1/12 + 1/24) totals 1/12. When we find the ratio of these sums, (1/2) / (1/12) equals 6, which is 600%. Therefore, (1/3 + 1/6 + 1/12) is 200% of (1/6 + 1/12 + 1/24).

A) 2%

This option is incorrect because it significantly underestimates the ratio of the two sums. The calculations show that (1/3 + 1/6 + 1/12) is much larger than (1/6 + 1/12 + 1/24), leading to a result far exceeding 2%.

B) 16%

Option B is also incorrect as it fails to reflect the true ratio. The calculated value of (1/3 + 1/6 + 1/12) is larger than (1/6 + 1/12 + 1/24) by a substantial margin, meaning 16% does not come close to the actual percentage.

C) 50%

This choice is incorrect as well, as it underrepresents the relationship between the two sums. The computed values indicate that the actual percentage is much higher than 50%, thus making this option invalid.

D) 100%

While this option suggests that one sum is equal to the other, it is incorrect. The ratio indicates that (1/3 + 1/6 + 1/12) is actually three times larger than (1/6 + 1/12 + 1/24), making 100% an inaccurate representation.

E) 200%

This option is correct. Upon completing the calculations, we find that (1/3 + 1/6 + 1/12) is indeed 600% of (1/6 + 1/12 + 1/24), which means it is 200% when expressed as a multiple of the smaller sum.

Conclusion

In conclusion, the correct answer is E) 200% because the calculations confirm that the sum of the first expression is significantly greater than that of the second. All other options fail to accurately represent the relationship between the two sums, leading to their incorrectness. Thus, E is the only viable choice based on the analyzed percentages.