Bunuel
Tough and Tricky questions: Percents.
A survey was sent to 80 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
A. 2%
B. 5%
C. 14%
D. 28%
E. 63%
We can use the percent change formula, which is (New - Old)/Old x 100, to determine the percent increase in the response rate:
[(9/63) - (7/80)]/(7/80) x 100 =
[(1/7) - (7/80)]/(7/80) x 100 =
Multiplying the left side by 560/560, we have:
(80 - 49)/49 x 100 =
31/49 x 100
We see that 31/49 is roughly 31/50 = 62/100 = 62%
Alternate Solution:
We can approximate the initial response rate of 7/80 as roughly 7/77, or 1/11. The new response rate is 9 /63, or 1/7. We can use the percent change formula, which is (New - Old)/Old x 100, to determine the percent increase in the response rate:
(1/7 - 1/11)/1/11 x 100 =
Multiplying the expression by 77/77, we obtain:
(11 - 7)/7 x 100 =
4/7 x 100
We see that 4/7 is slightly more than ½, so 4/7 x 100 will be slightly greater than 50%.
Answer: E