### Brain Teasers

# 101 Percent Surprise

The other day, I took an online survey in which there were two choices: "True" and "False". I made my selection and was surprised to see the results:

33% of people had selected "True"

68% of people had selected "False".

My biggest surprise was that most people didn't agree with me. The answer was obviously "True", how could anyone think otherwise?

I was also slightly surprised to see that the responses totaled 101 percent. Obviously the percentages were rounded to whole numbers. What is the minimum number of people that had completed the survey?

33% of people had selected "True"

68% of people had selected "False".

My biggest surprise was that most people didn't agree with me. The answer was obviously "True", how could anyone think otherwise?

I was also slightly surprised to see that the responses totaled 101 percent. Obviously the percentages were rounded to whole numbers. What is the minimum number of people that had completed the survey?

### Hint

Before rounding, the two percentages must total 100.### Answer

The exact results must be 32.5% and 67.5%. These values total 100% and both numbers would be rounded up to match the observed results of 33% and 68%.The percents can be written as fractions: 32.5/100 and 67.5/100.

Multiply top and bottom by two to avoid the decimals: 65/200 and 135/200.

Finally, reduce the fractions (both are divisible by 5): 13/40 and 27/40.

Thus there were a total of 40 votes; 13 voted "True" and 27 voted "False".

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