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A tricky PS

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by itzmyzone911 » Sat Oct 04, 2014 10:05 am
A merchandise feedback online portal accords ‘ratings’ to a product by recording the percentage of customers who have reported their views as either ‘satisfied’ or ‘unsatisfied’ only. The portal rounds off the exact percentage value calculated to the closest integral value. Given the fact that the exact percentage of people reported as ‘unsatisfied’ is closest to 57%, what is the LEAST possible number of people that could have reported their views as ‘satisfied’ ?

1. 2
2. 3
3. 12
4. 43
5. 57

[spoiler]OA:B[/spoiler]
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by Matt@VeritasPrep » Sat Oct 04, 2014 10:19 am
We know that 56.5% ≤ Unsatisfied% < 57.5%. From here, let's look at a few familiar fractions that are close to this range:

5/9 = .555... nope!
4/7 = .571428... success!
3/5 = .6 nope!
2/3 = .6666... nope!

So the smallest possibility is 4/7. This gives us 4 unsatisfied people and 7 total, so the number of satisfied people is 7 - 4, or 3.
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by [email protected] » Sat Oct 04, 2014 10:48 am
Hi itzmyzone911,

This prompt is rather wordy, but it's really just asking us to estimate the value of the fraction. The quirky part is that it does not give us the fraction to work with - it tells us what the fraction should be rounded to.

Since the answer choices are numbers, we have a great opportunity to TEST THE ANSWERS. Instead of randomly pulling numbers off the top of your head, you can use the answers to your advantage. Here's how:

We're told that the percentage of Unsatisfied customers is close to 57%, so the percentage of Satisfied customers is close to 43%. We're asked for the LEAST possible number of people who could be Satisfied AND fit this percentage data.

Let's start with Answer A: 2 people

2 Satisfied and 2 Unsatisfied = 2/4 = 50%
2 Satisfied and 3 Unsatisfied = 2/5 = 40%
Neither of these percents would round off to 43%, so Answer A is not correct.

Answer B: 3 people

3 Satisfied and 3 Unsatisfied = 3/6 = 50%
3 Satisfied and 4 Unsatisfied = 3/7 = over 42.6%
This has to be the answer. The percent rounds to 43%.

Since the question asked for the LEAST number of people, there's no need to check the other answers.

Final Answer: B

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