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200 people surveyed. Exam pack 2

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by prata » Sat Aug 27, 2016 7:27 am
Of 200 people surveyed, 80 percent own a cellular phone and 45 percent own a pager. If all 200 people surveyed own a cellular phone or a pager or both, what percent of those surveyed either do not own a cellular phone or do not own a pager?

1. 35%
2. 45%
3. 55%
4. 65%
5. 75%

[spoiler]OA: E[/spoiler]
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by [email protected] » Sat Aug 27, 2016 8:43 am
Hi prata,

This question is a modified version of a typical Overlapping Sets question. You can solve it with the tic-tac-toe board or the Overlapping Sets Formula:

Total = (Group 1) + (Group 2) - Both + Neither

In this prompt, we're told that ALL 200 people own at least one of the two items, so the 'Neither' group would be 0.

80% of 200 = 160 people own a cell phone
45% of 200 = 90 people own a pager

Plugging that data into the formula, we have...

200 = 160 + 90 - Both

200 = 250 - Both
Both = 50

Since 50 of the 200 people have both items, the other 200 - 50 = 150 people have just one item. As a percentage of the total, that is 150/200 = 75%

Final Answer: E

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by Matt@VeritasPrep » Thu Sep 01, 2016 5:45 pm
We know that

Cell + Pager - Both = Total

so

160 + 90 - Both = 200

and

Both = 50

That means that 150 only own one of the two. 150 = 75% of 200, since our answer is 75%.
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