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by Fab » Fri Sep 19, 2008 4:25 pm
If 75% of a class answered the first question on a certain test correctly, 55% answered the second question on the test correctly, and 20% answered neither of the questions correctly, what percent answered both correctly?

A. 10%
B.20%
C.30%
D.50%
E.60%

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by earth@work » Fri Sep 19, 2008 4:40 pm
not too sure but IMO its D=50%

Let x% answer both I and II correctly, we know 20% answered none. So in remaining 80% we need to find value of x
Those who answered I ONLY = (75-x)%
those who answered II ONLY = (55-x)%
we get, x + (75-x) + (55-x) = 80
therefore, x=50%

i wud also love to know correct answer for this, coz not too sure.
Last edited by earth@work on Fri Sep 19, 2008 4:53 pm, edited 1 time in total.
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by fajoni » Fri Sep 19, 2008 4:48 pm
The correct answer is 50%

You can solve this question by using the formula:

Group1 + Group2 + Neither - Both = Total.

In this case, Group1 represents the 75%, Group2 represents the 55%, Neither represents 20%, Both represents X, and Total equals 1, or 100%.

0.75+0.55+0.2-X=1 => 1.5-X=1 => -X=-0.5 => X=0.5 or 50%.

Good luck with the studies!
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by cramya » Fri Sep 19, 2008 6:55 pm
Adding a little bit more to the previous solution.

For percent problems take 100 as total(very easy to work with)

Using the same formula

grp1+grp2-both+neither = total

75+55-both+20 = 100
both=50

If u draw Venn diagram problems like these would be easy to understand(especially when there is a overlap between 3 sets. This problems had only 2 sets namely first question answer group and second question answer group)

Good luck!
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