20% answered neither correctly. So 80% would have answered one or both correctly.

80=75+55-Both
Both = D D

Assume 100 people. 20 answered neither question correctly, so 80 answered at least one question correctly. 75+55=130, but the people who answered both correctly are counted in each group, and we only want to count them once. Let x=the number of people who answered both correctly. 130-x=80. x=50. So, 25 answered only the first correctly, 5 answered only the second correctly, 50 answered both correctly, and 20 answered neither correctly. 25+5+20+50=100, so it checks out.

So, [spoiler]D. 50%[/spoiler] is the answer

a+b+c+d = 100

a+b = 75
b+c = 55
d = 20

adding all three equations =>
a+b+b+c+d = 150
100+b = 150
b = 50

Option D

rijul007 wrote:

a+b+c+d = 100

a+b = 75
b+c = 55
d = 20

adding all three equations =>
a+b+b+c+d = 150
100+b = 150
b = 50

Option D

Bit confused with the highlighted! Is it 100/150 ?

gmatblood wrote:

rijul007 wrote:

a+b+c+d = 100

a+b = 75
b+c = 55
d = 20

adding all three equations =>
a+b+b+c+d = 150
100+b = 150
b = 50

Option D

Bit confused with the highlighted! Is it 100/150 ?

Oh yes, got it now!!! Thanks a lot

gmatblood wrote:

rijul007 wrote:

a+b+c+d = 100

a+b = 75
b+c = 55
d = 20

adding all three equations =>
a+b+b+c+d = 150
100+b = 150
b = 50

Option D

Bit confused with the highlighted! Is it 100/150 ?

look at it closely,
the second eqn highlighted in blue has an extra b
we got this by adding the three equation in red.

gmatblood wrote:

gmatblood wrote:

rijul007 wrote:

a+b+c+d = 100

a+b = 75
b+c = 55
d = 20

adding all three equations =>
a+b+b+c+d = 150
100+b = 150
b = 50

Option D

Bit confused with the highlighted! Is it 100/150 ?

Oh yes, got it now!!! Thanks a lot

I am glad i could help mate

gmatblood wrote:If 75 percent of a class answered the first question
on a certain test correctly, 55 percent answered the
second question on the test correctly, and 20 percent
answered neither of the questions correctly, what
percent answered both correctly?

(A) 10%
(B) 20%
(C) 30%
(D) 50%
(E) 65%

For this overlapping sets problem, we can use the following equation:

Total percent = % in category A + % in category B - % in both categories + % in neither category

Since the answer choices are in percentage form we can use 100 as the total. We are given that 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly. Using these values, we have:

100 = 75 + 55 - B + 20

100 = 150 - B

B = 50

Answer: D