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by gmatblood » Mon Oct 31, 2011 11:12 am
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%
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by shankar.ashwin » Mon Oct 31, 2011 11:20 am
20% answered neither correctly. So 80% would have answered one or both correctly.

80=75+55-Both
Both = D D
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by GmatMathPro » Mon Oct 31, 2011 11:23 am
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
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by rijul007 » Mon Oct 31, 2011 11:46 am
Image

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
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by gmatblood » Mon Oct 31, 2011 1:01 pm
rijul007 wrote:Image

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 ?
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by gmatblood » Mon Oct 31, 2011 1:02 pm
gmatblood wrote:
rijul007 wrote:Image

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 :)
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by rijul007 » Mon Oct 31, 2011 1:05 pm
gmatblood wrote:
rijul007 wrote:Image

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.
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by rijul007 » Mon Oct 31, 2011 1:06 pm
gmatblood wrote:
gmatblood wrote:
rijul007 wrote:Image

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 :)
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by Jeff@TargetTestPrep » Sat Jul 14, 2018 6:40 pm
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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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