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In an examination 60% failed in Math and 40% failed in French. If 15%

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Math Expert
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Joined: 02 Sep 2009
Posts: 61484
In an examination 60% failed in Math and 40% failed in French. If 15%  [#permalink]

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New post 20 Dec 2019, 01:24
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (01:24) correct 28% (01:58) wrong based on 39 sessions

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Senior Manager
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Joined: 16 Feb 2015
Posts: 355
Location: United States
Re: In an examination 60% failed in Math and 40% failed in French. If 15%  [#permalink]

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New post 20 Dec 2019, 01:31
Bunuel wrote:
In an examination 60% failed in Math and 40% failed in French. If 15% failed in both. What % of students passed in both.

A. 30%
B. 25%
C. 20%
D. 15%
E. 10%


Explanation:

60% failed in Math (A)
40% in French (B) & 15% in both
those failing in A or B but not in A and B is
p(Au(notB))+p((notA)uB)=p(a)+p(b)-2p(AnB)
=60+40-30
=70%

% of students passed in both = 100 - 70 = 30%

IMO-A
Intern
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Joined: 16 Dec 2019
Posts: 2
Re: In an examination 60% failed in Math and 40% failed in French. If 15%  [#permalink]

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New post 02 Jan 2020, 03:19
1
Using a set diagram can help solve this. If 15 % failed both. Then the Percentage who only failed Math is 45%(60-15) and the percentage who only failed French is 25% (40-15).

So total percentage of those who failed at least one subject= 0.45+0.25+0.15. Which equals 0.85%. So the answer is Option D 15%.
GMAT Club Bot
Re: In an examination 60% failed in Math and 40% failed in French. If 15%   [#permalink] 02 Jan 2020, 03:19
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In an examination 60% failed in Math and 40% failed in French. If 15%

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