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Among the students who took maths and physics test,

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Among the students who took maths and physics test, [#permalink] New post   24 Mar 2023, 08:39
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Among the students who took maths and physics test, 4/5 of the students did not fail in Maths, and of those, 2/3 did not fail in Physics. Which of the following represents the fraction of numbers of students who failed in atleast one of these exam?

5/15
7/15
8/15
4/5
25/3


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Re: Among the students who took maths and physics test, [#permalink] New post   30 Mar 2023, 09:22
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Let's assume that there are 100 students who took both Math and Physics tests.

Then, 4/5 of the students did not fail in Math, which means that 1/5 of the students failed in Math, or 20 students failed in Math.

Of the 80 students who did not fail in Math, 2/3 of them did not fail in Physics. Therefore, the number of students who did not fail in both Math and Physics is:

80 × 2/3 = 160/3

So the number of students who failed in at least one of the exams is:

20 + 100 - 160/3 = 220/3

Therefore, the fraction of the number of students who failed in at least one of the exams is:

220/3 ÷ 100 = 22/3 ÷ 10 = 22/30 = 11/15

So the answer is option (B) 7/15.
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Re: Among the students who took maths and physics test, [#permalink] New post   01 May 2024, 15:32
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Re: Among the students who took maths and physics test, [#permalink]
01 May 2024, 15:32
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