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In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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17 Mar 2005, 04:19

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In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared in the examination, how many passed in either subject but not in both?

Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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17 Mar 2005, 06:53

c
if 35 failed in A and 42 in B and 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)
=42+35-30
=47%
1175

Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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28 Apr 2017, 03:54

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In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared in the examination, how many passed in either subject but not in both?

a) 325 b) 1075 c) 1175 d) 2125 e) 2250

We can use the following formula:

100 = Percent failed one subject + Percent failed another subject - Percent failed both subjects + Percent failed neither subject

100 = 35 + 42 - 15 + P

100 = 62 + P

P = 38

We see that 38 percent of the candidates failed neither subject, i.e., 38 percent passed both subjects. Now we can use the following formula to find the number who passed either subject but not both:

Number who passed either subject but not both = number who passed only one subject + number who passed only another subject = (number who passed one subject - number who passed both subjects) + (number who passed another subject - number who passed both subjects)

N = 2500 x 0.65 - 2500 x 0.38 + 2500 x 0.58 - 2500 x 0.38

N = 2500 x (0.65 - 0.38 + 0.58 - 0.38)

N = 2500 x 0.47

N = 1175

Alternate Solution:

We can use the following formula:

100 = Percent failed one subject + Percent failed another subject - Percent failed both subjects + Percent failed neither subject

100 = 35 + 42 - 15 + P

100 = 62 + P

P = 38

We know that the percentage that passed both exams is 38% and the percentage that failed both exams is 15%. Therefore, the percentage that passed exactly one exam is (100% - 38% - 15% = 47%). Thus, the number of individuals who passed exactly one exam is (0.47)(2500) = 1175.

Answer: C
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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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03 May 2017, 10:01

Rupstar wrote:

maaverick wrote:

In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared in the examination, how many passed in either subject but not in both?

a) 325 b) 1075 c) 1175 d) 2125 e) 2250

c if 35 failed in A and 42 in B and 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) =42+35-30 =47% 1175

Rupstar, your logic is correct to me but the question asked for those "PASSING" in A or B but not in A and B.

It does not look like OP typed the question correctly because it is not possible to find out how many students passed in A or B and not in A and B. It is difficult to see in a venn diagram but very easy to see in a table:

We know that 62% of students failed at least one test. Because of this, we know that 38% of students passed at least one test. However, we have no information about what % of users passed A, or B, or A&B.

In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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02 Aug 2017, 10:36

1

This post received KUDOS

joondez wrote:

Rupstar wrote:

maaverick wrote:

In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared in the examination, how many passed in either subject but not in both?

a) 325 b) 1075 c) 1175 d) 2125 e) 2250

c if 35 failed in A and 42 in B and 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) =42+35-30 =47% 1175

your logic is correct to me but the question asked for those "PASSING" in A or B but not in A and B.

It does not look like OP typed the question correctly because it is not possible to find out how many students passed in A or B and not in A and B. It is difficult to see in a venn diagram but very easy to see in a table:

We know that 62% of students failed at least one test. Because of this, we know that 38% of students passed at least one test. However, we have no information about what % of users passed A, or B, or A&B.

Hi,

The question asks for the no. of students who passed either A or B, not both the subjects A and B.

Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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06 Aug 2017, 15:58

Hi can please someone explain why the phrase below can't mean 3 different groups of student exactly: 35% failed in 1st subject and passed in another 42% failed in 2nd and failed the 1st 15% failed the 1st and the 2nd total 92% and 8% passed both subjects

Quote:

In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects.

so 100 = Percent failed one subject + Percent failed another subject + Percent failed both subjects + Percent failed neither subject

how do you define from the problem definition that it's indeed 100 = Percent failed one subject + Percent failed another subject - Percent failed both subjects + Percent failed neither subject