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

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

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17 Mar 2005, 05:19
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Question Stats:

58% (03:05) correct 42% (01:39) wrong based on 28 sessions

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

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17 Mar 2005, 07:53
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
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Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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17 Mar 2005, 08:03
rupstar

can u explain that formula with all of us whats that called can u send some info on the net that has the explnantion

i tried to do this problome with venn or grid i cud not

thanks

rxs0005
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Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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17 Mar 2005, 11:50
1
KUDOS
This can be solved using Venn diagrams.

35% failed in one subject and 42% in another. 15% failed in both.

Below is the venn diagram representing the failures, in a sample of 100.

____________
______|_________
20% | 15% | 27% |
|_____ |________|
|
____________|
Obviously, those failing in one of the subjects = 20 + 27 = 47%

Total = 47% of 2500 = 1175.
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Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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17 Mar 2005, 15:55
I think it is easier to use Venn diagrams...At least for me...
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Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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18 Mar 2005, 03:49
47% of 2500
Venn Diagram are a good idea. One will not commit any mistake.
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Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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18 Mar 2005, 10:43
Thanks guys, the OA is C
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Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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19 Mar 2005, 13:28
Ans is c i.e. 1175

since in A subject 35% of 2500 failed i.e. 875
in B subject 42% of 2500 failed i.e. 1050
Failed in both the subject 15%of 2500 i.e. 375

student failed in A alone=875-375=500
student failed in B alone=1050-375=675
Student failed in either of the two subjects=500+675=1175
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Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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01 Aug 2013, 12:49
I dont understand the answer. The question asks how many passed in either subject but not in both?

Aren't you guys calculating how many failed in either subject but not in both?
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Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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02 Aug 2013, 06:14
OA is not C but D.

The question asks for the number passed, not for failed.

I cross verified in another forums and the OA is those forums is D.

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

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28 Apr 2017, 04:54
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Re: In an examination, 35% candidates failed in one subject and 42% failed [#permalink]

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02 May 2017, 16:49
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Expert's post
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

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.

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

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03 May 2017, 11:01
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] 03 May 2017, 11:01
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