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# In an examination, 50% of the students passed in mathematics

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In an examination, 50% of the students passed in mathematics  [#permalink]

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Updated on: 15 Mar 2019, 21:32
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69% (02:32) correct 31% (03:00) wrong based on 68 sessions

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In an examination, 50% of the students passed in mathematics and 70% of the students passed in science while 10% students failed in both subjects. 300 students passed in atleast one subject. Find the total number of students who appeared in the examination, if they took examination in only two subjects.

a) 250
b) 333
c) 750
d) 1000
e) 367

Originally posted by AjjayKannan on 13 Mar 2019, 02:56.
Last edited by AjjayKannan on 15 Mar 2019, 21:32, edited 1 time in total.
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In an examination, 50% of the students passed in mathematics  [#permalink]

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Updated on: 15 Mar 2019, 21:56
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As 10% failed in both subjects
So 90% students passed in at least one exam
$$\frac{(90}{100)}$$ * x=300
x=333.33
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Originally posted by Noshad on 13 Mar 2019, 09:16.
Last edited by Noshad on 15 Mar 2019, 21:56, edited 2 times in total.
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Re: In an examination, 50% of the students passed in mathematics  [#permalink]

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13 Mar 2019, 10:10
2
Total = Science + Math -Both + Neither
100% = 70% +50% - Both + 10%
Both = 30% of total attendants

At least one = Science + Math - Both = 70% + 50% - 30% = 90% of total attendants = 300 students
Total attendants = $$\frac{300}{0.9} = \frac{1000}{3} = 333$$

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Re: In an examination, 50% of the students passed in mathematics  [#permalink]

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13 Mar 2019, 12:35
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TyrionLannister wrote:
Let x be the total number of students.

Total students = 100 %

Passed students = 100 - 10 (failed in both subjects)

= 90

Total passed students in at least one subject = (50 + 70) - 90

120 - 90

= 30 %

So, 30 % of the total students passed in at least in one subject.

⇒ (x*30)/100 = 300

⇒ 30x/100 = 300

⇒ 30x = 300*100

⇒ x = 30000/30

⇒ x = 1000

So, total 1000 students appeared in the examination

At least one subject wouldnd include Math, Science and Math + Science ?
Leading that 90% of the population passed in at least one which means the total population would be 333.
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Re: In an examination, 50% of the students passed in mathematics  [#permalink]

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15 Mar 2019, 20:35
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The mistake with the 1,000 solution is that it assumed 90% of people passed BOTH subjects. If 10% of people failed both subjects that implies 90% of people DID NOT FAIL both subjects. Just because you do not fail both subjects, it does not mean that you passed both. You could pass one and fail the other.

This problem can be solved only focusing on the 10% and the 300. If 10% failed both, that implies 90% DID NOT FAIL BOTH. The important connection to make is to realize that that is the same thing as stating. 90% PASSED AT LEAST ONE. 300 represents 90% of the population. So 300/.9=333.33 total students.
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Re: In an examination, 50% of the students passed in mathematics  [#permalink]

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13 Mar 2019, 09:57
P(a)=50/100,p(b)=70/100p(anb)=1-10/100=90/100
P(aorb)=70/100+50/100-90/100
300=30x/100=1000
No of students appeared is 1000
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Re: In an examination, 50% of the students passed in mathematics  [#permalink]

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15 Mar 2019, 06:00
AjjayKannan wrote:
In an examination, 50% of the students passed in mathematics and 70% of the students passed in science while 10% students failed in both subjects. 300 students passed in atleast one subject. Find the total number of students who appeared in the examination, if they took examination in only two subjects.

a) 250
b) 333
c) 750
d) 1000
e) 367

We can create the equation:

Total = Math + Science - Both + Neither

n = 0.5n + 0.7n - Both + 0.1n

n = 1.3n - Both

Both = 0.3n

Since 300 students passed in at least 1 subject:

300 = 0.5n + 0.7n - 0.3n

300 = 0.9n

n = 300/0.9 = 333.33

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Re: In an examination, 50% of the students passed in mathematics  [#permalink]

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15 Mar 2019, 20:10
This question has controversy of answer over 333 and 1000. Both seems to be logical. Which one is the correct one? Bunuel
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Re: In an examination, 50% of the students passed in mathematics  [#permalink]

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15 Mar 2019, 21:02
Henry S. Hudson Jr. wrote:
The mistake with the 1,000 solution is that it assumed 90% of people passed BOTH subjects. If 10% of people failed both subjects that implies 90% of people DID NOT FAIL both subjects. Just because you do not fail both subjects, it does not mean that you passed both. You could pass one and fail the other.

This problem can be solved only focusing on the 10% and the 300. If 10% failed both, that implies 90% DID NOT FAIL BOTH. The important connection to make is to realize that that is the same thing as stating. 90% PASSED AT LEAST ONE. 300 represents 90% of the population. So 300/.9=333.33 total students.

But consider this case

50% passed in maths. So, 50% failed in Maths. Similarly, 30% failed in science. Now, 10% failed in both the subjects.

Hence, 50% + 30% - 10% = 70% of the people failed in atleast one subject.

Subtracting,

100% - 70% = 30% . This percentage indicates people passed in atleast one subject.

So, 30% of 1000 is 300.

Why can't this be the right way?
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Re: In an examination, 50% of the students passed in mathematics  [#permalink]

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15 Mar 2019, 21:10
AjjayKannan wrote:
Henry S. Hudson Jr. wrote:
The mistake with the 1,000 solution is that it assumed 90% of people passed BOTH subjects. If 10% of people failed both subjects that implies 90% of people DID NOT FAIL both subjects. Just because you do not fail both subjects, it does not mean that you passed both. You could pass one and fail the other.

This problem can be solved only focusing on the 10% and the 300. If 10% failed both, that implies 90% DID NOT FAIL BOTH. The important connection to make is to realize that that is the same thing as stating. 90% PASSED AT LEAST ONE. 300 represents 90% of the population. So 300/.9=333.33 total students.

But consider this case

50% passed in maths. So, 50% failed in Maths. Similarly, 30% failed in science. Now, 10% failed in both the subjects.

Hence, 50% + 30% - 10% = 70% of the people failed in atleast one subject.

Subtracting,

100% - 70% = 30% . This percentage indicates people passed in atleast one subject.

So, 30% of 1000 is 300.

Why can't this be the right way?

Everything in your reasoning is correct except for one thing.

70% of the people failed at least one subject. so 30% of the people DID NOT FAIL AT LEAST ONE SUBJECT.

30% of people DID NOT FAIL ONE OR TWO SUBJECTS.

That means THEY PASSED BOTH. You said it's the percent of people who passed at least one subject but that would

mean you include the case where one passes one and fails the other. 30% of people DID NOT FAIL AT LEAST ONE SUBJECT.

Think about who those 30% of people can be. If you fail at least one subject, the condition is broken.Can they be someone who passes math and fails science? No, because then they failed a subject.

Can they be someone who failed math and passed science? No, because then they failed a subject.
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Re: In an examination, 50% of the students passed in mathematics  [#permalink]

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15 Mar 2019, 21:32
Henry S. Hudson Jr. wrote:
AjjayKannan wrote:
Henry S. Hudson Jr. wrote:
The mistake with the 1,000 solution is that it assumed 90% of people passed BOTH subjects. If 10% of people failed both subjects that implies 90% of people DID NOT FAIL both subjects. Just because you do not fail both subjects, it does not mean that you passed both. You could pass one and fail the other.

This problem can be solved only focusing on the 10% and the 300. If 10% failed both, that implies 90% DID NOT FAIL BOTH. The important connection to make is to realize that that is the same thing as stating. 90% PASSED AT LEAST ONE. 300 represents 90% of the population. So 300/.9=333.33 total students.

But consider this case

50% passed in maths. So, 50% failed in Maths. Similarly, 30% failed in science. Now, 10% failed in both the subjects.

Hence, 50% + 30% - 10% = 70% of the people failed in atleast one subject.

Subtracting,

100% - 70% = 30% . This percentage indicates people passed in atleast one subject.

So, 30% of 1000 is 300.

Why can't this be the right way?

Everything in your reasoning is correct except for one thing.

70% of the people failed at least one subject. so 30% of the people DID NOT FAIL AT LEAST ONE SUBJECT.

30% of people DID NOT FAIL ONE OR TWO SUBJECTS.

That means THEY PASSED BOTH. You said it's the percent of people who passed at least one subject but that would

mean you include the case where one passes one and fails the other. 30% of people DID NOT FAIL AT LEAST ONE SUBJECT.

Think about who those 30% of people can be. If you fail at least one subject, the condition is broken.Can they be someone who passes math and fails science? No, because then they failed a subject.

Can they be someone who failed math and passed science? No, because then they failed a subject.

Absolutely plausible! The answer is 333.

Thank you Henry Hudson!
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Re: In an examination, 50% of the students passed in mathematics  [#permalink]

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27 Mar 2019, 01:48
I'm not sure if this question make sense , the answer is b ,but how can the total number be 333.3 students ?
I mean what is 0.3 students , I suggest changing the text of the question and keeping the numbers
Thx
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Re: In an examination, 50% of the students passed in mathematics   [#permalink] 27 Mar 2019, 01:48
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