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In a class of 40 students, the number of students who passed the math

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rohan2345
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In a class of 40 students, the number of students who passed the math [#permalink] New post   Updated on: 31 Oct 2023, 23:45
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In a class of 40 students, the number of students who passed the math exam is equal to half the number of students who passed the science exam. Each student in the class passed at least one of the two exams. If 5 students passed both exams, then the number of students who passed the math exam is

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
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C

Originally posted by rohan2345 on 15 May 2017, 07:19.
Last edited by Bunuel on 31 Oct 2023, 23:45, edited 2 times in total.
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Re: In a class of 40 students, the number of students who passed the math [#permalink] New post   19 May 2017, 02:31
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rohan2345 wrote:
In a class of 40 students, the number of students who passed the math exam is equal to half the number of students who passed the science exam. Each student in the class passed at least one of the two exams. If 5 students passed both exams, then the number of students who passed the math exam is

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

Let x be the number of students who passed maths.
It follows that 2x passed in science.
5 passed in both.

So 2x + x - 5 = 40.
This gives x=15.

Option (C)
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Re: In a class of 40 students, the number of students who passed the math [#permalink] New post   20 May 2017, 00:43
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Let those who pass ONLY maths exam = x.
So those who passed in maths = x+5

Now, those who passed in science = 2(x+5) = 2x+10
Those who passed in ONLY science = 2x+10-5 = 2x+5

Total students in class = Only maths + Only science + both = x + 2x+5 + 5 = 3x+10
This is given to be 40
3x+10 = 40. Solve to get x=10

So those who passed maths = x+5 = 10+5 = 15. Hence C
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Re: In a class of 40 students, the number of students who passed the math [#permalink] New post   15 May 2017, 07:27
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rohan2345 wrote:
In a class of 40 students, the number of students who passed the math exam is equal to half the number of students who passed the science exam. Each student in the class passed at least one of the two exams. If 5 students passed both exams, then the number of students who passed the math exam is

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25


Let no of students who passed maths exam be "x". So no of students who passed science exam will be "2x"

Total No of Students = No. of students who passed only Maths + no of students who passed only science + no of students who passed both
40= x-5+2x-5+5
or x = 15

Hence option C
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Re: In a class of 40 students, the number of students who passed the math [#permalink] New post   22 May 2017, 18:49
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rohan2345 wrote:
In a class of 40 students, the number of students who passed the math exam is equal to half the number of students who passed the science exam. Each student in the class passed at least one of the two exams. If 5 students passed both exams, then the number of students who passed the math exam is

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25


Let’s denote the number of students who passed only the math exam by x and the number of students who passed only the science exam by y. Then, since there are 5 students who passed both exams, the number of students who passed the math exam is x + 5 and the number of students who passed the science exam is y + 5.

Since the number of students who passed the math exam is equal to half the number of students who passed the science exam, we have x + 5 = (y + 5)/2, or, 2(x + 5) = y + 5. Simplifying this equation, we get y = 2x + 5.

To determine the number of students who passed the math exam, we will use the following formula:

# of students in the class = # who passed math + # who passed science - # who passed both + # who passed neither

We are given that there are 40 students in total and each student passed at least one exam; therefore, # who passed neither = 0. Then, we have:

40 = (x + 5) + (y + 5) - 5 + 0

40 = x + y + 5

x + y = 35

Let’s substitute y = 2x + 5:

x + 2x + 5 = 35

3x = 30

x = 10

We see that the number of students who passed only the math exam is 10. We must add to this number those 5 students who passed both math and science. Thus, the total number of students who passed the math exam is x + 5 = 10 + 5 = 15.

Answer: C
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Re: In a class of 40 students, the number of students who passed the math [#permalink] New post   20 May 2017, 04:13
In a class of 40 students, the number of students who passed the math exam is equal to half the number of students who passed the science exam. Each student in the class passed at least one of the two exams. If 5 students passed both exams, then the number of students who passed the math exam is?

Total students = 40
Let number of students who passed in Science exam be = 2X
Therefore Students who passed in Math exam (half of number of students passed in science exam) = X
Students who passed both exams = 5

Total = Students passed in Science + Students passed in Maths - (Students passed in both subjects)
40 = X + 2X - 5
3X = 45
X = 15
Answer C...

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Re: In a class of 40 students, the number of students who passed the math [#permalink] New post   18 May 2019, 01:47
Can someone explain why it is wrong to interpret the statement as follow?

40= X/2 + X - 10 + 5

Obviously it is wrong from the result you get but don't know why

Thanks!
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Re: In a class of 40 students, the number of students who passed the math [#permalink] New post   31 Oct 2023, 21:45
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rohan2345 wrote:
In a class of 40 students, the number of students who passed the math exam is equal to half the number of students who passed the science exam. Each student in the class passed at least one of the two exams. If 5 students passed both exams, then the number of students who passed the math exam is

(A) 5
(B) 10
(C) 15
(D) 20
(E) 25

Source: Nova GMAT
Difficulty Level: 600


Number of students who passed Science = s
=> Number of students who passed Math = s/2
Since 5 passes both, we have:
s + s/2 - 5 = 40
=> s = 30
=> Number of students who passed Math = s/2 = 15

Answer C
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Re: In a class of 40 students, the number of students who passed the math [#permalink]
31 Oct 2023, 21:45
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