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A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?
- a)40
- b)50
- c)60
- d)70
- e)80
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A class was tested on two subjects-Mathematics and Physics. 80% of the...
Step 1: Question statement and Inferences
We are given the performance of students in a class test that consists of two subjects: Physics and Mathematics. Let’s say the total number of students who appeared for the quiz be N. So, the Venn diagram for the given information can be drawn as under:
Let
P = Number of students who passed only in Physics
M = Number of students who passed only in Mathematics
Z = Number of students who passed neither in Physics nor in Mathematics.
Let us now analyze the pieces of given information, one by one.
First, we are told that 80% of the students passed in Mathematics. The point to note here is that the statement doesn’t say ‘ONLY Mathematics’. Therefore, this percentage term includes students who passed only in Mathematics as well as students who passed in both Mathematics and Physics.
Therefore, we can write the equation:
M+180=80 of N
Or, M=0.8N - 180 . . . (1)
We are also told that the number of students who passed in Mathematics was 120 more than the number of students who passed in Physics.
Again, we note that this statement doesn’t say ‘Only Mathematics’ or ‘Only Physics’. The number of students who passed in Physics will be equal to the number of students who passed only in Physics PLUS the number of students who passed in both subjects.
Thus, we can write the equation:
M + 180 = (P+180) + 120
Or, M = P + 120 . . . (2)
Finally, we are given that
Or, M = 7P . . . (3)
Step 2: Finding required values
Substituting the value of M from Equation 3 in Equation 2:
7P = P + 120
6P = 120
P = 20
From Equation 2:
M = 140
From Equation 1:
140 = 0.8N – 180
N = 400
Step 3: Calculating the final answer
Now, P + 180 + M + Z = N
Substituting the values of P, M and Z in this equation, we get:
20 + 180 + 140 + Z = 400
340 + Z = 400
Z = 60
So, the number of students who failed in both the subjects is 60
Answer: Option (C)
Most Upvoted Answer
A class was tested on two subjects-Mathematics and Physics. 80% of the...
To solve this problem, let's break it down step by step:
Step 1: Understand the given information
- 80% of the students passed in Mathematics.
- The number of students who passed in Mathematics is 120 more than the number of students who passed in Physics.
- 180 students passed in both subjects.
- The ratio of students who passed only in Physics to students who passed only in Mathematics is 1:7.
Step 2: Calculate the number of students who passed in Mathematics and Physics
Let's assume the total number of students in the class is "x".
- Since 80% of the students passed in Mathematics, the number of students who passed in Mathematics is 0.8x.
- According to the given information, the number of students who passed in Mathematics is 120 more than the number of students who passed in Physics. So, we can write the equation: 0.8x = (number of students who passed in Physics) + 120.
Step 3: Calculate the number of students who passed in only Mathematics and only Physics
- The ratio of students who passed only in Physics to students who passed only in Mathematics is 1:7. Let's assume the number of students who passed only in Physics is y, then the number of students who passed only in Mathematics would be 7y.
- Since 180 students passed in both subjects, the number of students who passed in only Mathematics and Physics can be calculated as follows:
- Number of students who passed in only Mathematics and Physics = (number of students who passed only in Mathematics) + (number of students who passed only in Physics) - (number of students who passed in both subjects)
- Number of students who passed in only Mathematics and Physics = 7y + y - 180 = 8y - 180
Step 4: Solve the equations
Now we can solve the equations to find the values of x and y.
- From step 2: 0.8x = (number of students who passed in Physics) + 120
- From step 3: 8y - 180 = (number of students who passed in Physics) + 120
Since the number of students who passed in Physics is the same in both equations, we can equate the two equations:
0.8x = 8y - 60
Step 5: Find the value of x
Solving the equation 0.8x = 8y - 60, we get:
0.8x - 8y = -60
0.8x = 8y - 60
8x = 80y - 600
x = 10y - 75
Step 6: Calculate the number of students who passed in neither subject
To find the number of students who passed in neither subject, we need to subtract the number of students who passed in both subjects and the number of students who passed in only Mathematics and Physics from the total number of students.
Number of students who passed in neither subject = Total number of students - (number of students who passed in both subjects) - (number of students who passed in only Mathematics and Physics)
Number of students who passed in neither subject = x - 180 - (8y - 180)
Using the value of x from step 5, we substitute it into the equation:
Number of students who passed in neither
Step 1: Understand the given information
- 80% of the students passed in Mathematics.
- The number of students who passed in Mathematics is 120 more than the number of students who passed in Physics.
- 180 students passed in both subjects.
- The ratio of students who passed only in Physics to students who passed only in Mathematics is 1:7.
Step 2: Calculate the number of students who passed in Mathematics and Physics
Let's assume the total number of students in the class is "x".
- Since 80% of the students passed in Mathematics, the number of students who passed in Mathematics is 0.8x.
- According to the given information, the number of students who passed in Mathematics is 120 more than the number of students who passed in Physics. So, we can write the equation: 0.8x = (number of students who passed in Physics) + 120.
Step 3: Calculate the number of students who passed in only Mathematics and only Physics
- The ratio of students who passed only in Physics to students who passed only in Mathematics is 1:7. Let's assume the number of students who passed only in Physics is y, then the number of students who passed only in Mathematics would be 7y.
- Since 180 students passed in both subjects, the number of students who passed in only Mathematics and Physics can be calculated as follows:
- Number of students who passed in only Mathematics and Physics = (number of students who passed only in Mathematics) + (number of students who passed only in Physics) - (number of students who passed in both subjects)
- Number of students who passed in only Mathematics and Physics = 7y + y - 180 = 8y - 180
Step 4: Solve the equations
Now we can solve the equations to find the values of x and y.
- From step 2: 0.8x = (number of students who passed in Physics) + 120
- From step 3: 8y - 180 = (number of students who passed in Physics) + 120
Since the number of students who passed in Physics is the same in both equations, we can equate the two equations:
0.8x = 8y - 60
Step 5: Find the value of x
Solving the equation 0.8x = 8y - 60, we get:
0.8x - 8y = -60
0.8x = 8y - 60
8x = 80y - 600
x = 10y - 75
Step 6: Calculate the number of students who passed in neither subject
To find the number of students who passed in neither subject, we need to subtract the number of students who passed in both subjects and the number of students who passed in only Mathematics and Physics from the total number of students.
Number of students who passed in neither subject = Total number of students - (number of students who passed in both subjects) - (number of students who passed in only Mathematics and Physics)
Number of students who passed in neither subject = x - 180 - (8y - 180)
Using the value of x from step 5, we substitute it into the equation:
Number of students who passed in neither
Community Answer
A class was tested on two subjects-Mathematics and Physics. 80% of the...
180-120=60
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A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?a)40b)50c)60d)70e)80Correct answer is option 'C'. Can you explain this answer?
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A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?a)40b)50c)60d)70e)80Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?a)40b)50c)60d)70e)80Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?a)40b)50c)60d)70e)80Correct answer is option 'C'. Can you explain this answer?.
A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?a)40b)50c)60d)70e)80Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?a)40b)50c)60d)70e)80Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?a)40b)50c)60d)70e)80Correct answer is option 'C'. Can you explain this answer?.
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A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?a)40b)50c)60d)70e)80Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?a)40b)50c)60d)70e)80Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?a)40b)50c)60d)70e)80Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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