Question: In a class of 100 students 70 passed in physics, 62 passed in mathematics, 84 passed in English and 82 passed in chemistry. 37 students passed in all 4 subjects. What is the maximum number of students who could have failed all four subjects?
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“In a class of 100 students 70 passed in physics, 62 passed in mathematics,”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
Given condition states that- In a class of 100 students 70 passed in physics, 62 passed in mathematics, 84 passed in English and 82 passed in chemistry. 37 students passed in all 4 subjects.
In order to find the maximum number of students who could have failed in all the four subjects, the problem needs to be solved with the help of the following evaluations.
The total marks scored by the students in all the subjects are-
70+62+84+82=298
The total number of students who passed in all subjects-
37 * 4 = 148
The remaining students who pass in 3 exams-
298 - 150 = 150
= 150/3 = 50
Out of the total students the maximum number of students that passed = 37 + 50 = 87
Maximum number of students failed = total number of students in class - maximum students that passed
= Max students that failed = 100 - 87
= 13
Hence, a total of 13 students at maximum failed in the class
Correct Answer: C
Approach Solution 2:
According to the given factor, out of a class of 100 students, 70 students passed physics, 62 students passed mathematics, 84 students passed English, and 82 students passed chemistry. 37 students earned passing grades in all subjects.
With the aid of the subsequent evaluations, the issue must be resolved in order to determine the greatest number of students who might have failed in all four subjects.
The students' overall grade point average (GPA) is 298 (70+62+84+82).
37 * 4 = 148 is the total number of students who passed in all disciplines.
298 - 150 = 150 = 150/3 = 50 for the remaining students who pass all three tests.
Maximum number of students who passed out of all students: 37 + 50 = 87
Maximum number of students failing equals the entire number of students enrolled in the class minus the maximum number of students passing, or 100 minus 87, or 13
Therefore, a maximum of 13 students failed the class.
Correct Answer: C
Approach Solution 3:
A class of 100 students, according to the above factor, had 70 students pass physics, 62 students pass math, 84 students pass English, and 82 students pass chemistry. 37 students achieved passing marks across the board.
The problem must be addressed with the assistance of the succeeding exams in order to ascertain the largest number of students who may have failed in all four subjects.
The cumulative grade point average (GPA) of the students is 298 (70+62+84+82).
The overall number of students who passed across all subjects was 37 * 4 = 148.
For the remaining students who pass all three examinations, 298 - 150 = 150 = 150/3 = 50.
Maximum number of graduates from all students: 37 + 50, totaling 87.
The maximum number of failing students is equal to the total number of registered students in the class less the maximum number of passing students, or 100 minus 87, or 13.
Thus, a maximum of 13 students might have failed the class.
Correct Answer: C
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