In a Class of 60 Students, 20 Like Math, 25 Like English GMAT Problem Solving

Question: In a class of 60 students , 20 like math , 25 like english and 30 like science; if 5 like both math and English , 7 like both math and science , 8 like both English and science and 3 like neither of these subjects , how many like all of the three subjects ?

1. 2
2. 3
3. 4
4. 5
5. 0

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

There are a total of 60 students in a classroom, and all of them like different subjects.
20 students like Math
25 out of the 60 students like English
30 students out of the 60 like science.

Further, the question also states a few points, like there are 7 students in the class who like both math, and science, and 8 students in the classroom who like both English, and science. Then there are 3 students who neither like any of the three subjects mentioned. That is math, english, and science. So in order to group the students as per the subjects, let us make three major groups, group M comprises students who like the subjects math. Group E comprises students who like the subjects English, and group S comprises students who like the subjects Science.
Now to approach the question, we need to place an equation. As per the question, there are a total of 60 students, which comprises all the students who like and do not like the subjects. Hence the equation would be like:

All the students in the class=Students who like Maths + Students who like English + Students who like science + Students who like none of the three subjects + students who like all the three subjects - Students who like english and math - Students who like math and science - Students who like science and english

According to this:

Total = M + E + S - (M and E) - (M and S) - (E and S) + All 3 + Neither 3
60 = 30 + 20 + 25 - 5 - 7 - 8 + 3 + All3
All 3 = 60 - 20 - 25 - 30 + 5 + 7 + 8 - 3
All 3 subjects = 80 - 78 = 2

Approach Solution 2:
All of the students in the class are divided into three groups: those who enjoy math, English, and science, as well as those who enjoy none of the three courses or all three. - Students who enjoy math and science - Students who enjoy math and english - Students who enjoy science and math

As evidenced by this:

Total = A + B + C - (A and B) - (B and C) - (C and E) + All 3 subjects + Neither 3 subjects
60 = 30 + 20 + 25 - 5 - 7 - 8 + 3 + All3
All 3 = 60 - 20 - 25 - 30 + 5 + 7 + 8 - 3
Students liking Math, English, and Science = 80 - 78 = 2

Approach Solution 3:
Every student in the class is equal to every student who enjoys math, English, science, or none of the other three disciplines. Additionally, there are kids who enjoy all three courses. English and math enthusiasts; math and science enthusiasts; and science and english enthusiasts

This is the case:

Total = X + Y + Z - (X and Y) - (Y and Z) - (Z and X) + All 3 subjects + Neither 3 subjects
60 = 30 + 20 + 25 - 5 - 7 - 8 + 3 + All3
All 3 = 60 - 20 - 25 - 30 + 5 + 7 + 8 - 3
Students liking All 3 subjects = 80 - 78 = 2

“In a class of 60 students , 20 like math , 25 like english”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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