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.

Suggested GMAT Problem Solving Samples

• In United States Currency, a Nickel is Worth 5 Cents GMAT Problem Solving
• After 200 Grams of Water were Added to the 24%- Solution of Alcohol GMAT Problem Solving
• Which of The Following Numbers is A Perfect Square? GMAT Problem Solving
• What is 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6) + 1/(6*7) GMAT Problem Solving
• What is the Remainder When\( 2^{99}\) is Divided by 99? GMAT Problem Solving
• The First Five Numbers in a Regular Sequence are 4, 10, 22, 46, and 94 GMAT Problem Solving
• A Bar is Creating a New Signature Drink. There are Five possible Alcohol GMAT Problem Solving
• A Can Complete a Certain Job in 12 Days. B is 60% More Efficient than GMAT Problem Solving
• An Alloy of Gold,Silver and Bronze Contain 90% Bronze, 7% Gold and GMAT Problem Solving
• When Positive Integer n is Divided by 5, the Remainder is 1 GMAT Problem Solving
• A is Thrice as Efficient as B and Hence Takes 12 Days Less to Complete GMAT Problem Solving
• A Tank is Filled by Three Pipes with Uniform Flow. The First Two Pipes GMAT Problem Solving
• Each Person in a Group of 110 Investors Has Investments in Either GMAT Problem Solving
• Jim Travels the First 3 Hours of His Journey at 60 mph Speed GMAT Problem Solving
• A Committee Of 7 Members Is To Be Formed To Put Up The Christmas GMAT Problem Solving
• In A Class Of 60 Students, 23 Play Hockey, 15 Play Basketball GMAT Problem Solving
• The Area Of An Equilateral Triangle With Side Length X Is The Same GMAT Problem Solving
• Which Of The Following Has A Decimal Equivalent That Is A GMAT Problem Solving
• A Number when Divided by a Divisor Leaves a Remainder of 24 GMAT Problem Solving
• How many Integers Less than 1000 have no Factors (other than 1) GMAT Problem Solving
• How Many Prime Numbers are there Between 50 and 70? GMAT Problem Solving
• If a Circle Passes through Points (1, 2) (2, 5), and (5, 4) GMAT Problem Solving
• If the Perimeter of Square Region S and the Perimeter of Rectangular GMAT Problem Solving
• If x^9= 9^9^9, What is the Value of x? GMAT Problem Solving
• In a Competition, a School Awarded Medals in Different Categories GMAT Problem Solving
• In How Many Ways can 5 Apples (Identical) be Distributed Among 4 Children? GMAT Problem Solving
• What is Greatest Positive Integer n such that 2^n is a Factor of 12^10? GMAT Problem Solving
• All The Five Digit Numbers In Which Each Successive Digit Exceeds Its GMAT Problem Solving
• A Box Contains Two White Balls, Three Black Balls And Four Red Balls GMAT Problem Solving
• Consider An Obtuse-Angled Triangles With Sides 8 Cm, 15 Cm GMAT Problem Solving
• I Travel The First Part Of My Journey At 40 Miles Per Hour GMAT Problem Solving
• Profit Earned By Selling An Article At 1060 Is 20 % More Than The Loss GMAT Problem Solving
• A Perfect Square is a Number that Becomes an Integer when Square GMAT Problem Solving
• If x + y = 2 and x^2 + y^2 = 2, What is the Value of xy? GMAT Problem Solving
• The Owner of A Local Jewellery Store Hired 3 Watchmen to Guard his Diamonds GMAT Problem Solving
• What is the smallest integer n for which 25^n>5^12 GMAT Problem Solving
• Ten Coins are Tossed Simultaneously. In how many of the Outcomes GMAT Problem Solving
• A Pool can be Filled in 4 Hours and Drained in 5 Hours GMAT Problem Solving
• If x^2 − 2 < 0, which of the following specifies all the possible GMAT Problem Solving
• If x = ^5 √-37 then which of the following must be true?
• What is the unit’s digit of (17^3)^4−1973^3^2?
• After the Division of a Number Successively by 3, 4, and 7 GMAT Problem Solving
• What is the value of square root{25 + 10square root(6)} + square root{25 - 10square root(6)} GMAT Problem Solving
• Which of the Following Represents the Range for all x Which Satisfy Inequality GMAT Problem Solving
• If 65 Percent of a Certain Firm’s Employees are Full-Time GMAT Problem Solving
• What is the Remainder When 3^24 is Divided by 5? GMAT Problem Solving
• A={1,2,3,4,5} is Given. If There are 1,2,…,n Subsets of A, Let A1 GMAT Problem Solving
• If 100 Centimetres = 1 Meter, then What is the Value of 100 Centimetre GMAT Problem Solving
• A Positive Integer x is Divisible by 2,3, and 5. What is The Smallest GMAT Problem Solving
• A Solid Metallic Cube is Melted to Form Five Solid Cubes Whose Volumes GMAT Problem Solving