100 Students Appeared for Two Examinations. 60 Passed the First GMAT Problem Solving

Question: 100 students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has failed in both the examinations?

1. \(\frac{1}{5}\)
2. \(\frac{1}{7}\)
3. \(\frac{5}{7}\)
4. \(\frac{5}{6}\)
5. \(\frac{6}{7}\)

“100 students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has failed in both the examinations?”- 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 amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution (1):

Let’s calculate the number of the students failed in each of the two exams.

A- 40, B- 50. Now, the next thing to figure out is if these two events are dependent or independent events. These two events are independent events as the outcome of one does not influence the outcome of other. In this ase the following formula hold true.

P (A and B) = P (A) * P (B)

P (A) = \(\frac{2}{5}*\frac{1}{2}=\frac{1}{5}\)

Correct Answer: A

Approach Solution (2):

We can solve this problem by applying the set theory.

Let A = PPL who passed in \(1^{st}\) test = 60
Let C = PPL who passed in \(2^{nd}\) test = 50
Let B = overlap i.e., PPL who passed in both = 30

Then A + B = 60
Therefore A = 30
B + C = 50

Therefore C = 20
A + B + C = 80

Remaining = 20 (PPL who did not pass at all)
= \(\frac{200}{100}=\frac{1}{5}\)

Correct Answer: A

Suggested GMAT Problem Solving Questions

• What is the Value of [√7+√29−√7−√29]2 GMAT Problem Solving
• What is The Area of a Triangle with the Following Vertices GMAT Problem Solving
• The Product of the Five Smallest Two-Digit Prime Numbers GMAT Problem Solving
• The Square of 5^√2 =? GMAT Problem Solving
• Two Adjacent Angles of a Parallelogram are in the Ratio of 1:3 GMAT Problem Solving
• Which of The Following is a Perfect Cube? GMAT Problem Solving
• If a Right Angled Isosceles Triangle Has an Area of 2x^2 + 2x + ½. GMAT Problem Solving
• A number N^2 has 35 factors. How many factors can N have? GMAT Problem Solving
• If the Total Surface Area of a Cube is 24, What is the Volume of the Cube? GMAT Problem Solving
• There are 5,280 Feet in 1 Mile and 12 Inches in One Foot GMAT Problem Solving
• An Isosceles Right Triangle has an Area of 50. What is the Length of the Hypotenuse? GMAT Problem Solving
• A is Thrice as Good a Workman as B and Takes 10 days Less to do a Piece of Work GMAT Problem Solving
• 999,999^2−1 equals? GMAT Problem Solving
• If A Equals the Sum of the Even Integers from 2 to 20, Inclusive GMAT Problem Solving
• A Store Currently Charges The Same Price for Each Towel That It Sells. GMAT Problem Solving
• Which of the following represents the largest 4 digit number GMAT Problem Solving
• The Lengths of the Sides of an Obtuse-Angled Triangle are x, y, and z, Where x, y and z are Integers GMAT Problem Solving
• If the expression sqrt2+2+2+2+ ... extends to an infinite number of roots GMAT Problem Solving
• How Many Different Lines Are Determined by 4 Distinct Points in a Plane If No 3 GMAT Problem Solving
• If The Diagonal of Rectangle Z is d, And The Perimeter of Rectangle Z is p GMAT Problem Solving