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Out of the 60 employees of a startup, only 10 are non-engineers. How many employees of the startup are engineers with a MBA degree?
(1) Only 1 out of every 12 employees with a MBA degree is a non-engineer
(2) More than 55 percent of all employees have a MBA degree
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  • d)
    EACH statement ALONE is sufficient to answer the question asked.
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
Out of the 60 employees of a startup, only 10 are non-engineers. How m...
Steps 1 & 2: Understand Question and Draw Inferences
Given: 60 employees classified on 2 attributes:
  • Engineer/Non-Engineer
  • MBA Degree/ No MBA Degree
  • (Number of Non-engineers) = 10
    • So, (Number of Engineers) = 60 – 10 = 50
      • Note: In the above table and the other tables in this solution, black font color is used to denote the given information, whereas blue font color is used to denote the inferred information
To find:  Number of Engineers with MBA Degree
Step 3: Analyze Statement 1 independently
Statement 1 says that ‘Only 1 out of every 12 employees with a MBA degree is a non-engineer’
  • Let the total number of employees with a MBA degree be x
    • x≤60
  • So, (Number of non-engineers with a MBA degree) = x/12
  • Since number of people must be an integer, x must be a multiple of 12
    • We have already seen that x≤60
    • So, multiples of 12 that are less than equal to 60 are: {12, 24, 36, 48, 60}
  • Therefore, (Number of engineers with a MBA degree) = 11x/12
  • 11x/12
 must be less than equal to the row total of 50
  • Out of {12, 24, 36, 48, 60}, we can reject the value 60 on this basis (because , which is greater than the row total of 50)
  • So, possible values of x = {12, 24, 36, 48}
  • Since we do not know still know a unique value of x, Statement 1 is not sufficient
Step 4: Analyze Statement 2 independently
Statement 2 says that ‘More than 55 percent of all employees have a MBA degree’
  • Let the total number of employees with a MBA degree be x
  • So, x > 55% of 60
  • That is, x > 33
However, this doesn’t answer the question about number of Engineers with MBA Degree
Not Sufficient.
Step 5: Analyze Both Statements Together (if needed)
  • From Statement 1:
    • x = {12, 24, 36, 48}
  • From Statement 2, x > 33
  • Combining the 2 statements, we get that:
    • x = {36, 48}
  • So, the 2 statements together are also not sufficient to answer the question
Answer: Option E
This question is part of UPSC exam. View all GMAT courses
Most Upvoted Answer
Out of the 60 employees of a startup, only 10 are non-engineers. How m...
Question Analysis:
We are given that there are 60 employees in a startup and we need to determine the number of employees who are engineers with an MBA degree. We are also given two statements to analyze.

Statement 1: Only 1 out of every 12 employees with an MBA degree is a non-engineer.

Statement 2: More than 55 percent of all employees have an MBA degree.

Analyzing Statement 1:
This statement provides information about the ratio of non-engineers to engineers with an MBA degree, but it does not give us any information about the total number of employees or the number of non-engineers in the company. Therefore, statement 1 alone is not sufficient to answer the question.

Analyzing Statement 2:
This statement tells us that more than 55 percent of all employees have an MBA degree. However, it does not provide any information about the ratio of engineers to non-engineers or the total number of employees. Therefore, statement 2 alone is not sufficient to answer the question.

Combining the Statements:
By combining the statements, we can deduce some additional information.

From statement 2, we know that more than 55 percent of all employees have an MBA degree. Let's assume that 56 percent of the employees have an MBA degree. This means there are 0.56 * 60 = 33.6 employees with an MBA degree.

From statement 1, we know that only 1 out of every 12 employees with an MBA degree is a non-engineer. This means that out of the 33.6 employees with an MBA degree, only 1/12 * 33.6 = 2.8 employees are non-engineers.

Since we cannot have a fraction of an employee, we can conclude that there are 3 employees with an MBA degree who are non-engineers.

Now, we can subtract this number from the total number of employees to find the number of engineers with an MBA degree: 60 - 3 = 57.

Conclusion:
By combining the statements, we can determine that there are 57 employees who are engineers with an MBA degree. Therefore, both statements together are sufficient to answer the question. The correct answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
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Out of the 60 employees of a startup, only 10 are non-engineers. How many employees of the startup are engineers with a MBA degree?(1) Only 1 out of every 12 employees with a MBA degree is a non-engineer(2) More than 55 percent of all employees have a MBA degreea)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer?
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