Operations: Business Aptitude Questions for MBA Placements

Ans: C

Explanation:The Charnes method of penalty, also known as the Big-M method, is used in linear programming to handle artificial variables introduced into the constraints. It assigns a large penalty (M) to these artificial variables in the objective function to discourage their presence in the optimal solution unless absolutely necessary.
Correct_Option:C

Ans: C

Explanation:Operations Research (OR) is a quantitative discipline that uses mathematical modeling and analytical techniques to optimize decision-making. It relies on data and seeks to find the best solutions by analyzing measurable inputs and outputs. Therefore, OR is most effective when dealing with factors that can be expressed numerically and objectively measured, rather than subjective or qualitative aspects.
Correct_Option:C

Ans: D

Explanation:Strategic quality management involves defining competitive priorities, which include quality as a key dimension. Supplier selection should indeed consider quality and schedule alongside cost. Quality improvement is a company-wide effort, requiring understanding and participation from all employees, not just manufacturing. Therefore, stating that only the manufacturing unit should focus on quality improvement is incorrect.
Correct_Option:D

Ans: A

Explanation:The Average Run Length (ARL) in control charts is the expected number of samples before a signal is given. For a simple exponential smoothing (EWMA) control chart with a smoothing constant alpha ($\alpha$), the ARL for detecting a shift is approximately $1/\alpha$. Given $\alpha = 0.0015$, the ARL is $1/0.0015 = 666.66…$. Rounding this to the nearest whole number gives approximately 667. Option A states 666, which is the closest and aligns with the formula.
Correct_Option:A

Ans: B

Explanation:Six Sigma is a quality management methodology that aims to reduce defects and variation in processes. A process that is Six Sigma compliant means that it operates at a very high level of quality. In a Six Sigma process, the expected number of defects per million opportunities is 3.4. This corresponds to a defect-free rate of 99.99966%, which is approximated by 0.9999966. However, the options provided are much lower. There’s a common misunderstanding or a simplified definition sometimes used where “Six Sigma” is associated with a certain percentage of acceptable outcomes. Historically, when Six Sigma was introduced, it was often cited as achieving 99.99966% of output within specifications (accounting for a 1.5 sigma shift in the mean). If we consider the standard definition of a 6-sigma process, it means that the process mean is 6 standard deviations away from the nearest specification limit. This leads to a defect rate of approximately 2 defects per billion. Therefore, the percentage of products within specifications would be extremely high, close to 100%.

However, given the options, it’s possible the question is referring to a specific, perhaps simplified or a slightly different interpretation, or even a common misconception. Let’s consider the percentages given.

A “3-sigma” process typically has about 99.73% of its output within specifications.
A “4-sigma” process has about 99.9937% of its output within specifications.
A “5-sigma” process has about 99.999943% of its output within specifications.

The provided options are significantly lower than the actual Six Sigma defect-free rate. Let’s re-evaluate the question and common interpretations or potential errors.

It’s highly likely that the question is flawed or referring to a less precise definition. However, if forced to choose from the given options, and understanding that Six Sigma aims for extremely high quality, the closest option that suggests a very high percentage of products within specifications is needed.

Let’s consider a potential misunderstanding where “Six Sigma” is being conflated with a different concept, or the options are simply wrong.

If we consider a process that is performing *reasonably well* but not necessarily at the stringent Six Sigma level, a 3-sigma process is often cited as having ~99.73% within spec. This is option B.

Given the context of placement aptitude tests, they sometimes use simplified or commonly known figures. The 99.73% figure associated with 3-sigma is a very well-known statistic in quality control. If the question *intended* to refer to a process with a high percentage within specifications and *mistakenly* used “Six Sigma” to imply “very good quality,” then 99.73% is the most recognizable high-quality benchmark among the options that isn’t extremely close to 100%.

However, the true Six Sigma level (3.4 DPMO) means the yield is 99.99966%. None of the options are close to this. This suggests a fundamental flaw in the question or options.

Let’s assume the question is asking for the percentage of products within specifications for a *highly capable* process, and that one of the options, though not perfectly aligned with the strict definition of Six Sigma, is the intended answer.

If we consider the common benchmark for a process that is performing very well, a 3-sigma process yields about 99.73% within specifications. This is the most commonly cited high-yield figure in introductory quality concepts.

Given the options, and the prevalence of the 3-sigma yield in general quality discussions, it is the most plausible intended answer despite the incorrect terminology of “Six Sigma.”

Correct_Option:B

Ans: C

Explanation:In statistics and mathematics, orthogonality is a concept that implies a lack of linear relationship or association. When two factors are orthogonal, their variations are independent of each other. This means that a change in one factor does not predictably affect the other. Options A, B, and D describe characteristics related to correlation, experimental design, and comparative analysis, but not the fundamental definition of orthogonality. Orthogonality specifically means the absence of correlation.
Correct_Option:C

Ans: A

Explanation:A Pareto chart is a type of chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line. It is used to highlight the most significant factors among a set of variables. The “80/20 rule” (also known as the Pareto principle) states that roughly 80% of effects come from 20% of causes. A Pareto chart visually displays this principle, making it ideal for identifying the most frequent defects or problems.
Correct_Option:A

Ans: C

Explanation:Continual improvement is a fundamental principle in quality management systems. When an audit identifies non-conformities (Audit Result), corrective actions are implemented to address these issues. The effectiveness of these corrective actions and the ongoing drive to enhance processes and performance are what constitute continual improvement. Environmental objectives are specific targets related to environmental performance, and while improvement can be applied to them, continual improvement itself is a broader concept realized through the corrective action process.
Correct_Option:C

Ans: D

Explanation:In project management, total float (or total slack) is the amount of time a task can be delayed without delaying the project’s end date. Free float (or free slack) is the amount of time a task can be delayed without delaying the start of any subsequent tasks. The difference between total float and free float is the time a task can be delayed without delaying any successor tasks. This is often referred to as interference or interference float, as it represents the portion of total float that is “used up” by the dependencies on subsequent activities.

Correct_Option:D

Ans: C

Explanation:Six Sigma is a methodology that uses a structured approach to improve processes. Within Six Sigma, there are different levels of expertise and responsibility, commonly referred to as belts. Black Belts and Green Belts are two of the primary belt levels, each with distinct roles and responsibilities in leading and participating in Six Sigma projects. Therefore, both are integral to Six Sigma.
Correct_Option:C

Ans: D

Explanation:In Statistical Process Control (SPC), control charts typically use lines that represent control limits set at +/- three standard deviations from the process mean. These limits are chosen because they encompass approximately 99.73% of the data points expected from a stable process, making them effective in detecting statistically significant deviations.
Correct_Option:D

Ans: D

Explanation:In project management, crashing is the process of accelerating project completion by adding resources. The crash time is the shortest possible time an activity can be completed, and the crash cost is the cost associated with completing the activity at its crash time. Therefore, the activity cost corresponding to the crash time is called the crash cost.
Correct_Option:D

Ans: B

Explanation:In a system of linear equations represented by a matrix equation Ax = b, where A is an m x n matrix (m < n), the number of basic variables is equal to the rank of the coefficient matrix A. For a system with m equations and n unknowns (m < n), the rank of A can be at most m. In a consistent system, the number of basic variables is equal to the rank of the augmented matrix [A|b], which is also equal to the rank of A. Therefore, the number of basic variables will be at most m. Since m < n, it's possible to have fewer than n basic variables. The number of free variables is n - rank(A). Thus, the number of basic variables is equal to the rank, which is at most m. For a system to have a unique solution, m must be equal to n and the rank must be n. However, when m < n, we are generally looking at cases where there might be infinitely many solutions. In such cases, the number of basic variables is determined by the rank of the coefficient matrix, which cannot exceed the number of rows (m). Therefore, there will be at most m basic variables. In the context of linear algebra, when we are dealing with a system of m equations and n unknowns where m < n, and assuming the system is consistent and we are looking for a particular solution or understanding the structure of solutions, the number of basic variables is equal to the rank of the coefficient matrix, which is at most m. Therefore, the maximum number of basic variables is m.

Correct_Option:B