Congratulations on securing an invitation for a 1st round interview with McKinsey! It's great to see your dedication to preparation and your commitment to making the most of this opportunity. I understand your concerns about the case interview, particularly the quantitative aspects, and I'm here to provide some guidance to help you succeed.

1. Improving Quantitative Problem-Solving: a) Start with fundamentals: Brush up on basic math concepts, including algebra, percentages, ratios, and data interpretation. Ensure you are comfortable with these concepts as they form the basis of many case interview calculations.

b) Practice mental math: Since you mentioned being good with numerical calculations, continue honing your mental math skills. The faster and more accurate you are with mental math, the more time you'll have to analyze the problem and formulate your approach.

c) Tackle case math strategically: In case interviews, focus on the big picture before diving into detailed calculations. Understand what the problem is asking and think about the key data needed to solve it. Approach the math step-by-step and communicate your thought process clearly to the interviewer.

d) Practice, practice, practice: Work through quantitative case problems from various sources, including MBA casebooks, online resources, and case interview books. As you tackle each case, pay attention to the specific quantitative aspects and work on improving your approach to solving them.

1. Challenging Case Practice: a) Seek diverse case resources: While MBA casebooks are a great starting point, don't limit yourself to them. Look for case interview examples from different industries, functions, and difficulty levels. This exposure will help you handle a wide range of cases during your actual interview.

b) Learn from solutions: After attempting a case, review the solution thoroughly, even for the quantitative parts. Understand the reasoning and calculations provided by experienced interviewers. This will enhance your ability to approach similar problems in future cases.

1. Practice Intensity and Quantity: a) 4 hours a day is commendable dedication to preparation. Consistency and focused practice are essential. Ensure you use your study time effectively by simulating the actual interview environment and time constraints.

b) Quality over quantity: While the number of cases you practice is important, prioritize learning from each case you attempt. Focus on refining your problem-solving approach, identifying areas for improvement, and applying those lessons to subsequent cases.

c) Seek feedback: Whenever possible, practice with a partner or in a case practice group. Feedback from others can be invaluable in identifying blind spots and providing fresh perspectives on your performance.

Given your engineering background and limited formal business or finance knowledge, don't be disheartened. Many successful consultants come from non-business backgrounds. McKinsey values problem-solving abilities, analytical thinking, and adaptability. Emphasize these skills during your interview.

Lastly, consider exploring additional resources online. There are numerous blogs, YouTube channels, and forums where experienced consultants share tips and advice for case interviews.

Remember, preparation is the key to success. Practice diligently, stay positive, and believe in your abilities. Wishing you all the best for your McKinsey interview! You have what it takes to excel, so go in with confidence and showcase your potential. Good luck!