What kind of puzzles, estimation, probability, calculus, or statistics questions are asked in IIM interviews?

Question

V Gupta · Accepted Answer

IIM panels sometimes slide into puzzle mode just to see how calmly you think through numbers when there&rsquo;s pressure.
A few real ones that came up: &bull; &ldquo;You have 9 balls, one is heavier &mdash; find it using a weighing scale in 2 tries.&rdquo; &bull; &ldquo;Estimate the number of cabs operating in Mumbai on a weekday.&rdquo; &bull; &ldquo;What&rsquo;s the probability of drawing two face cards in a row from a standard deck without replacement?&rdquo; &bull; &ldquo;If a company&rsquo;s revenue grew from ₹10 lakh to ₹15 lakh in a year, what&rsquo;s the CAGR?&rdquo; &bull; &ldquo;An item&rsquo;s price is cut by 20% and then increased by 20% &mdash; is it back to the original price?&rdquo; &bull; &ldquo;You have 3 light switches in one room and 3 bulbs in another room &mdash; you can only enter the bulb room once. How do you figure out which switch controls which bulb?&rdquo;
Some go beyond pure math. One candidate got, &ldquo;If traffic speed is halved, how much earlier should a bus start to reach on time?&rdquo; These aren&rsquo;t about getting the quickest answer &mdash; they&rsquo;re watching if you break it into steps, explain your logic, and check your own work.

Aarushi S · Answer

IIM interview puzzles and math-based questions usually test how you think, not just whether you know the formula. Common areas include estimation, probability, calculus, and basic statistics,  and the numbers are often simple enough to do in your head.
Recent examples include: &ldquo;Estimate the number of petrol pumps in Delhi&rdquo; or &ldquo;How many footballs can fit in a 747 aircraft?&rdquo; For probability, they&rsquo;ve asked, &ldquo;If you toss two coins, what&rsquo;s the probability of at least one head?&rdquo; and follow-ups like &ldquo;What if one coin is biased to land on heads 70% of the time?&rdquo; In statistics, questions like &ldquo;Explain mean vs. median and give a real-life example where the median is better&rdquo; are common, along with &ldquo;If the standard deviation of exam scores is high, what does it tell you about the class?&rdquo;
Even calculus can appear in basic form ,  &ldquo;If y = x^2, what&rsquo;s dy/dx?&rdquo; ,  with a follow-up on how it&rsquo;s used in economics or physics. Preparing for concepts and their applications is more important than memorising tricky formulas.