Question:
There are 500 cars on a sales lot, all of which have either two doors or four doors. There are 165 two-door cars on the lot. There are 120 four-door cars that have a back-up camera. Eighteen percent of all the cars with back-up cameras have standard transmission. If 40% of all the cars with both back-up cameras and standard transmission are two-door cars, how many four-door cars have both back-up cameras and standard transmission?
Hello,
Based on my experience, this type of "out-of-context" sizing questions have became out of fashion. Nevertheless, it is likely that you will be asked to do a sizing exercise related to a case (e.g., what is the size of x market segment?).
That said, the following steps (and skills tested) apply to both cases (some of the steps are not applicable in the case of online test - only interview):
0. Clarify the question: What are we sizing? where? when?
1. Choose the approach: Top-down vs. bottom-up - usually, strategy consultants think top-down (i.e., start from a broad perspective and then narrow it down)
2. Break the problem into small, logical pieces: e.g., Market size = total number of addressable customers x % adoption x average spend per customer
3. Make assumptions - and make them explicit: i.e., Consultants never have perfect info! With this exercise, firms are basically testing if you are the kind of person that does not get stuck and can progress in the right direction in moments of uncertainty)
4. Do the math accurately: it is better to take your time and do each step carefully than getting it wrong; try to sanity-check with figures you know from real life (e.g., GDP, industry sizes)
5. Communicate the answer in an executive manner: put the answer into the case context (seems trivial but I have seen candidates totally forget the case when doing this exercise); for extra points, communicate in ranges (e.g., 15-20M€) - you should be able to recognize that there is high uncertainty around the final answer as it is a broad estimate
Hey there :)
Yes, that’s very much the style of quantitative reasoning you can expect in MBB online tests (McKinsey Solve, Bain SOVA, BCG Potential Test, etc.). They often combine basic arithmetic, ratios, and logical steps under time pressure. I would it solve as follows:
Total cars = 500
Two-door cars = 165
Four-door cars = 335
Four-door cars with back-up camera = 120
So total with back-up camera = 120 + x (where x = two-door with camera)
We’re told:
18% of cars with camera → have standard transmission.
Let total cars with camera = T. Then standard transmission & camera = 0.18T.
Of those, 40% are two-door. So 60% are four-door.
We want: four-door with camera & standard = 0.6 × (0.18T) = 0.108T.
Now we need T.
We know among the 335 four-door cars, 120 have camera. But we don’t know how many two-door cars have cameras, so T is not directly given. But the trick is: we don’t need exact x. We just leave it in terms of T.
So answer is: 10.8% of all cars with cameras. If T is given, you can compute the exact number.
If for example T = 200, then four-door with both = 0.108×200 = 21.6 ≈ 22 cars.
So the structure is: carefully translate wording → assign variables → use given percentages.
These layered percentage / subset logic puzzles are exactly what to expect. Practicing a few like this will make you faster.
best, Alessa :)
Hi there,
Yes this a typical question combining both logical and mathematical skills, so you can expect to have this type of question during the online test.
You can find other mock-up questions online, and I would recommend practising regularly, so that you get the gist of it. The questions can be different, but their essence and the pitfalls are fairly similar
Feel free to reach out to me if you wish some help to prepare for MBB interviews!
Best,
Oussama
Yes, for online tests you should be able to answer those kind of questions.
