Math improvement

Math improvement
Recent activity on Apr 26, 2019
5 Answers
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Eugene asked on Apr 09, 2019
Let's practice cases. I have several good Bain cases that I got through.

Please see the question to the Preplounge community below.


James is able to sell 15 of product A and 16 of the product B a week, Sally is able to sell 25 of product A and 10 of the product B a week, and Andrew is able to sell 18 of the product A and 13 of the product B a week. If product A sells for $35.75 each and product B sells for $42.25 each, what is the difference in the amount of money earned between the most profitable and the least profitable seller?


James’s profit: 35.75 ∙ 15 + 42.25 ∙ 16 = 536.25 + 676 = 1212.25$.

Sally’s profit: 35.75 ∙ 25 + 42.25 ∙ 10 = 1316.25$.

Andrew’s profit: 35.75 ∙ 18 + 42.25 ∙ 13 = 1192.75$.

Thus, the most profitable seller is Sally, and the least profitable is Andrew.

The difference between their profits is 1316.25 − 1192.75 = 123.5.


To answer this question we have to make 10 operations. And all this in 80 seconds - i.e. understand the questions and make 10 operations, which leaves less than 8 seconds per operation. How to solve this question faster? Any ideas?

If there's no shortcut, can you share the sources to improve math?

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Best answer
replied on Apr 26, 2019
BCG | Kellogg MBA |82% Success rate| 450+ case interview| 5+ year consulting | 30+ projects in ~10 countries

First, I assume that cost of those products are zero

This question does not look like it has a short cut. However, was this questions multiple choice?

If this was the case, then you can follow different methodology like estimating the potential difference range by checking answers.



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Arnaud replied on Apr 10, 2019

Hi Eugene,

There's a convoluted way, if you set one of the three persons as a baseline and calculate the difference with the 2 others (that way you only calculate the revenue for 2 persons, and with smaller numbers).

A. B
JAMES . 15 16

SALLY 25 . 10

ANDREW 18 13

Since Sally has the highest number, let's take here as a baseline, your table then becomes:

A . B

JAMES . -10 . +6

SALLY . 0 . 0 .

ANDREW . -7 . +3

So the difference between James and Sally is -10*35.75 + 6*42.25 ~= -360 + 240 ~= -120

and the difference between Andrew and Sally is -7*35.75 + 3*42.25 ~= -250 +120 ~= -130

So then you calculate the exact difference between Andrew and Saly and find 123.50 (absolute value)

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Eugene on Apr 10, 2019

Thanks, that is very useful. But why do we take Sally as a baseline?


Arnaud on Apr 10, 2019

Sally was partially a random choice, but what I liked about choosing Sally or James as a baseline was that you had a difference of 10 in product A, which is then easier to calculate (if you take andrew as a baseline, then you end up with 3 and 7 which I like less - but I have not tried to calculate anything)

Anonymous A replied on Apr 09, 2019

By looking on the numbers, without making large multiplications, you can see that the sales from Sally > James > Andrew. (E.g., product B is more expensive than A, while James and Andrew have the same number of products, but James has more of product B, etc.).

So your first step is to discard James from calculations.

Second step is to write the equation:

Sally – Andrew = 35.75*25 + 42.25*10 – (35.75*18 + 42.25*13) = 35.75*7 - 42.25*3 = 123.5. This would cut your operations maybe by 30-50%.

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Eugene on Apr 09, 2019

Thank you! That's helpful. Also not so obvious.


Content Creator
replied on Apr 09, 2019
McKinsey / Accenture Alum / Got all BIG3 offers / Harvard Business School


Several things:

  1. In the multiple answer questions, you should use the process of elimination
  2. If the average time per question is 80 sec, this means that some questions can take more than 80 and some questions will take less. You should just control the overall timing


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Eugene on Apr 09, 2019

Hi Vlad, thanks! Could you suggest how to prepare for Bain online test? Any sources? Any books with similar tasks/questions?


replied on Apr 09, 2019
McKinsey Senior EM & BCG Consultant | Interviewer at McK & BCG for 7 years | Coached 350+ candidates secure MBB offers

Sorry, from this question you don't need to make any calculations since it can not be answered. As long as we don't get information on the costs or profit per product, the question as it was posed can not be answered. Regardless of the selling price, each product can have vastly different profitability.

Not sure whether you paraphrased the question incompletely or whether it was posed in such a poor way.

Cheers, Sidi

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Eugene on Apr 09, 2019

It was posted like this in SHL test. You are right, but probably it's just a mistake, of course there should be revenue.