The GMAT and black cats

Let’s start off with a typical GMAT question – one of the hurdles one has to overcome when applying to business school. According to a certain estimation, the total number of black cats is 25% greater than the number of black male cats, and the number of all female cats is 5 times the number of black female cats. If the male cats are 50% of all cats, then what percent of male cats are black?
– 10
– 20
– 40
– 50
– 80
Got it? Great! You’ll find the solution to this question at the end of this post.

But first things first: where does this test come from? In the early fifties, 9 business schools including Wharton, Kellogg, Booth, Columbia and HBS discussed the possibility to define a standardized entry test for graduate programs. In 1954, the first tests were taken. It took only 25 years (in 1981) before 200.000 tests would be administered – an amazing number considering that only US based schools would use the GMAT up until 1995. In recent years, the GMAT has evolved to 250.000 tests per year with a record high number of tests taken in 2009.

Graph 1: GMAT exams taken (sources:

Thus, questions related to black cats have been administered for more than 60 years. As this is the type of question one will face on a GMAT exam, the ability to respond to it in a timely and correct matter will impact the type of business school one can successfully apply to. However, determining the impact of a GMAT score on the chances of admission to the top business schools is very difficult, so let’s see what the statistics say.

50% of HBS MBA students class of 2014 have a GMAT of 730 or more, i.e. the 96th percentile or up. With the HBS middle 80% ranging from 670 (or 85th percentile) to an almost perfect score, any score below 670 will leave you with only a small chance of being accepted.

Graph 2: GMAT scores and percentiles (sources: & GMAT scores of HBS Class of 2014 (source:

Similar trends can be seen at other top-tier B-schools.

Graph 3: Average GMAT scores by Business School (source:

Finally, here are some interesting facts on the GMAT:
In 2011, 45% of GMAT exams were taking in the US (down from 53% just four year earlier)

  • 77% of examinees of the GMAT would attend a US-based school in 2011 (down from 83% in 2007)
  • 40% of GMAT tests are taken by women. However, in China, more women than men take the GMAT.
  • Men tend to slightly outperform women on the test, with the median score for men totalling 554 compared to 530 for females (except in East and SouthEast Asia, where they score the same)
  • Highest Median score can be found in the ‘Australia and Pacific islands’ region

 As promised, I’ll end this post by counting black male cats.
Any cat can be either male or female, and black or not black. Take x as the number of black male cats. With the information provided, and assuming that there are 100 male cats, you can build the following table:

Now we can write the following equation:

Which we can simplify to:

Or, finally:

 Good luck!


3 responses to “The GMAT and black cats

  1. right number of cats – wrong %

  2. oops – you are right!

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