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Math logic with % calculations help

Math problem
New answer on Oct 31, 2021
4 Answers
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Anonymous A asked on Oct 16, 2021

The question asks to calculate the impact of introducing a new counterfeit tracking system for pharmaceuticals.

  • average annual revenue of pharmaceuticals manufacturers is USD 5 M
  • share of illegal goods in circulation will fall from 20% to 10%, resulting in an equivalent growth in legal sales

Answer: New rev = 5.625M

Can someone explain why we need to find the percentage increase in legal goods i.e 90% (which is new share of legal goods) - 80% (which is old share of legal goods) / 80% = 12.5%..we then take a 12.5% increase of 5M

My question is why can't we deal with this as percentage points increase i.e 20% to 10% so a 10 percentage point increase in legal goods and then apply this 10% to 5M? 

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Hagen
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 replied on Oct 16, 2021
#1 Bain coach | >95% success rate | interviewer for 8+ years | mentor and coach for 7+ years

Hi there,

This is indeed an interesting question which is probably relevant for quite a lot of users, so I am happy to provide my perspective on it:

  • The reason is very simple: Without any further information, you need to assume that the total amount of goods in circulation stays the same.
  • As such, the initial share of legal goods in circulation is 80% which also is the basis for the calculation. A total increase of 10% on the basis of just 80% is 10% / 80% = 12.5%. The 100% + 12.5% = 112.5% of $5M is then $5.625M.

In case you want a more detailed discussion on how to solve this type of quantitative questions, please feel free to contact me directly.

I hope this helps,

Hagen

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Pedro
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 replied on Oct 16, 2021
30% off in April 2024 | Bain | EY-Parthenon | Roland Berger | Market Sizing | DARDEN MBA

Yes, you can apply percentage points - but you must note the 10% and 20% refer to the total goods in circulation, not to the 5M of “legal” goods.

So if 80% of the goods are legal and are 5M, then 100% of total goods are 5M/80%=6.25M 

If you now only have 10% of illegal, then you have: 6.25 * 90% = 5.625M

Or you can use the % as they did: 

10%/80%=12.5% (10% of total goods is the same as 12.5% of legal goods). 

5M * (1+12.5%) = 5,625M

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Ian
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 replied on Oct 17, 2021
#1 BCG coach | MBB | Tier 2 | Digital, Tech, Platinion | 100% personal success rate (8/8) | 95% candidate success rate

Hi there,

Honestly you can take both approaches as long as you do the math/logic right.

Percent increase and percentage point increase need to be multiplied differently…setup the math and do it yourself and you'll see that both can get the same result!

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Marco-Alexander
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 replied on Oct 31, 2021
Former BCG | Case author for efellows book | Experience in 6 consultancies (Stern Stewart, Capgemini, KPMG, VW Con., Hor

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