You're not alone if you're nervous about dealing with % in numerical test problems. Unfortunately, alot of questions in data interpretation and numerical reasoning tests and cases involves application and rapid calculation of percentages. A lot of business terms - gross margin, operating margin, net income %, cost as a % of revenue and so on all involve percentages.
This post is not about how to deal with % overall, but to talk about one specific way of dealing with it. Let's say you have a question that is
"A company has revenue of X. 30% of this is cost of materials, 40% of the remaining is wages, 20% of the remaining is all other expenses. The money left over is profit. What is the profit %? (i.e profit as a % of revenues)"
People go wrong in 3 ways.
1. Blindly adding up 30, 40, 20 and saying profit is 10%. Wrong! It says 'remaining amount', so this has to be applied progressively.
2. Or they multiply the actual percentages forgetting that they need to be applied to the amount remaining! So the equation really is
X*(1-30%)*(1-40%)*(1-20%) and not X*30%*40%*20%
Be careful of these questions - they come in different forms, e.g. material wastes, interview rejection ratio, funnelling problems etc. We have some in our tests
2. So, the actual way to calculate is the remaining amount is really X*(70%)*(60%)*(80%)
Now, many people struggle with the calculations. It's all nice to write down on paper
X*70%*60%*80% and then start multiplying - some people can do it quickly, some others get all messed up with either the multiplication or the 0's and this can spell disaster in a time-pressure numerical test or a case interview. (see our post on confusion with zeros)
Now, take a step back. Percent => 'for a hundred'. So don't bother with X. In a problem that starts with no number, simply take 100 as the revenue and work from there.
so let's go back to the problem
This post is not about how to deal with % overall, but to talk about one specific way of dealing with it. Let's say you have a question that is
"A company has revenue of X. 30% of this is cost of materials, 40% of the remaining is wages, 20% of the remaining is all other expenses. The money left over is profit. What is the profit %? (i.e profit as a % of revenues)"
People go wrong in 3 ways.
1. Blindly adding up 30, 40, 20 and saying profit is 10%. Wrong! It says 'remaining amount', so this has to be applied progressively.
2. Or they multiply the actual percentages forgetting that they need to be applied to the amount remaining! So the equation really is
X*(1-30%)*(1-40%)*(1-20%) and not X*30%*40%*20%
Be careful of these questions - they come in different forms, e.g. material wastes, interview rejection ratio, funnelling problems etc. We have some in our tests
2. So, the actual way to calculate is the remaining amount is really X*(70%)*(60%)*(80%)
Now, many people struggle with the calculations. It's all nice to write down on paper
X*70%*60%*80% and then start multiplying - some people can do it quickly, some others get all messed up with either the multiplication or the 0's and this can spell disaster in a time-pressure numerical test or a case interview. (see our post on confusion with zeros)
Now, take a step back. Percent => 'for a hundred'. So don't bother with X. In a problem that starts with no number, simply take 100 as the revenue and work from there.
so let's go back to the problem
"A company has revenue of X. 30% of this is cost of materials, 40% of the remaining is wages, 20% of the remaining is all other expenses. The money left over is profit. What is the profit %? (i.e profit as a % of revenues)"
break it down quickly, let 100 be the revenue
30% of this is cost of materials => 30 => remaining is 100-30 = 70
40% of remaining is wages => 60% left => 70 * 60% = 42
20% of remaining is other expenses => 80% left => 42 * 80% =~32 (we use ~32 because the answers will probably be close to this)
Since we started with 100 as a the base and the final remaining about is 32, that itself is the answer! so the net income margin (or profit margin) is 32%. This line of calculation is often more manageable and often easy to do even in the head - of course assuming that you can do single digit multiplications quite rapidly.
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