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Print How Big is Big?

I I’ve come across a lot of UKCAT questions that require you to do a calculation which involves various values with ‘hidden’ zeroes. These hidden zeroes are often skulking at the top of a column of data, in a table heading, on a chart axis or in the wording used in the question. Between them they determine the order of magnitude of the answer.

Let’s look at a typical question from a UKCAT exam to see what I mean…

Question: If 56.2% of all liver disease sufferers are men, how many women suffer from liver disease in France?

A – 227114    B – 22711   C – 2271    D – 227   E – 23

OK, so I’ve shortened the table to show just the information we need which makes it a little easier but it can still demonstrate the point I wish to make.

The problem to solve

The number of people with liver disease is simply the population multiplied by the rate or prevalence of the disease within that population which is given in the table. This is:

60084 * 86.3

Of these people 56.2% of them are men and so (100-56.2)% or 43.8% must be women and so the number of women sufferers is:

60084 * 86.3 * 43.8 = 227113914.96

This answer shouldn’t come as any great surprise as all the answers given are effectively this but with the decimal point moved as this is the whole point of this article.

The value has been also rounded to the nearest whole number. This rounding is reasonable as we are talking about a number of people and you can’t have 0.96 of a person suffering from liver disease – even if they are missing a couple of toes.

The answer we have clearly isn’t right as it is more than the entire population of France but where do we move the decimal point to? We need to adjust our answer to account for the order of magnitude.

The step-by-step methodology

1.    Let’s look at each term in turn. We started with the population of France which was given as 60084 but this is in thousands as stated at the head of the column of population data. As such we need to multiply the answer we have by 1000:

227113915 * 1000 = 227113914960

2.    This is getting worse! Do not despair; help is on the way. The second term that we usedwas the rate of sufferers in the population. The table heading tells us that this is per 100,000 of the population and so we need to divide the answer we have by 100,000:

227113915000 / 100000 =2271139.1496

3.    Next, we took a percentage of this number and, by definition, per cent means ‘per 100’ so we must divide the answer we have again by 100:

2271139.1496 / 100 = 22711.391496

4.    Finally, as stated above, we can round this to the nearest whole number to give us our final answer of 22711 which is answer B.


Interested in practicing more? Check our huge database of UKCAT quantitative reasoning tests!

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