﻿ The numerical reasoning test takers’ worst nightmare: unit conversion ### Dear Customer,

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# I’ve noticed over the last few months that, for some reason, many numerical reasoning test takers seem to have difficulty with unit conversions. Alright, they in fact dread unit conversions!

For example, a question might state:

“A car travels 168 miles at a constant 60mph averaging 42 miles per gallon. How many litres per minute does the car use in fuel?”

And somewhere in the question data will be the additional useful information:

• 1 gallon = 4.64 litres

The unit problem

The problem is not a particularly difficult one but it is complicated slightly by the fact that the units of the answer are not those stated in the question. We need to convert from miles, hours and gallons to litres and seconds.

Do we multiply or divide?

Here’s a very useful piece of advice I was given at school nearly 40 years ago which I have never forgotten and used countless times: “Keep track of the units”. What does this mean?

Quite simply, when you multiply or divide two quantities then you always multiply or divide their units as well. For example, if you do: Note that the first term divides by gallons and the second term multiplies by gallons which cancel each other out and leaves miles/hour.

In practice this means...

In our original question we are told we have driven a number of miles at a particular rate of consumption in miles per gallon. If you multiply these together, you would end up with miles2 per gallon which is meaningless. However, if you divide then this is the same as inverting the fraction and multiplying it.

Therefore:

[168 miles / 42 miles/gallon] is the same as [168 miles * (1/42) gallons/mile]

Now you can see that in the second form of the equation the ‘miles’ cancel out leaving an answer of 4 gallons. We now know that travelling 168 miles using fuel at a rate of 42mpg will use 4 gallons of fuel.

From the data supplied we know that there are 4.64 litres per gallon. If we multiply gallons by litres per gallon then the gallons cancel out and we end up with (4*4.64)=18.56 litres.

The solution to the problem

The question states that we travelled 168 miles at 60mph so if we divide miles by miles/hour it is the same as multiplying miles by hours/mile and the miles cancel out and leave (168/60)= 2.8 hours. So we use 18.56 litres of fuel in 2.8 hours.

The original question requires the answer in litres per minute so we need to convert hours to minutes. To do this simply multiply by 60, (2.8*60)=168 minutes and then to get the final answer divide the number of litres by the number of minutes, (18.56/168)=0.11 litres per minute.

Makes more sense? With so many units of measurement flying around, this could be very useful advice for your success at the numerical reasoning tests.

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