Author Archives: Numerical Reasoning

Increase & Decrease

Classic Question 1: By what percent would Sprit’s fourth quarter 2012 sales have to increase in order to equal its third quarter sales figures?

increase decrease

Step 1: find the right numbers from the chart.

Make sure you are comparing the right numbers. This means reading and understanding the question. We are looking at the increase required to get from 3.5 (£million ) to 4.8 (£million). We’ll ignore the £million since the units have no effect on the increase.

Step 2: Recast the equation to solve.

The problem boils down to: 3.5 x ( ? ) = 4.8. This can be recast as:

? = (4.8 ÷ 3.5)

? = 1.371

Ans = 37.1% increase

 

Whilst you probably won’t have time to do this in your real numerical reasoning test, for our training it is worth double-checking that this answer is correct. To do this we say is 3.5 x 1.371 = 4.8? Putting this into the calculator we see that yes, this works!

 

Ratios

Classic Question 1: If sales revenue in 2011 was split between online and offline sales in the ratio 7:2, what was the revenue from offline sales in 2011 (to the nearest £100)?

ratios

 

Step 1: Analyse the problem

From the table we see that the sales revenue in 2011 was 15,470 (£ thousands).

We are told that online:offline sales are in the ratio of 7:2. And it is safe to assume there are no other categories (i.e. we assuming all sales are either online or offline, nothing else). So the offline portion of these sales will be 2 out of a total of 9 (7 + 2).

Step 2: Apply the ratio

Offline sales will be 2 ÷ (7 + 2) x 15,470 = 3,437.78

Ans = £3,437,800

Note that we divided by 9 because we want the fraction of offline sales relative to all sales revenue.

 

Classic Question 2: Which manufacturing plant had the lowest ratio of Servicing to Utilities, and what was this ratio?

ratios

Step 1: Quickly scan the data to see if any of the options are obviously not correct, thus saving you time by not having to calculate them. Personally, I can’t see an obvious contender to leave out, so I will calculate all five.

Step 2: For all five manufacturing plants divide Service by Utilities:

Midlands:  225 ÷ 90 = 2.5
Bordeaux:  1,180 ÷ 236 = 5.0
Berlin  820 ÷ 164 = 5.0
Amsterdam  735 ÷ 245 = 3.0
Glasgow  240 ÷ 180 = 1.3333

Warning: make sure you get the numbers the right way round when you are dividing one by the other.

Step 3: Convert to a fractions.

We can see that part of the answer is Glasgow because it has the lowest number, now we just need to convert 1.333(recuring) to a fraction. Whilst some scientific calculators will turn 1.333 recurring into a fraction, there are certain fractions you will be expected to know. This is one of them and you should be able to see that this is 4/3.

Ans: Glasgow 4:3

Other common ratios you would be expected to recognise are:

0.1 = 1/10
0.2  = 1/5
0.25 = 1/4
0.33 recurring = 1/3
0.5 = 1/2

Percentages

Classic Question 1: “What was the percentage change in current assets from March to April?”

figure-percentage

Step 1: Locate the right numbers 65,000 and 68,000

Make sure you start with the right numbers from the table, since there are no ‘method marks’ for numerical reasoning tests. Double check that you are looking at the ‘current assets’ row and the March – April columns.

Step 2: Know how to calculate percentage changes

The key here is to know the shortcut method: simply calculate 68,000 ÷ 65,000 = 1.046.

Ans = 4.6% increase.

 

So how did I know the answer is an increase of 4.6%?

I could have calculated the next step (1.046 – 1) x 100 = 4.6% but from experience I knew that I could just look at the number 1.046 and covnert this into an increase of 4.6% in my head. I know that with this shortcut method a number larger than 1 is an increase, and a number less than 1 is a decrease. The shortcut method is simply a cancelled-down version of the long-hand version:

[ (68,000 – 65,000) ÷ (65,000) ] x 100 = 4.6%

Watch out: the trick to any percentage change question is getting the ‘from’ and ‘to’ number the right way around. The ‘to’ number needs to go on top of the division calculation (the ‘numerator’) and the ‘from’ number needs to go on the bottom (the ‘denominator’). So looking again at our shortcut method we have:

68,000 ÷ 65,000 NOT 65,000 ÷ 68,000.

What if we were asked:

Classic Question 2: What was the percentage change in property assets from Jan to Feb?”

Using the same method we would calculate: 35,500 ÷ 36,000 = 0.9861

Ans = 1.4% decrease

So instead of a percentage increase, we have a decrease this time because the number is below 1.0.