How to Pass Numerical Reasoning (29 page)

Percentage formulae practice questions

Find the part

Q1
What is 50% of 36?

Q2
What is 75% of 160?

Q3
What is 30% of 130?

Q4
What is 24% of 24?

Q5
What is 20% of 12.5% of 80?

Find the whole

Q6
15 is 25% of what number?

Q7
125 is 62.5% of what number?

Q8
32% of 60 is 60% of what number?

Q9
25 is 16
²
⁄
₃
% of what number?

Q10
112 is 87.5% of what number?

Find the percentage

Q11
18 is what percentage of 48?

Q12
What percentage of 160 is 4?

Q13
12 is what percentage of 200?

Q14
What is 37.5% of 12.5% of 512?

Q15
2.4 is what percentage of 320?

Increasing or decreasing a value by a percentage

Percentage increases and decreases are one of the most common calculations you will be asked to perform in aptitude tests. Being familiar with basic formulae and estimating techniques will save you a lot of time during the test. The key to working out a percentage change quickly and correctly is to estimate the answer first. This will lead you to the right order of operations and will help you to identify the place where you made an error in your calculation, should you find that your original estimate and calculation are way off.

There are two basic methods to work out a percentage increase or decrease. Pick the method that suits you (or your numbers) and use the other to validate your answer.

Method 1

Find the actual value of the percentage increase (or decrease) and add the value of the increase (or decrease) to the original value.

Percentage increase formula

Percentage decrease formula

Worked example, percentage increase method 1

The price of a barrel of oil increased from $20 to $24 between January and April 1992. By what percentage did the price of oil increase during this period?

Estimate the answer

An increase of 50% on the original whole amount of $20 would give a new price of $30 ($20 + (0.5 × $20) = $30). An increase of 10% would give a new price of $22. ($20 + (0.1 × $20) = $22). So you know that your answer will be in the range of 10–50% and will be closer to 10% ($22) than to 50% ($30).

Calculate the answer

Use the formula to find a percentage increase and plug in the numbers.

The actual amount of increase = the difference in price between January and April = $24 – $20 = $4:

Reduce the fraction to its lowest terms:

Percentage increase = 20%

Worked example, percentage decrease method 1

The travel agent list price of a flight from London to Santa Domingo is £600. If you purchase the flight online direct from the airline, you can buy the flight for a one-off discounted price of £510. By what percentage is the flight discounted if you buy online?

Estimate the answer

The cost of a £600 flight after a 10% decrease is £600 – £60 = £540. After a 20% decrease, the same flight would cost £600 – (2 × £60) = £480. So you know that your answer will be somewhere between 10% and 20%.

Calculate the answer

Use the formula to find a percentage decrease and plug in the numbers.

The actual amount of decrease = original whole (£600) – new whole (£510) = £90.

Reduce the fraction to its lowest terms:

Percentage decrease = 15%

Method 2

To find the new value multiply by the original whole + percentage increase:

= 1 + percentage increase (expressed as a decimal)

To find the new value multiply by the original whole – percentage decrease:

= 1 – percentage decrease (expressed as a decimal)

Worked example, percentage increase method 2

The price of a bicycle lock before VAT is £8.50. For how much, to the nearest penny, does the lock sell retail? VAT in the UK is currently 17.5%.

Estimate the answer

A 10% tax on an item costing £8.50 is £0.85. A 20% tax would be (2 × 10%) = £1.70. A 17.5% tax would increase the original whole by an amount between 85p and £1.70. The answer will be between (£8.50 + £0.85) and (£8.50 + £1.70).

Calculate the answer

To find the new value multiply by the original whole + percentage increase:

Worked example, percentage decrease method 2

A wholesale tyre company offers a discount of 8% to its preferred customers. If a set of four tyres sells for £160 to regular customers, how much does the set cost to a preferred customer?

Estimate the answer

A 10% discount would reduce the price by £16, so your approximate answer will be £160 – £16 = £144.

Calculate the answer

To find the new value multiply by the original whole – percentage decrease. Calculate the decrease by subtracting the amount of percentage change from 100%. In this question, the percentage decrease is 8%, so 1 – 0.08 = 0.92:

Combining percentages

Percentage questions will often require that you complete the question in several stages. The questions are not difficult as long as you remember a couple of basic rules. First, remember that you cannot just combine all the percentages in a question and find the total percentage of the original whole. Second, always identify the original whole as the starting point.