Civil Service Practice
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Professional and Subprofessional · Civil Service Exam

Word problems

A word problem hides one equation inside a situation. Name the unknown, write what the sentence says about it, then solve.

The difficulty is almost never the arithmetic. It is turning a paragraph into a line of algebra, and the reliable way to do that is to write down what you are looking for before you read the numbers - not after.

Work-rate problems are the ones that catch people out. Two workers finishing a job in different times do not average; their rates add. Convert each to a rate per hour, add the rates, and invert.

Journey problems with a different speed each way behave the same way. The average speed is not the average of the two speeds, because you spend longer at the slower one.

Worked examples

Try these, then read why.

Written for this platform and generated from the same bank the practice sets draw on. Every wrong option is explained, because knowing why a distractor was tempting is most of the learning.

A cleaning crew can wash all the windows of the building in 5 days. Working at the same rate, what part of the job is finished after 3 days?

  1. A2/5
  2. B3/5 (correct)
  3. C3/8
  4. D5/3

A uniform rate means each day finishes the same share of the job: one day is 1/5 of it. After 3 days the crew has finished 3/5, which reduces to 3/5. Check the direction before dividing: the part done is always the smaller number over the larger one.

  • A This is the part of the job still to do, which is what is left rather than what is done.
  • C This compares the elapsed days with the total of both figures instead of with the length of the job.
  • D This divides the whole by the part. The part finished cannot be larger than the whole job.

Practise this properly.

Three examples show you the format. Finding out whether word problems is actually costing you marks takes a measured set, which is what the free diagnostic is for.

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