Problem Questions

‘Problem questions’ are often the most difficult in 11+ and 13+ Maths papers.

There are several different kinds, but they all have one thing in common: they all ‘hide’ the sums that you have to do.

That means the first thing you have to do is work out the actual calculations you’re being asked for.

Here’s an example from a 10-11+ Bond book that I was going through today with one of my pupils:

What is the nearest number to 1000, but smaller than 1000, into which 38 will divide with no remainder?

He couldn’t answer it, so I told him something I always say in these situations. There are three ways of answering a question in Maths:

  1. Use a proper mathematical technique.
  2. Use trial and error.
  3. Guess!

Method 1

The first method is usually the most efficient and reliable. In this case, you need to do two calculations:

  1. 1000 ÷ 38 (ignoring any remainder)
  2. Multiply the answer by 38.

The first step should be done using long division and should give the answer 26.








The second should be done by long multiplication and give the answer 988.

Method 2

It’s all very well saying you have to use ‘proper’ Maths, but what if you don’t know how to do it? That’s when trial and error comes in handy.

Trial and error just means thinking of a number that you think is ‘about right’ and then adding or subtracting from it if the answer is too low or too high.

In this case, there’s no easy answer, but you might round up 38 to 40, and 40 goes into 1,000 25 times. However, that still leaves a difference of 25 lots of 2, which is 50, so the actual total is only 950. If you add on another 38, you get 988, which is the answer.

Method 3

If you’re doing a multiple choice paper, the worst mistake in the world is to leave an answer blank. It only takes a second to guess A, B, C, D or E, so it’s worth doing because you’ll always have a 20% chance of getting it right—and that beats zero!

The key is to make sure your guesses are at least possible. For example, if the question asks for a number between 1 and 10, don’t guess 12!

For this question, it isn’t easy to guess, but the answers to a lot of questions at 11+ or 13+ level can be narrowed down quite easily to a common fraction or a single-digit number.

As Sherlock Holmes once told Dr Watson, “Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth!”


  1. Mark is 11 and Julie is 9 years old. If they get £80 pocket money shared according to their ages, how much does each of them get?
  2. If a dress costs £240 after VAT at 20% is added on, what is the original price?
  3. Candy floss is on sale at £2 for three sticks at Stall A and £2.50 for five sticks at Stall B. Which stall is cheaper per stick?
  4. A garden measures 10 x 8 metres in total. There’s a lawn surrounded by a path 1 metre wide around the outside. What’s the area of the grass?
  5. If school starts at 9.15am and there are four 45-minute lessons in the morning followed by three lessons of 1 hour 15 minutes in the afternoon with an hour for lunch, what time do the children go home?

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