Verbal Reasoning
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Verbal Reasoning · Topic 5

Number & logic puzzles

These are the questions where you work something out one step at a time: swapping letters for numbers, filling the gap in a sum, and using a few facts to reason your way to the answer. No tricks needed — just steady working. Everything you need is on this page.

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These three question types all reward the same calm habit: read carefully, take it one step at a time, and check that your answer fits. None of them need a clever trick. They need neat working.

Two of them are really mental maths in a costume. The third is a small logic puzzle: a handful of facts that, once you line them up in the right order, point to a single answer.

Each one below starts with a short explanation and a worked example taken slowly, then lets you try it.

1. Letters for numbers

You are given a little key, where each letter stands for a number. You then work out a small sum and give your answer as the letter that matches — not the number. It looks unusual, but it is just two easy jobs: do the maths, then turn the answer back into a letter.

A little tip

Do the swap first, the maths second. Replace every letter with its number before you start calculating — trying to do both at once is where slips happen.

Worked example
A=2B=3C=4D=8E=12
Work out C × A and give the answer as a letter.
  1. Swap the letters for numbers. C is 4 and A is 2, so the sum is 4 × 2.
  2. Do the maths. 4 × 2 = 8.
  3. Turn it back into a letter. Look down the key: which letter is 8? That is D.
Answer: D.
1

Your go: letters for numbers

Use the key to swap the letters for their numbers, do the sum, then choose the letter that matches your answer.

2. Complete the sum

Here a calculation has one number missing, shown as a ? box. Often there is a sum on each side of the equals sign. The two sides have to balance — end up equal — so you work out the side you can first, then find the number that makes the other side reach it.

A little tip

An equals sign means “the same as”. Find the value of the complete side first, then ask: what does my side need so it reaches that number too?

Worked example
Find the missing number.
7 × ? = 20 + 15
  1. Work out the finished side. The right side has no box: 20 + 15 = 35. That is the target.
  2. Look at the box side. It says 7 times something must equal 35.
  3. Use the opposite operation. Times undoes with divide: 35 ÷ 7 = 5. So the box is 5.
Answer: 5  (check: 7 × 5 = 35, and 20 + 15 = 35).
2

Your go: complete the sum

Work out the side without the box first, then find the number that makes the box side balance with it.

3. Reading information

You are given a few short facts, then asked a question. The facts together point to one answer. The whole skill is lining the facts up — usually into an order, and sometimes by crossing out what cannot be true.

A little tip

A quick sketch beats holding it all in your head: a line for an order, or a small grid for who-has-what. Jot the facts down as you read them.

Worked example · putting things in order
Mia, Ben and Priya are standing in a queue.
Mia is in front of Ben. Priya is behind Ben.
Who is at the front?
  1. Start with the first fact. Mia is in front of Ben, so the order begins: Mia, then Ben.
  2. Add the next fact. Priya is behind Ben, so she goes last: Mia, Ben, Priya.
  3. Read off the answer. The person at the front of that line is Mia.
Answer: Mia.

Another kind: working by crossing out

Some facts are about who has what rather than an order. Here you work by elimination: use each fact to rule a possibility out, and keep going until only one option can be true.

Worked example · crossing out
Sara, Tom and Raj each own one pet: a cat, a dog or a rabbit.
Sara does not own the dog. Raj owns the cat.
Which pet does Sara own?
  1. Use the surest fact first. Raj owns the cat, so the cat is taken — Sara cannot have it.
  2. Use the next fact. Sara does not own the dog either.
  3. See what is left. Cat and dog are both ruled out for Sara, so the only pet left for her is the rabbit.
Answer: the rabbit.
3

Your go: reading information

Read the facts, line them up (or cross out what cannot be true), then choose the answer they point to.

That is number & logic puzzles

Letters for numbers, completing the sum and reading information, all cracked. When you are ready, head back and pick another topic.

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