Verbal Reasoning › Number & logic puzzles
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.
- Letters for numbers — each letter is given a number, and you do a small sum, then give the answer back as a letter.
- Complete the sum — a calculation with one number missing; you work out the gap so both sides balance.
- Reading information — a few facts, then a question you answer by lining the facts up.
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.
- Write the key where you can see it. Each letter has its own number. Keep them in front of you.
- Swap the letters for their numbers. Replace each letter in the sum with its value, then work it out.
- Turn the answer back into a letter. Find which letter has that value. That letter is your answer.
- The trap: giving the number. The answer must be a letter, so always do the last step.
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.
- Swap the letters for numbers. C is 4 and A is 2, so the sum is 4 × 2.
- Do the maths. 4 × 2 = 8.
- Turn it back into a letter. Look down the key: which letter is 8? That is D.
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.
- Work out the finished side first. The side with no box can be totalled up straight away.
- That total is your target. The side with the box must come out to the very same number.
- Use the opposite operation to find the box. Adding undoes with taking away; multiplying undoes with dividing.
- Check by putting your number in. Both sides should now match exactly.
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?
7 × ? = 20 + 15
- Work out the finished side. The right side has no box: 20 + 15 = 35. That is the target.
- Look at the box side. It says 7 times something must equal 35.
- Use the opposite operation. Times undoes with divide: 35 ÷ 7 = 5. So the box is 5.
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.
- Read every fact before you answer. The last one often decides it.
- Line them up. For “taller”, “older” or “in front” facts, build one single order from biggest to smallest.
- Cross out what is ruled out. For “who has what” facts, knock out the impossible until one answer is left.
- Use only what you are told. Don’t add anything from outside the facts.
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.
Mia is in front of Ben. Priya is behind Ben.
Who is at the front?
- Start with the first fact. Mia is in front of Ben, so the order begins: Mia, then Ben.
- Add the next fact. Priya is behind Ben, so she goes last: Mia, Ben, Priya.
- Read off the answer. The person at the front of that line is 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.
Sara does not own the dog. Raj owns the cat.
Which pet does Sara own?
- Use the surest fact first. Raj owns the cat, so the cat is taken — Sara cannot have it.
- Use the next fact. Sara does not own the dog either.
- See what is left. Cat and dog are both ruled out for Sara, so the only pet left for her is the rabbit.
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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