Concept 2 of 5
Numeric Analogy: Find the Operation
Today's big idea
Find the operation turning A into B, then run it on C.
One operation turns the first number into the second; apply it to finish the pair.
How it works
👀 What's going on?
The same A is to B as C is to what, except now the terms are numbers. The hidden link is an operation, and your job is to work out which one.
💡 Here's the trick
Look at the pair above. 5 becomes 25, and 25 is 5 x 5, so the rule is squaring. Apply it to 6 and you reach 36. The catch is that more than one rule can fit a single pair, so check yours against everything else the question gives you.
🪄 How to do it
- 1.Work out what turns A into B, as the picture above spots squaring.
- 2.Check that rule against any other pair the question shows you.
- 3.Apply the surviving rule to C.
✍️ Try it
12 : 4 :: 18 : ? Then 7 : 14 :: 9 : ? Work out the rule for each of them.
12 becomes 4 by dividing by 3, so 18 gives 6. 7 becomes 14 by doubling, so 9 gives 18. Both were single operations, but different ones, so a rule never carries from one question to the next.
⚠️ Watch out
You might be thinking 5 to 25 has to mean squaring. It could equally mean multiply by 5. Both fit that pair, and only a second pair tells you which is meant. Where a question shows just one pair, take the simpler rule.
🌟 Why this matters
Noticing that one amount is always double another, or always three less, is how people read prices, recipes and timetables quickly. The operation is the pattern.
Exam tip: When two rules both fit, try each on the options, because usually only one of them is listed.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“8 : 64 :: 9 : ?”
- 1
Spot the rule
8² = 64.
- 2
Apply
9² = 81.
- 3
Answer ✓
81
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
A is to B as C is to ? — tap a rule to test it on 4. The right rule turns 4 into 12.
NUMERIC ANALOGY · ROUND 1 OF 3
Quick check
✅ VERIFICATION
9 : 3 :: 25 : ?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Shape Analogy
Family, sides, 2D→3D, find the link, complete the pair.