About Analogies
An analogy question gives one completed pair and the first half of a second pair. The two pairs are related in the same way, so the task is to name the relationship in the first pair and then apply it. The difficulty is that a single pair of numbers can often be explained by more than one rule, and only the simplest of those rules is intended.
What you need to understand
- Read the completed pair as a sentence: the second number is made from the first in one specific way.
- An exact power is the most striking relationship, so a square or a cube takes precedence over a multiplication that happens to produce the same number.
- A clean multiplication is preferred to a plain addition when both would work.
- The rule must be derived from the completed pair, never from the pair you are being asked to complete.
- Because several rules can fit one pair, the competing reading is usually planted among the wrong options.
How to work through these questions
- Write the completed pair and describe how the second number is built from the first.
- Test the relationships in order of simplicity: a square or cube, then a multiplication, then an addition.
- Confirm that the rule you have chosen reproduces the completed pair exactly.
- Apply that rule to the third term to get the answer.
- Before answering, ask whether a simpler rule also fits the completed pair. If one does, the simpler rule is the intended one.
Mistakes that cost marks
- Choosing a rule that fits the completed pair but is more complicated than another rule that also fits it.
- Applying the relationship in the wrong direction, so the answer is the number that the given term came from.
- Deriving the rule from the unfinished pair, which makes the question circular.
- Answering with the second number of the completed pair instead of computing a new value.
- Ignoring a rule that involves both a multiplication and an addition when none of the simpler rules fit.
Worked example
Complete the analogy: 5 : 25 :: 7 : ?
- Read the completed pair as a sentence: 25 is made from 5.
- Test the simplest relationships first. 25 is the square of 5, since 5 x 5 = 25.
- Check the competing reading: 25 is also 5 multiplied by 5, but a square is the simpler description of the same numbers.
- Apply the square rule to the third term: 7 x 7 = 49.
- The answer is 49, and the multiplication reading is planted as a wrong option.
Answer: 49
Practice questions with answers
A few Analogies questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
Complete the analogy: 4 : 16 :: 8 : ?
Answer: Option D — with explanation
The pair is related by one rule: the second number is the square of the first.
4 becomes 16, so 8 becomes 64.
Common mistakes
- subtracted the number from its square: 56
- doubled the square: 128
- added the number to its square: 72
Question 2
Complete the analogy: 5 : 125 :: 2 : ?
Answer: Option B — with explanation
The pair is related by one rule: the second number is the cube of the first.
5 becomes 125, so 2 becomes 8.
Common mistakes
- subtracted the number from its cube: 6
- squared the number instead of cubing it: 4
- added the number to its cube: 10
Question 3
Complete the analogy: 6 : 24 :: 4 : ?
Answer: Option C — with explanation
The second number is the first multiplied by 4: 6 x 4 = 24.
So 4 x 4 = 16.
Common mistakes
- added 4 instead of multiplying by it: 8
- multiplied by 5 instead of 4: 20
- left the second number unchanged: 4
Question 4
Choose the number that completes the analogy 28 : 48 :: 35 : ?
Answer: Option B — with explanation
Each pair differs by 20: 28 + 20 = 48.
So 35 + 20 = 55.
Common mistakes
- subtracted 20 instead of adding it: 15
- left the second number unchanged: 35
- added 20 twice: 75
Question 5
Choose the number that completes the analogy 8 : 72 :: 4 : ?
Answer: Option A — with explanation
The pair is related by one rule: the second number is the first multiplied by one more than itself.
8 becomes 72, so 4 becomes 20.
Common mistakes
- subtracted the number instead of adding it: 12
- squared the number but forgot to add it: 16
- added twice the number instead of once: 24
Frequently asked questions
What is an analogy question?
It gives a completed pair of values and the first value of a second pair. Both pairs follow the same relationship, so you identify the relationship in the completed pair and apply it to the unfinished one.
How do I know which relationship is intended?
Test the relationships in order of simplicity and stop at the first one that fits: a square or cube, then a multiplication, then an addition. An exact power is a more striking relationship than a multiplication that reaches the same number.
What if two rules fit the completed pair?
Use the simpler one. Questions are written so that the intended rule is the most natural reading, and the alternative is usually placed among the wrong options rather than being left as a genuine second answer.
Are letter analogies solved the same way?
Yes. Convert the letters to alphabet positions, identify the relationship between the first two, and apply it to the third. The same preference for the simplest fitting rule applies.
Why is a wrong option often close to the right answer?
Because the wrong options are the results of specific mistakes, such as using the competing rule, reversing the relationship, or stopping one step early. They are designed to catch a particular error rather than to be random.
