CAT4 Quantitative Reasoning: Free Practice Test & Tips to Help You Master This Section
Welcome to your complete practice guide for the CAT4 Quantitative Reasoning battery, one of the four batteries of the test.
On this page, you’ll find:
- Lifelike CAT4 Quantitative practice questions with full explanations
- Common mistakes to avoid
- Solving tips to help you answer questions quickly and accurately
Let’s dive right in!
This page was created by Roman, a CAT4 test prep specialist.
Have a question about the test or our practice materials? Email me at roman@prepopedia.com - I'm here to help your child succeed!
What Questions to Expect on the CAT4 Quantitative Reasoning Battery?
The CAT4 Quantitative Reasoning battery consists of two sub-sections that measure your mathematical reasoning: Number Analogies and Number Series.
You do not need to memorize any math formulas, as the questions focus on logic and pattern-spotting.
Number Analogies
Number of questions: 18, each with 5 answer choices
Time limit: 10 minutes
Instructions: Each question starts with two numbers that are linked together in some way. Next, there are two more numbers that are linked in exactly the same way. You have to work out how the numbers are linked and complete the third pair.
Number Analogies Solving Tips
For lower test levels, such as CAT4 Level A and B, the connection between the pair of numbers is straightforward.
They include a 1-step calculation of one of these: addition, subtraction, multiplication, or division.
For example:
[21 → 9] [44 → 32] [70 → ?]
We get from 21 to 9 by subtracting 12 (the pattern is -12).
Likewise, we get from 44 to 32 by using the same pattern (rule) -12.
The next series of numbers should follow the same pattern, meaning that the rule between 70 and ? should be -12 as well: 70 – 12 = 58, meaning that the correct answer will be 58.
However, if your child takes higher CAT4 test levels, these questions become harder.
For higher levels, some of the number analogies questions involve 2-step calculations between pairs, and may even include squaring or taking square roots.
Let’s see an example for a 2-step connection between the pair of numbers:
[12→ 7] [30 → 10] [54 → ?]
Look for the pattern in the first series of numbers.
Note that we cannot just subtract 5 from 12, since the pattern (-5) does not apply to the second pair.
So in this case, we must assume it’s a 2-step calculation.
Since the right number is smaller than the left number, we will first divide the left number.
We get from 12 to 7 by dividing by 6 and then adding 5 [÷6 + 5]. Indeed, 12 ÷ 6 = 2 + 5 = 7.
Likewise, we get from 30 to 10 by dividing by 6 and then adding 5 [÷6 + 5]. Indeed, 30 ÷ 6 = 5 + 5 = 10.
The next two numbers should follow the same pattern, meaning that the rule between 54 and ? should be [÷6 + 5] as well: 54 ÷ 6 = 9 + 5 = 14, meaning that the correct answer will be 14.
Number Series
Number of questions: 18, each with 5 answer choices
Time limit: 8 minutes
Instructions: Each question shows a series of numbers. You have to work out the rule or rules used to arrange the order of the numbers and decide which number comes next.
Number Series Solving Tips
Similarly to the Number Analogy questions, the difficulty level of these questions increases as the CAT4 test level rises.
So, for lower test levels, the rule or rules between the numbers are straightforward, and they become more and more challenging at higher test levels.
Let’s start with an easier example:
3.2 5.2 7.2 9.2 11.2 13.2 ?
In this series, every number is larger than the previous number by 2.0 (or 2).
The pattern is: +2, +2, +2, …
So the last number is this series is:
13.2 + 2 = 15.2
Now, let’s see a more challenging example that aligns with higher test levels:
2 10 5 6 30 15 16 ?
In this series, the pattern is as follows: first, multiply by 5, then divide by 2, and add 1; then multiply by 5 again, then divide by 2, and add 1, and so on.
The pattern is: x5, ÷2, +1 | x5, ÷2, +1, …
The last two numbers in the series are 15 and 16.
15 is smaller than 16 by 1, so the following number should be 16 multiplied by 5.
16 x 5 = 80.
How to Get Better at Solving These Questions?
The only way to improve your accuracy and speed with these questions is to solve as many practice questions as possible.
The more you practice, the better you become at recognizing the patterns between the numbers, as these rules or patterns tend to repeat themselves.
Many parents mention that Number Analogies and Number Series are two of the most challenging sections for their children. So, if your child struggles with these questions, we recommend giving them extra focus in your practice sessions.
CAT4 Quantitative Reasoning Practice Test (Including PDF)
The following math practice questions are in various difficulty levels and highly resemble actual exam questions. Each question is followed by a detailed explanation to help you learn and improve.
CAT4 Number Analogies Practice Questions
Question 1
[ 7 → 3 ] [ 17 → 8 ] [ 13 → ? ]
Show Correct Answer & Explanation
The correct answer is C. 6.
We need one rule that works for both examples.
Look at the first pair:
7 → 3
Try this:
Step 1: subtract 1 → 7 – 1 = 6
Step 2: divide by 2 → 6 ÷ 2 = 3
That works.
Now test the same rule on the second pair:
17 → 8
Step 1: subtract 1 → 17 – 1 = 16
Step 2: divide by 2 → 16 ÷ 2 = 8
That also works.
Now do the same for:
13 → ?
Step 1: subtract 1 → 13 – 1 = 12
Step 2: divide by 2 → 12 ÷ 2 = 6
So the missing number is 6.
Quick Tip for Students 💡
In number analogies, if one-step ideas do not seem exact, try a 2-step pattern like:
- add, then divide
- subtract, then divide
- multiply, then add
- divide, then subtract
Question 2
[ 6 → 35 ] [ 3 → 17 ] [ 8 → ? ]
Show Correct Answer & Explanation
The correct answer is D. 47.
We need to find the same rule for both examples.
Start with the first pair:
6 → 35
What can we do to 6 to get 35?
Try a 2-step rule:
Step 1: multiply by 6 → 6 × 6 = 36
Step 2: subtract 1 → 36 – 1 = 35
That works.
Now test it on the second pair:
3 → 17
Step 1: multiply by 6 → 3 × 6 = 18
Step 2: subtract 1 → 18 – 1 = 17
That works too.
Now use the same rule for:
8 → ?
Step 1: multiply by 6 → 8 × 6 = 48
Step 2: subtract 1 → 48 – 1 = 47
So the missing number is 47.
Quick Tip for Students 💡
In number analogies, when the answer gets much bigger, try:
- multiplying first
- then adding or subtracting a small number
Question 3
[ 21 → 7 ] [ 3 → 1 ] [ 24 → ? ]
Show Correct Answer & Explanation
The correct answer is B. 8.
We need to find the rule that changes the number on the left into the number on the right.
Look at the first pair:
21 → 7
How do we get from 21 to 7?
21 ÷ 3 = 7
Now test that on the second pair:
3 → 1
3 ÷ 3 = 1
That works again.
Now use the same rule for the last pair:
24 → ?
24 ÷ 3 = 8
So the missing number is 8.
Quick Tip for Students 💡
When the number on the right is smaller, first check simple subtraction or division rules like:
- divide by 2
- divide by 3
- divide by 4
Question 4
[ 20 → 8 ] [ 12 → 4 ] [ 10 → ? ]
Show Correct Answer & Explanation
The correct answer is D. 3.
We need to find the same rule in both example pairs.
Start with the first pair:
20 → 8
Try a 2-step rule:
Step 1: divide by 2 → 20 ÷ 2 = 10
Step 2: subtract 2 → 10 – 2 = 8
That works.
Now test the same rule on the second pair:
12 → 4
Step 1: divide by 2 → 12 ÷ 2 = 6
Step 2: subtract 2 → 6 – 2 = 4
That works too.
Now use the same rule for:
10 → ?
Step 1: divide by 2 → 10 ÷ 2 = 5
Step 2: subtract 2 → 5 – 2 = 3
So the missing number is 3.
Quick Tip for Students 💡
When the answer gets smaller, do not only test one-step rules, like just subtracting.
Also, try 2-step rules such as:
- divide, then subtract
- subtract, then divide
- divide, then add
Question 5
[ 6 → 10 ] [ 12 → 20 ] [ 9 → ? ]
Show Correct Answer & Explanation
The correct answer is B. 15.
This question is more challenging because the pattern is not obvious right away.
The number on the right is bigger than the number on the left, but it is not:
- just adding the same amount
- just doubling
- just multiplying by a whole number
So we should test the rule carefully.
Start by Looking for a Rule That Works for Both Examples
We have:
6 → 10
12 → 20
A good strategy is to ask:
- Did the number get bigger by adding?
- Did it get bigger by multiplying?
- Could it be a 2-step rule?
Compare the two pairs more closely:
- 6 becomes 10
- 12 becomes 20
Notice something helpful:
Both 6 and 12 can be divided by 3.
Try that:
6 ÷ 3 = 2
12 ÷ 3 = 4
Now see if those results can turn into 10 and 20.
2 × 5 = 10
4 × 5 = 20
It works.
So the rule is:
Step 1: divide by 3
Step 2: multiply by 5
Apply the Same Rule to 9
9 → ?
Use the same two steps:
Step 1: 9 ÷ 3 = 3
Step 2: 3 × 5 = 15
So: 9 → 15
The correct answer is B. 15.
Quick Tip for Students 💡
When a number analogy looks difficult, try this order:
Step A: Check simple rules
- add
- subtract
- multiply
- divide
Step B: If those do not work, try 2-step rules
- divide, then multiply
- multiply, then add
- divide, then add
- subtract, then divide
Step C: Always test your rule on both example pairs
A rule is only correct if it works for:
- the first example
- the second example
- the missing number
Question 6
[ 10 → 22 ] [ 8 → 18 ] [ 4 → ? ]
Show Correct Answer & Explanation
The correct answer is E. 10.
We need to find one rule that works for both example pairs.
Let’s start with:
10 → 22
A good first thought is: the answer is bigger, so maybe we:
- multiply
- then add a small number
Try this:
Step 1: multiply by 2 → 10 × 2 = 20
Step 2: add 2 → 20 + 2 = 22
That works.
Now test the same rule on the second pair:
8 → 18
Step 1: multiply by 2 → 8 × 2 = 16
Step 2: add 2 → 16 + 2 = 18
That works too.
Now use the same rule for:
4 → ?
Step 1: multiply by 2 → 4 × 2 = 8
Step 2: add 2 → 8 + 2 = 10
So the missing number is 10.
Quick Tip for Students 💡
When the number on the right is larger, use this order:
1. Check simple addition first
Ask:
Did it just go up by the same amount each time?
In the question above:
10 → 22 is +12
8 → 18 is +10
So that does not match.
2. Then check multiply-based rules
Ask:
- Did the number double?
- Did it triple?
- Was there a multiply step plus a small add or subtract step?
In the question above:
10 × 2 = 20, then +2 = 22
8 × 2 = 16, then +2 = 18
That gives a clear pattern.
3. Always test your rule on both examples
A rule is only reliable if it works for the first pair, the second pair, and the missing number.
4. Prefer the simplest rule that fits all pairs
The best answer is usually based on the most direct rule, not a complicated one.
CAT4 Number Series Practice Questions
Question 7
1, 5, 7, 7, 5, ?
Show Correct Answer & Explanation
The correct answer is B. 1.
We need to find the pattern in this number series:
1, 5, 7, 7, 5, ?
A very helpful thing to notice is that the numbers seem to go up, then stay the same, then go down.
Let’s look at them carefully:
- 1 to 5 = +4
- 5 to 7 = +2
- 7 to 7 = 0
- 7 to 5 = -2
What should come next?
The changes are:
+4, +2, 0, -2
This pattern is going down by 2 each time.
So next should be -4
Now apply that:
5 – 4 = 1
So the missing number is 1.
Another Way to See It:
You can also notice that the series is symmetrical:
1, 5, 7, 7, 5, 1
It reads the same from both ends:
first and last = 1
second and second-last = 5
third and fourth = 7
That also shows that the missing number should be 1.
Quick Tip for Students 💡
When a number series does not follow one simple rule, try these steps:
- Look at how much the number changes each time
- Check whether the jumps are getting bigger or smaller
- See whether the pattern is symmetrical
Question 8
54, 108, 18, 36, 6, 12, ?
Show Correct Answer & Explanation
The correct answer is A. 2.
At first, this series looks messy, because the numbers go up, down, up, down again.
That usually means the pattern is alternating between two different steps.
Let’s check:
- 54 → 108 = multiply by 2
- 108 → 18 = divide by 6
- 18 → 36 = multiply by 2
- 36 → 6 = divide by 6
- 6 → 12 = multiply by 2
Now the pattern is clear:
×2, ÷6, ×2, ÷6, ×2, …
So the next step should be:
12 ÷ 6 = 2
So the missing number is 2.
Quick Tip for Students 💡
When a series keeps going up and down, try this method:
1. Check whether the pattern alternates
Ask:
- Does one step do one thing, and the next step do something different?
- Does it repeat in pairs?
2. Test multiplication and division, not only addition and subtraction
Some number series are not based on “how much more” or “how much less.”
They are based on:
- multiplying
- dividing
- alternating between the two
3. Look for a repeating cycle
Once you find the cycle, continue it.
4. Always check several steps, not just one
A good pattern should explain:
- the first jump
- the second jump
- the third jump
- and the missing number
That helps you avoid choosing a rule that works only once by accident.
Question 9
2, 3, 5, 8, 13, 21, ?
Show Correct Answer & Explanation
The correct answer is C. 34.
This is a famous type of growing pattern.
Look at the series:
2, 3, 5, 8, 13, 21
Check what happens each time:
- 2 + 3 = 5
- 3 + 5 = 8
- 5 + 8 = 13
- 8 + 13 = 21
So each new number is made by adding the previous two numbers.
Now do the same for the next term:
13 + 21 = 34
So the missing number is 34.
Quick Tip for Students 💡
When a series keeps growing, but not by a fixed amount or alternative pattern, try this:
1. Check whether each term is made from earlier terms
- Is the next number the sum of the last two?
- Is it the difference of the last two?
- Is it made by multiplying earlier numbers?
2. Test the same rule several times
Once the same rule works again and again, you can trust it.
3. Do not stop after spotting only one step
A good pattern should explain the whole series, not just one part of it.
4. Watch for well-known patterns
The question above is like a Fibonacci-style pattern, where each term comes from the two before it.
Question 10
3, 7, 8, 12, 13, ?
Show Correct Answer & Explanation
The correct answer is D. 17.
We need to find the pattern in:
3, 7, 8, 12, 13, ?
A very good first step is to check how much the number changes each time:
- 3 → 7 = +4
- 7 → 8 = +1
- 8 → 12 = +4
- 12 → 13 = +1
Now the pattern is clear:
+4, +1, +4, +1
So the next step should be:
+4
Now apply that:
13 + 4 = 17
So the missing number is 17.
Question 11
4, 12, 24, 3, 9, 18, 2, ?
Show Correct Answer & Explanation
The correct answer is C. 6.
This series looks confusing if you try to solve it as one long line.
A better strategy is to check whether it can be split into small repeating groups.
Look at the numbers like this:
- 4, 12, 24
- 3, 9, 18
- 2, ?
Now study what happens inside each group.
First group:
4 → 12 → 24
4 × 3 = 12
12 × 2 = 24
Second group:
3 → 9 → 18
3 × 3 = 9
9 × 2 = 18
So the pattern inside each group is:
multiply by 3, then multiply by 2
Now apply that same rule to the third group:
2 → ?
2 × 3 = 6
So the missing number is 6.
Quick Tip for Students 💡
When a series suddenly seems to “break” or restart, try this method:
1. Check whether the numbers can be split into groups
Look for:
- pairs
- groups of 3
- repeated blocks
Here, the natural grouping is:
2. Look for the same mini-pattern inside each group
Ask:
- Is each group using the same operations?
- Does the same structure repeat?
4. Do not force one rule across the whole row
Some questions can be tricky, as your first instinct is to look for one continuous rule.
When that does not work, try grouping.
Question 12
2111, 2112, 2122, 2222, ?
Show Correct Answer & Explanation
The correct answer is E. 3222.
This series is made of 4-digit numbers, but the pattern is not about adding or subtracting in the usual way.
A better strategy is to look at which digit changes each time.
We have:
- 2111
- 2112
- 2122
- 2222
Let’s compare them one step at a time.
From 2111 to 2112
Only the last digit changes:
2111 → 2112
From 2112 to 2122
Now the third digit changes:
2112 → 2122
From 2122 to 2222
Now the second digit changes:
2122 → 2222
So each time, one more 1 turns into a 2, moving from right to left.
Now, all the digits except the first one have already changed to 2.
So the next step should change the first digit.
But this time, the first digit is already 2, so it increases to the next number:
2 → 3
That gives:
3222
So the correct answer is E. 3222.
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