Logical Reasoning · Series & Analogies
Number Series — Questions & Answers
Number series questions give a sequence of numbers built on a hidden rule and ask for the next or missing term. The rule may be a constant difference or ratio, squares and cubes, primes, or two series alternating.
- 5 solved questions
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How to approach
Subtract each term from the next. If the gap is the same every time, keep adding (or subtracting) that same amount. Decimal steps work exactly like whole-number steps: line up the decimal points and add the same decimal each time.
If the gaps keep growing or shrinking fast, divide each term by the one before it. A constant ratio means every term is multiplied (or divided) by the same number. Fractions follow the same rule: halving 1/4 gives 1/8.
When the gaps go up and down, look at every other gap. Two operations are applied in turn (for example add 5, then subtract 3). Work out which operation comes next from the position, then apply only that one.
If a number appears twice in a row, the series may repeat each term before moving on. If a number keeps coming back at every other position, the series is two separate series woven together: split the odd positions from the even positions and continue whichever series comes next.
5 solved Number Series questions
What is the next number in the series 13, 20, 27, 34, 41, ...?
Solution — answer C
The series adds 7 each time: 41 + 7 = 48.
4 steps · reveal one at a timeStep 1: Examine the Series
Look at the given numbers: 13,20,27,34,41,…. We need to find the pattern to predict the next number in this sequence.
Step 2: Find the Pattern
Let's calculate the difference between consecutive numbers to identify the rule. We see: 20−13=7, 27−20=7, 34−27=7, and 41−34=7.
Step 3: Apply the Rule
The pattern is consistent: each number in the series is obtained by adding 7 to the previous number. To find the next number, we must apply this rule to the last given number.
Step 4: The answer
So the answer is (C) 48. We add 7 to the last number in the series: 41+7=48.
Find the missing number in the series: 8, 15, __, 29, 36
Solution — answer A
The series adds 7 each time: 15 + 7 = 22, and 22 + 7 = 29 checks out.
4 steps · reveal one at a timeStep 1: Analyze the series
Let's look at the given numbers: 8, 15, __, 29, 36. We need to find the relationship between consecutive numbers to discover the pattern.
Step 2: Find the rule
Calculate the difference between the first two numbers: 15−8=7. This suggests that the series might be adding 7 each time.
Step 3: Calculate missing number
If the rule is to add 7 to each preceding number, then the missing number should be 15+7. This calculation gives us 22.
Step 4: The answer
So the answer is (A) 22. We can verify this by checking the next numbers: 22+7=29, and 29+7=36, which matches the given series.
In the series 10, 16, 13, 20, 16, 22, 19, one number does not follow the pattern. Which number is wrong?
Solution — answer D
The rule is add 6, then subtract 3: 10, 16, 13, 19, 16, 22, 19. The fourth term should be 19, not 20.
5 steps · reveal one at a timeStep 1: Analyze the series
We need to find the number that breaks the pattern in the given series: 10,16,13,20,16,22,19. Let's look for a consistent rule between consecutive numbers.
Step 2: Find the rule
Let's examine the first few terms. From 10 to 16 is an increase of 6 (10+6=16). From 16 to 13 is a decrease of 3 (16−3=13). This suggests a pattern of add 6, then subtract 3.
Step 3: Test the pattern
Let's apply this rule to the rest of the series. We have 10+6=16 (correct) and 16−3=13 (correct). Following the rule, the next number should be 13+6=19. However, the series shows 20.
Step 4: Confirm the error
If the fourth term were 19 instead of 20, the pattern would continue: 19−3=16 (correct), then 16+6=22 (correct), and 22−3=19 (correct). Thus, 20 is the incorrect number.
Step 5: The answer
So the answer is (D) 20. The number 20 does not follow the 'add 6, then subtract 3' pattern, as it should be 19.
What are the next two numbers in the series 6, 13, 20, 27, 34, ...?
Solution — answer D
The series adds 7 each time: 34 + 7 = 41, then 41 + 7 = 48.
5 steps · reveal one at a timeStep 1: Find the pattern
Let's examine the given series: 6,13,20,27,34. We need to find a consistent rule or pattern that connects these numbers.
Step 2: Calculate differences
Let's find the difference between consecutive numbers. 13−6=7. 20−13=7. 27−20=7. 34−27=7. The pattern is to add 7 each time.
Step 3: First missing number
Since the pattern is to add 7 to the previous number, the first missing number will be 34+7=41. This extends our series to 6,13,20,27,34,41,...
Step 4: Second missing number
To find the second missing number, we apply the same rule to 41. So, 41+7=48. The series continues as 6,13,20,27,34,41,48,...
Step 5: The answer
So the answer is (D) 41, 48, because the pattern is to add 7 to each number in the series to get the next term.
Which rule produces the series 4, 12, 36, 108?
Solution — answer A
Multiply by 3 each time: 4 × 3 = 12, 12 × 3 = 36, 36 × 3 = 108. Adding 8 fits only the first step.
5 steps · reveal one at a timeStep 1: Examine the series
Let's look at the numbers in the series: 4, 12, 36, 108. We need to find a consistent rule that transforms each number into the next one.
Step 2: Check for addition
First, let's see if a constant number is being added. The difference between the first two numbers is 12−4=8. However, the difference between the second and third is 36−12=24. This shows it's not a simple addition rule.
Step 3: Check for multiplication
Now, let's check for a multiplication rule. If we divide the second number by the first, we get 12÷4=3. Let's see if this pattern continues for the rest of the series.
Step 4: Confirm the rule
Applying the multiplication by 3: 4×3=12. Then, 12×3=36. And finally, 36×3=108. This rule works perfectly for every step in the series.
Step 5: The answer
So the answer is (A) Multiply by 3 each time, because multiplying each number by 3 consistently produces the next number in the sequence.
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