Input Output: Reasoning Concepts
Input-Output questions test your ability to identify a pattern or rule from a series of rearrangements. You are given a set of words, numbers, or both in an initial arrangement, followed by the output produced after one or more steps.
The key skill is simple: observe what changes from one step to the next and identify the rule.
How Input-Output Works
An Input-Output question generally looks like this:
Input:
48 17 63 25 91 36
Step I:
17 48 63 25 91 36
Step II:
17 25 48 63 91 36
Step III:
17 25 36 48 63 91
Here, the machine is arranging the numbers in ascending order, one number at a time.
Each line represents one step of the machine.
The actual question may ask you to:
- Find the next step
- Find a particular step
- Identify the position of an element
- Determine which step contains a given arrangement
- Identify the underlying rule
The Most Important Idea: Find the Pattern
Do not try to understand the entire output at once.
Instead, compare Input → Step I, then Step I → Step II, and so on.
Look for:
- Which element moved?
- Where did it move?
- Which elements remained unchanged?
- Is the machine processing numbers from left to right or right to left?
- Are elements being arranged according to size, alphabetical order, or some other property?
Once you understand what happens in the first step, the remaining steps usually become predictable.
Common Input-Output Patterns
1. Ascending Order
Numbers are arranged from smallest to largest.
For example:
42 15 63 27 8
may gradually become:
8 15 27 42 63
The machine may place the smallest number in its correct position during each step.
2. Descending Order
Numbers are arranged from largest to smallest.
For example:
18 72 35 91 46
may ultimately become:
91 72 46 35 18
3. Alphabetical Arrangement
Words may be arranged alphabetically.
For example:
MANGO APPLE GRAPE BANANA
can become:
APPLE BANANA GRAPE MANGO
The machine may place one word in its correct position at each step.
4. Arrangement According to Number Properties
Sometimes the machine does not simply sort numbers.
It may arrange them according to:
- Number of digits
- Sum of digits
- Product of digits
- Even and odd numbers
- Prime and composite numbers
- Increasing or decreasing digit values
- Value of a particular digit
For example, numbers may be arranged according to the sum of their digits.
41 → 5
72 → 9
53 → 8
So the ordering may be based on 5, 9 and 8 rather than the actual numbers.
5. Words and Numbers Combined
A common bank-exam pattern contains both words and numbers.
For example:
28 CAT 73 DOG 15 APPLE 46
The machine may simultaneously:
- Arrange numbers in ascending order
- Arrange words alphabetically
- Move one number and one word during each step
The important point is to check whether two separate operations are taking place simultaneously.
The “One Element Per Step” Rule
Many questions use a machine that fixes one element in every step.
Suppose:
Input:
42 17 65 29 81
Step I:
17 42 65 29 81
Step II:
17 29 42 65 81
Notice that the smallest remaining number is being placed into its correct position.
Once a position has been fixed, it generally does not change in later steps.
Shortcut: Look for the element that becomes permanently fixed after each step.
How to Solve Input-Output Questions
Step 1: Compare Input and Step I
Ignore everything that remains unchanged.
Focus only on the element(s) that moved.
Step 2: Identify the Operation
Ask:
What determined the element that moved?
Was it:
- Smallest/largest?
- Alphabetically first/last?
- Even/odd?
- Digit sum?
- Some other numerical property?
Step 3: Check Step II
Do not assume your rule is correct after looking at only one step.
Verify it against the next step.
Step 4: Extend the Pattern
Once the rule is confirmed, apply it to the remaining elements.
Step 5: Answer the Question
You usually do not need to construct every step if the question asks only about a particular position or element.
Position Tracking Shortcut
A useful way to solve Input-Output questions quickly is to track fixed positions rather than rearranging the entire sequence.
For example:
Input:
54 21 73 16 42
If the machine places the smallest remaining number at the beginning in every step:
- Step I → 16 is fixed
- Step II → 21 is fixed
- Step III → 42 is fixed
Therefore, you can determine later arrangements without repeatedly rewriting the entire sequence.
Important Observations
Fixed Elements
If the first few elements remain unchanged in subsequent steps, they have probably already been processed.
Moving Elements
If one element repeatedly moves toward the left or right, the machine is likely placing elements in a particular order.
Direction
The machine may process:
- Left → Right
- Right → Left
- Alternate positions
- Both ends simultaneously
Multiple Operations
Some difficult questions combine two rules, such as:
Smallest number → left
Alphabetically last word → right
So always check whether more than one element changes in a step.
Input-Output Questions: Quick Strategy
Before solving, ask these 5 questions:
- What changed? Identify the elements that moved.
- What was selected? Smallest, largest, first alphabetically, etc.
- Where was it placed? Beginning, end, or a specific position?
- Is the same rule repeated? Verify using at least two steps.
- Can I answer without constructing every step? Often, you can.
Common Mistake
The biggest mistake in Input-Output questions is trying to guess the final arrangement immediately.
The machine does not necessarily sort everything in one go. It may process the input step by step, and understanding how an element is selected and moved is more important than knowing the final arrangement.
Remember
Input-Output = Observe → Identify the rule → Verify → Apply
Once the machine’s rule is identified, the question becomes largely mechanical.