Logical Reasoning · Codes, Relations & Directions
Input-Output — Questions & Answers
Input-output questions show a machine rearranging words or numbers step by step. Work out the rule from the given steps, then apply it to a new input.
- 5 solved questions
- Step-by-step AI walkthroughs
- How-to-approach tips
How to approach
Compare the example's input with Step I to see what moved. In ordering machines, one word (alphabetical) or one number (largest or smallest) is moved into place per step, and the rest keep their order.
Track words and numbers separately: here words fill in from the left in alphabetical order, while numbers fill in from the right, largest first.
Find which numbers changed between steps (here the outermost pair first, then the next pair in) and what was done to them: rounding down, adding digits or reversing digits.
The words don't change, only their places. Work out where each position's word comes from in the next step, then apply the same shift to the new input.
5 solved Input-Output questions
A word-arrangement machine rearranges its input step by step. Here is an example:
Input: rose lily jasmine tulip daisy lotus
Step I: daisy rose lily jasmine tulip lotus
Step II: daisy jasmine rose lily tulip lotus
Step III: daisy jasmine lily rose tulip lotus
Step IV: daisy jasmine lily lotus rose tulip
The machine follows the same rule for every input.
Input: mango apple peach cherry banana grape
What is Step III for this input?Solution — answer C
Each step moves the next word in alphabetical order into place from the left. Working it through: Step I: apple mango peach cherry banana grape; Step II: apple banana mango peach cherry grape; Step III: apple banana cherry mango peach grape.
5 steps · reveal one at a timeStep 1: Understand the Rule
Let's analyze the example to find the machine's rule. Compare the Input: "rose lily jasmine tulip daisy lotus" with Step I: "daisy rose lily jasmine tulip lotus". 'daisy' is the first word alphabetically and it moved to the front. The other words shifted right.
Step 2: Continue Analysis
From Step I to Step II, 'jasmine' (the next alphabetically smallest word from the remaining list) moved to the second position. The rule is: each step moves the next word in alphabetical order into its correct place from the left.
Step 3: Apply to New Input
Our input is: "mango apple peach cherry banana grape". First, find the alphabetically smallest word: 'apple'. Step I: apple mango peach cherry banana grape
Step 4: Find Step II and III
Next, find the alphabetically smallest word from the remaining: 'banana'. Step II: apple banana mango peach cherry grape\nThen, find the alphabetically smallest word from the remaining: 'cherry'. Step III: apple banana cherry mango peach grape
Step 5: The answer
So the answer is (C) apple banana cherry mango peach grape. This is Step III, with 'apple', 'banana', and 'cherry' placed in alphabetical order from the left.
A word-and-number machine rearranges its input step by step. Here is an example:
Input: 78 12 sun 45 bird apple 30 gate
Step I: apple 12 sun 45 bird 30 gate 78
Step II: apple bird 12 sun 30 gate 45 78
Step III: apple bird gate 12 sun 30 45 78
Step IV: apple bird gate sun 12 30 45 78
The machine follows the same rule for every input.
Input: 64 pen 19 kite 83 drum 41 lamp
What is Step II for this input?Solution — answer D
Each step moves the next word in alphabetical order into place from the left, and the next largest number into place from the right. Working it through: Step I: drum 64 pen 19 kite 41 lamp 83; Step II: drum kite pen 19 41 lamp 64 83.
5 steps · reveal one at a timeStep 1: Understand the machine's rules
Let's carefully examine the example to find the pattern. Compare the Input to Step I: 'apple' (the first word alphabetically) moved to the front, and '78' (the largest number) moved to the end. The other items shifted.
Step 2: Identify the full pattern
From Step I to Step II: 'bird' (the next word alphabetically) moved to the second position, and '45' (the next largest number) moved to the second-to-last position. This pattern continues: each step moves the next alphabetical word to the left and the next largest number to the right.
Step 3: Apply rules for Step I
Our input is: 64 pen 19 kite 83 drum 41 lamp. The words are: pen, kite, drum, lamp. Alphabetical order: drum, kite, lamp, pen. The numbers are: 64, 19, 83, 41. Largest to smallest: 83, 64, 41, 19. For Step I, move 'drum' to the front and '83' to the end. Remaining: 64 pen 19 kite 41 lamp. So, Step I: drum 64 pen 19 kite 41 lamp 83.
Step 4: Apply rules for Step II
Now, from Step I (drum 64 pen 19 kite 41 lamp 83), we need Step II. The next word alphabetically is 'kite'. The next largest number is '64'. Move 'kite' to the second word position and '64' to the second number position from the right. This gives: drum kite pen 19 41 lamp 64 83.
Step 5: The answer
So the answer is (D) drum kite pen 19 41 lamp 64 83. This matches our calculated Step II by moving the next alphabetical word and next largest number into place.
A number machine rearranges its input step by step. Here is an example:
Input: 47 18 65 32 91 54
Step I: 40 18 65 32 91 50
Step II: 40 10 65 32 90 50
Step III: 40 10 60 30 90 50
The machine follows the same rule for every input.
Input: 38 72 15 64 27 83
What is Step II for this input?Solution — answer E
Each step removes the units digit (rounds down to the ten) of the next pair of numbers, working in from both ends. Working it through: Step I: 30 72 15 64 27 80; Step II: 30 70 15 64 20 80.
5 steps · reveal one at a timeStep 1: Understand the Rule
Let's analyze the example to find the pattern. The machine modifies numbers by removing their units digit (rounding down to the nearest ten). It works on a pair of numbers in each step, moving inwards from both ends.
Step 2: Apply Step I
For the input 38 72 15 64 27 83, Step I modifies the first and last numbers. Remove the units digit from 38 to get 30, and from 83 to get 80. The other numbers stay the same.
Step 3: Calculate Step I Result
So, Step I for the input 38 72 15 64 27 83 will be 30 72 15 64 27 80. This is our starting point for Step II.
Step 4: Apply Step II
Now, for Step II, we apply the rule to the next pair of numbers inwards from the ends of the Step I result. These are the second number (72) and the second-to-last number (27). Remove their units digits.
Step 5: The answer
Removing the units digit from 72 gives 70, and from 27 gives 20. The numbers 30,15,64,80 remain unchanged. So the answer is (E) 30 70 15 64 20 80, as it correctly applies the rule to the second pair of numbers.
A sentence machine rearranges its input step by step. Here is an example:
Input: we will meet at the park
Step I: meet we will park at the
Step II: will meet we the park at
The machine follows the same rule for every input.
Input: birds sing early in the morning
What is Step II for this input?Solution — answer A
In each half of the sentence (the first three words and the last three), the last word moves to the front at every step. Working it through: Step I: early birds sing morning in the; Step II: sing early birds the morning in.
5 steps · reveal one at a timeStep 1: Understand the Machine
The question describes a sentence machine that rearranges words. We need to figure out the rule it follows by looking at the example provided. The example shows how an input sentence transforms into Step I and then Step II.
Step 2: Find the Rule
Let's analyze the example: 'we will meet at the park'. The sentence is split into two halves: 'we will meet' and 'at the park'. In each half, the last word moves to the front. So, 'we will meet' becomes 'meet we will', and 'at the park' becomes 'park at the'. This gives us Step I: 'meet we will park at the'.
Step 3: Apply Rule for Step II
To get Step II, we apply the same rule to Step I: 'meet we will park at the'. The first half is 'meet we will' and the second is 'park at the'. 'meet we will' becomes 'will meet we'. 'park at the' becomes 'the park at'. This gives Step II: 'will meet we the park at'.
Step 4: Solve for New Input
Now, apply this rule to the new input: 'birds sing early in the morning'. Split it: 'birds sing early' and 'in the morning'. For Step I: 'birds sing early' becomes 'early birds sing'. 'in the morning' becomes 'morning in the'. So Step I is: 'early birds sing morning in the'.
Step 5: The answer
To find Step II, apply the rule to Step I: 'early birds sing morning in the'. The first half 'early birds sing' becomes 'sing early birds'. The second half 'morning in the' becomes 'the morning in'. So the answer is (A) sing early birds the morning in, as this is the result of applying the rule twice.
A word-arrangement machine rearranges its input step by step. Here is an example:
Input: rose lily jasmine tulip daisy lotus
Step I: daisy rose lily jasmine tulip lotus
Step II: daisy jasmine rose lily tulip lotus
Step III: daisy jasmine lily rose tulip lotus
Step IV: daisy jasmine lily lotus rose tulip
The machine follows the same rule for every input.
Input: mango apple peach cherry banana grape
How many steps are needed to complete the arrangement?Solution — answer A
Each step moves the next word in alphabetical order into place from the left. For this input the last step is Step IV: apple banana cherry grape mango peach. So 4 steps are needed.
4 steps · reveal one at a timeStep 1: Understand the machine's rule
Let's analyze the example. The input is 'rose lily jasmine tulip daisy lotus'. The final sorted order would be 'daisy jasmine lily lotus rose tulip'. Notice that in each step, the next word in alphabetical order is moved to its correct position from the left.
Step 2: Apply the rule to the new input
Our new input is 'mango apple peach cherry banana grape'. First, let's list these words in alphabetical order: 'apple', 'banana', 'cherry', 'grape', 'mango', 'peach'. The machine will arrange them one by one from left to right.
Step 3: Trace the arrangement steps
Input: mango apple peach cherry banana grape\nStep I: apple mango peach cherry banana grape (apple moved)\nStep II: apple banana mango peach cherry grape (banana moved)\nStep III: apple banana cherry mango peach grape (cherry moved)\nStep IV: apple banana cherry grape mango peach (grape moved)
Step 4: The answer
So the answer is (A) 4. After Step IV, all words are in their correct alphabetical positions, meaning 4 steps were needed to complete the arrangement.
Free to start
Get exam-ready on Input-Output
Generate fresh input-output practice sets in Test Studio, get step-by-step AI explanations the moment you slip, and close the gaps in Socrative Mode.
- Step-by-step AI solutions
- Fresh practice sets on demand
- Guided Socrative Mode drills