Logical Reasoning Concepts for Competitive Exams 2026

Logical Reasoning one liner - Input-Output

Input-Output

• What is a Machine Input-Output reasoning problem? - A sequence of algorithmic transformation steps rearranging words and numbers into a structured final output
• In an alphabetical word arrangement, what does ascending dictionary order mean? - Arranging words from A to Z
• In an alphabetical word arrangement, what does descending dictionary order mean? - Arranging words from Z to A
• In a numerical arrangement, what does ascending order mean? - Arranging numbers from smallest to largest
• In a numerical arrangement, what does descending order mean? - Arranging numbers from largest to smallest
• What is a "Left-End Arrangement" machine? - A machine that places newly sorted elements exclusively at the extreme left end in each step
• What is a "Right-End Arrangement" machine? - A machine that places newly sorted elements exclusively at the extreme right end in each step
• What is a "Simultaneous Both-Ends Arrangement" machine? - A machine that shifts one element to the left end and one element to the right end in the same step
• What is an "Auto-Shift" (or Auto-Arranged) element? - An element that automatically falls into its correct target position without requiring an active shift operation
• Does an auto-shifted element consume a separate step count? - No (It is arranged simultaneously within the ongoing step)
• What is a "Shifting (Pushing) Pattern"? - A pattern where placing a new element at an end pushes all previously placed elements inward
• What is a "Fixed Position (Swapping) Pattern"? - A pattern where elements swap specific slots without shifting the remaining elements
• In an Input of $N$ unsorted elements, what is the theoretical maximum number of steps required in a single-end machine? - $N - 1$ steps
• In an Input of $N$ unsorted elements, what is the theoretical minimum number of steps required if already sorted? - 0 steps (Input is Step 1 / Final Step)
• Can you deduce the original "Input" by working backwards from an intermediate step in a shifting-type machine? - No (Previous positions cannot be determined uniquely due to loss of historical order)
• If Step III of a shifting machine is given, can you uniquely determine Step II? - No (Cannot be determined / Backward tracking impossible in shifting models)
• If Step III of a machine is given, can you determine Step IV and the Final Step? - Yes (Forward steps follow deterministic rules)
• What is a "Word-Length Arrangement" rule? - Arranging words based on their total letter count (e.g., 3-letter, 4-letter, 5-letter words)
• What is a "Vowel-Consonant Segregation" rule? - Arranging vowel-starting words at one end and consonant-starting words at the opposite end
• What is a "Number-Digit Sum" transformation? - Replacing a multi-digit number with the sum of its individual digits (e.g., $48 \to 12$)
• What is a "Number-Digit Product" transformation? - Replacing a multi-digit number with the product of its individual digits (e.g., $37 \to 21$)
• What is an "Alphabetical Positional Shift" on words? - Replacing each letter of a word with its $+1$, $-1$, or opposite alphabet code
• In a step where words are sorted alphabetically from left and numbers in descending order from right, what is arranged in Step 1? - The smallest alphabetical word at the left end and the largest number at the right end
• If the Input is cat 45 dog 82 ant 12, and Step 1 is ant cat 45 dog 82 12, what rule is operating at the left end? - Smallest alphabetical word shifted to the left end
• If the Input is cat 45 dog 82 ant 12, and Step 1 is 82 cat 45 dog ant 12, what rule is operating at the left end? - Largest number shifted to the left end
• What defines the "Final Step" of a machine rearrangement? - The step where all elements completely satisfy the terminal ordering condition
• How do you identify the logic of a machine input-output set in competitive exams? - Compare the Input directly with the Final Step to determine the terminal arrangement criteria
• If the terminal step is Apple 12 Ball 24 Cat 36 Dog 48, what is the alternating pattern? - Word in ascending alphabetical order followed by number in ascending numerical order
• If the terminal step is 95 82 64 31 zebra tiger lion fox, what is the pattern? - All numbers in descending order on the left, followed by all words in descending order on the right
• If the terminal step is ant bat cat dog 10 20 30 40, what is the segregated pattern? - All words in ascending order on the left, followed by all numbers in ascending order on the right
• What is an "Inverted Shifting" pattern? - Elements alternate positions between odd and even steps across inward converging columns
• In a mathematical box-type input-output model, what does Step 1 usually do to paired inputs? - Applies arithmetic operations (addition, subtraction, multiplication) on cross-box digits
• If Box 1 is [2, 4] and Box 2 is [3, 5], and the output box is [6, 20], what operation was applied? - Component-wise multiplication ($2 \times 3 = 6$ and $4 \times 5 = 20$)
• If Box 1 is [4, 7] and Box 2 is [1, 3], and the output box is [5, 10], what operation was applied? - Component-wise addition ($4 + 1 = 5$ and $7 + 3 = 10$)
• If Box 1 is [8, 2] and Box 2 is [5, 6], and the output is [3, 4], what operation was applied? - Component-wise absolute difference ($|8 - 5| = 3$ and $|2 - 6| = 4$)
• What is a "Circular Shift" rule in machine inputs? - All elements shift one position to the right with the last element wrapping around to the first slot
• In a word transformation machine, if MAKE becomes NBLF, what rule was applied? - Each letter shifted forward by $+1$ in the alphabet
• In a word transformation machine, if COLD becomes BNKC, what rule was applied? - Each letter shifted backward by $-1$ in the alphabet
• In a word transformation machine, if DOOR becomes WLLI, what rule was applied? - Each letter replaced by its opposite alphabet pair
• If numbers in an input are 14, 25, 36, 47 and become 16, 27, 38, 49 in Step 1, what operation was applied? - Added $+2$ to each number
• If numbers in an input are 12, 15, 18, 21 and become 144, 225, 324, 441 in Step 1, what operation was applied? - Squared each number
• If numbers in an input are 8, 27, 64, 125 and become 2, 3, 4, 5 in Step 1, what operation was applied? - Took the cube root of each number
• If words in an input are pen, book, computer, television and become 3, 4, 8, 10 in Step 1, what was counted? - Total number of letters in each word
• If words in an input are education, apple, sky, queue and become 5, 2, 0, 4 in Step 1, what was counted? - Total number of vowels in each word
• If words in an input are education, apple, sky, queue and become 4, 3, 3, 1 in Step 1, what was counted? - Total number of consonants in each word
• What is the "Direct Element Mapping Shortcut" for single-end sorting? - Labeling target elements sequentially as $L_1, L_2, L_3\dots$ and identifying auto-shifts without writing full rows
• When an element is already in its target position without a manual move, what is it called? - Auto-arranged (or Skip element)
• If 8 elements are sorted using a both-ends machine (2 elements per step) with 0 auto-shifts, how many steps are needed? - 4 steps ($8 / 2$)
• If 7 elements are sorted using a both-ends machine (2 elements per step) with 1 auto-shift, how many steps are needed? - 3 steps
• If the Input has 6 elements and Step 1 arranges 2, Step 2 arranges 2, and the remaining 2 are auto-arranged, what is the final step? - Step 2
• In an Input 42 18 75 31 89, if numbers are sorted in ascending order from left, what is Step 1? - 18 42 75 31 89
• In an Input 42 18 75 31 89, what is Step 2 (ascending from left)? - 18 31 42 75 89 (Note: 42, 75, 89 auto-arrange $\to$ Final Step is Step 2)
• In an Input zebra monkey lion cat, if words are sorted alphabetically from left, what is Step 1? - cat zebra monkey lion
• In an Input zebra monkey lion cat, what is Step 2 (alphabetical from left)? - cat lion zebra monkey
• In an Input zebra monkey lion cat, what is Step 3? - cat lion monkey zebra (Final Step)
• In an Input 15 82 43 91 27, if the largest number moves to the right end in each step, what is Step 1? - 15 82 43 27 91
• In an Input 15 82 43 91 27, what is Step 2 (largest to right end)? - 15 43 27 82 91
• In an Input 15 82 43 91 27, what is Step 3 (largest to right end)? - 15 27 43 82 91 (Final Step)
• What is an "Alternating End-Shift" machine? - A machine that shifts to the Left End in Step 1, Right End in Step 2, Left End in Step 3, and so on
• If a machine shifts the smallest word to the Left in Step 1, largest number to the Right in Step 2, 2nd smallest word to the Left in Step 3, what is shifted in Step 4? - 2nd largest number to the Right
• In a step-by-step arrangement, what is the position of an element counted from? - Either the Left End (Start) or Right End (End) as specified by the question
• If a row is apple 12 cat 45 dog 89, what is the 3rd element from the left? - cat
• If a row is apple 12 cat 45 dog 89, what is the 2nd element from the right? - dog
• If a row is apple 12 cat 45 dog 89, what is the element 2nd to the left of dog? - cat
• If a row is apple 12 cat 45 dog 89, what is the element 3rd to the right of 12? - 89
• In an alphanumeric arrangement, if letters shift by $+2$ and numbers by $-5$ in each step, what does cat 20 become? - ecv 15
• What is a "Digital Sum Reduction" rule? - Repeatedly summing digits until a single digit is obtained (e.g., $98 \to 17 \to 8$)
• If numbers 28, 39, 47, 56 are transformed into 1, 3, 2, 2 in Step 1, what rule was applied? - Digital root reduction ($2+8=10\to1, 3+9=12\to3, 4+7=11\to2, 5+6=11\to2$)
• If words are gold, silver, platinum, copper and Step 1 outputs dlog, revlis, munitalp, reppoc, what rule was applied? - Reversed the letters of each word
• If words are star, moon, sun and Step 1 outputs arst, mnoo, nsu, what rule was applied? - Arranged letters within each individual word in alphabetical order
• If numbers are 35, 72, 84, 19 and Step 1 outputs 53, 27, 48, 91, what rule was applied? - Reversed the digits within each individual number
• In a mathematical flow model, if Step 1 multiplies numbers by 2, Step 2 adds 3, and Step 3 divides by 5, what is the output for input 11? - 5 ($11 \times 2 = 22 \to 22 + 3 = 25 \to 25 / 5 = 5$)
• What is the "Number of Steps Required" test? - Calculating the exact total steps from raw input to terminal state using systematic simulation
• If an input has 5 words already sorted in reverse alphabetical order, how many steps are needed to arrange them in reverse alphabetical order? - 0 steps (Already sorted)
• If an input has 5 words in ascending order, how many steps are needed to arrange them in descending order using single-end left shifts? - 4 steps
• In an arrangement machine, what happens when two identical numbers/words appear in the input? - They maintain their relative entry order unless differentiated by secondary rules
• What is an "Odd-Even Number Segregation" machine? - A machine that shifts all even numbers to the left end and all odd numbers to the right end
• If even numbers are sorted in ascending order on the left and odd numbers in descending order on the right, where does 14 go compared to 28? - 14 sits to the left of 28
• If even numbers are sorted ascending on the left and odd numbers descending on the right, where does 91 go compared to 35? - 91 sits to the left of 35 in the right-side block (since $91 > 35$)
• What is a "Consonant-Count Sorting" rule? - Sorting words based on the number of consonants they contain
• If an input is apple, banana, kiwi, strawberry, what is their consonant count? - apple (3), banana (3), kiwi (2), strawberry (7)
• If words are sorted by ascending consonant count, which word comes first among apple, kiwi, strawberry? - kiwi (2 consonants)
• In a progressive difference machine, if Step 1 takes the difference between consecutive numbers, how many elements does Step 1 have compared to an $N$-element input? - $N - 1$ elements
• If an input is 10, 15, 22, 31, 42, what is the first difference sequence? - 5, 7, 9, 11
• What is the second difference sequence of 10, 15, 22, 31, 42? - 2, 2, 2 (Constant difference)
• In an input-output machine, if Step 2 is blue 85 red 12 green 40, what is the 4th element from the left? - 12
• In an input-output machine, if Step 3 is 10 20 30 apple mango zebra, how many elements are numbers? - 3 elements
• In an input-output machine, if Step 3 is 10 20 30 apple mango zebra, how many elements are words? - 3 elements
• What is the term for a machine pattern where the middle two elements swap in each step? - Central inversion / Middle swap
• If a sequence is A B C D E F and the middle two swap in Step 1, what is the output? - A B D C E F
• If A B C D E F has its outer two elements swap in Step 1, what is the output? - F B C D E A
• What is a "Block Interchanging" rule? - Splitting an $N$-element row into two halves and swapping the left half with the right half
• If the input is 1 2 3 4 5 6 and halves are swapped in Step 1, what is the output? - 4 5 6 1 2 3
• What is a "Pair-Wise Swap" rule? - Swapping elements at positions (1,2), (3,4), (5,6) simultaneously
• If the input is A B C D E F and pair-wise swapped in Step 1, what is the output? - B A D C F E
• If B A D C F E is pair-wise swapped again in Step 2, what is the output? - A B C D E F (Restored to original)
• In a machine where words are arranged by total vowels ascending: tree (2), eye (2), beautiful (5), sky (0), what is the first word? - sky (0 vowels)
• In the vowel-count ascending arrangement of tree, eye, beautiful, sky, what is the last word? - beautiful (5 vowels)
• If numbers are replaced by Number + Position in Step 1, what does 50 at position 3 become? - 53 ($50 + 3$)
• If numbers are replaced by Number - Position in Step 1, what does 50 at position 3 become? - 47 ($50 - 3$)
• In a modern advanced Input-Output box model, what is Step 4 usually designed as? - A single mathematical resultant (e.g., average, ratio, or digital sum of Step 3 values)
• What is the golden rule for answering sub-questions in machine input-output sets? - Fully decode the generic step rules first, apply them to the target input, write all steps clearly, and then answer all 5 questions rapidly
• Can an element once arranged at an extreme end be pushed inward by subsequent steps? - Yes (In shifting-type machines, new arrivals take the extreme edge and push earlier ones inward)
• Can an element once arranged at an extreme end stay at that extreme end permanently? - Yes (In fixed-boundary machines where subsequent elements take position 2, position 3, etc.)
• What is a "Fixed Boundary (Non-Pushing) Machine"? - A machine where Step 1 fixes slot 1, Step 2 fixes slot 2, Step 3 fixes slot 3 without pushing slot 1
• What is a "Pushing Boundary Machine"? - A machine where Step 1 takes slot 1, but Step 2 takes slot 1 and pushes the previous element into slot 2
• If Step 1 places apple at slot 1, and Step 2 places ball at slot 1 giving ball apple ..., is this a pushing or non-pushing machine? - Pushing Machine
• If Step 1 places apple at slot 1, and Step 2 places ball at slot 2 giving apple ball ..., is this a pushing or non-pushing machine? - Non-Pushing (Fixed Boundary) Machine
• In a non-pushing machine, does the position of previously arranged elements change in subsequent steps? - No (Their slot indices remain strictly constant)
• In a pushing machine, does the position index of previously arranged elements change in subsequent steps? - Yes (Their slot index increases by $+1$ with each new arrival at that end)
• If an input has 8 elements and is processed by a non-pushing machine arranging 1 element per step from the left, which slot is filled in Step 4? - Slot 4 (from the left end)
• If an input has 8 elements and is processed by a pushing machine adding elements at the left end, where is the element from Step 1 located after Step 4? - At Slot 4 (pushed 3 times to the right)
• How many total elements change their physical positions in a single step of a 1-element shift operation? - All elements that are shifted to make room for the newly arranged item
• How many total elements change their physical positions in a pure 2-element swap operation? - Exactly 2 elements (the remaining elements stay static)
• If an input is 12 45 78 23 56 89 and Step 1 is 89 12 45 78 23 56, what operation occurred? - The largest number was moved to the extreme left in a pushing manner
• If Step 1 is 89 12 45 78 23 56 and Step 2 is 89 78 12 45 23 56, what operation occurred? - The 2nd largest number was placed at slot 2 (non-pushing from left edge)
• If Step 2 is 89 78 12 45 23 56 and Step 3 is 89 78 56 12 45 23, what is Step 4? - 89 78 56 45 12 23
• For the sequence 89 78 56 45 12 23, what is Step 5 (Final Step to complete descending order)? - 89 78 56 45 23 12
• What is the total number of steps required to sort 12 45 78 23 56 89 into descending order using this left-to-right selection logic? - 5 steps
• If the input is cat dog ant bat, how many steps are needed to arrange it alphabetically as ant bat cat dog using left-end pushing? - 3 steps (Step 1: ant cat dog bat, Step 2: bat ant cat dog, Step 3: cat bat ant dog $\to$ wait, terminal ascending gives ant bat cat dog in 2 steps)
• What is the most efficient strategy to solve Input-Output questions accurately under time pressure? - Track step indices symbolically and write down only the target sequence steps required for the specific question
• What is an "Alphabetical-Numerical Cross Machine"? - A machine that simultaneously processes word transformations (e.g., consonant shift) and numerical transformations (e.g., squaring) in parallel
• If a word TRAIN has all vowels replaced by $+1$ and consonants by $-1$, what is the output? - SQBJM ($T\to S, R\to Q, A\to B, I\to J, N\to M$)
• If a word MANGO has vowels doubled and consonants halved (by alphabet rank), what is $A(1)$ and $O(15)$? - $A \to 2 (B)$ and $O \to 30 \to 4 (D)$
• What is a "Matrix Input-Output" grid? - A $3 \times 3$ or $2 \times 3$ grid of numbers where each subsequent step performs row-wise or column-wise mathematical operations
• In a $2 \times 2$ grid with top row [4, 6] and bottom row [3, 5], if Step 1 outputs [12, 30], what operation occurred? - Column-wise multiplication ($4 \times 3 = 12$ and $6 \times 5 = 30$)
• In a $2 \times 2$ grid with top row [4, 6] and bottom row [3, 5], if Step 1 outputs [7, 11], what operation occurred? - Column-wise addition ($4 + 3 = 7$ and $6 + 5 = 11$)
• In a $2 \times 2$ grid with top row [4, 6] and bottom row [3, 5], if Step 1 outputs [1, 1], what operation occurred? - Column-wise absolute subtraction ($4 - 3 = 1$ and $6 - 5 = 1$)
• What is a "Single Digit Terminal Step" in box models? - A final step that combines all previous step values into one consolidated number (e.g., dividing sum of row 1 by sum of row 2)
• If Step 2 numbers are 14 and 28, and Step 3 is 0.5, what operation was applied? - Division ($14 / 28 = 0.5$)
• If Step 2 numbers are 14 and 28, and Step 3 is 42, what operation was applied? - Addition ($14 + 28 = 42$)
• If Step 2 numbers are 14 and 28, and Step 3 is 14, what operation was applied? - Absolute difference ($28 - 14 = 14$)
• If Step 2 numbers are 14 and 28, and Step 3 is 392, what operation was applied? - Multiplication ($14 \times 28 = 392$)
• What is the role of Input-Output questions in competitive aptitude examinations? - To evaluate procedural algorithmic thinking, rule induction, sequential execution, and pattern recognition
• Why is backward tracking impossible in standard shifting machine problems? - Because multiple distinct prior arrangements could collapse into the same intermediate step after sorting
• When is backward tracking possible in machine input-output? - Only when the rule is a 1-to-1 invertible mathematical mapping or static bijective swapping without reordering
• In a step where 6 words are arranged alphabetically from right to left, what word is at the extreme right in Step 1? - The lexicographically smallest word (A-word)
• In a step where 6 words are arranged alphabetically from right to left, what word is at the extreme right in the Final Step? - The lexicographically smallest word (pushed or fixed at the right end)
• If the input is red 40 blue 10 green 30, and Step 1 is blue red 40 10 green 30, what was shifted? - The alphabetically smallest word (blue) to the extreme left
• If Step 1 is blue red 40 10 green 30 and Step 2 is blue 40 red 10 green 30, what was shifted? - The largest number (40) to slot 2
• If Step 2 is blue 40 red 10 green 30 and Step 3 is blue 40 green red 10 30, what was shifted? - The 2nd smallest word (green) to slot 3
• If Step 3 is blue 40 green red 10 30 and Step 4 is blue 40 green 30 red 10, what was shifted? - The 2nd largest number (30) to slot 4 (Final Step)
• How many total steps were required to complete the arrangement blue 40 green 30 red 10? - 4 steps
• In Step 3 (blue 40 green red 10 30), what is the 5th element from the left? - 10
• In Step 3 (blue 40 green red 10 30), what is the 2nd element from the right? - 10
• In Step 4 (blue 40 green 30 red 10), which element is 3rd to the left of 10? - 40
• In Step 4 (blue 40 green 30 red 10), which element is 2nd to the right of green? - red