Input–output for LIC AAO

Input–output sets look intimidating: a line of eight to twelve words and numbers, then five or six rearranged versions of it. In practice they are among the most predictable sets in reasoning. The machine follows one rule. Once you have the rule, you can write every step yourself, and the questions become lookups. All the risk lies in two places: finding the rule too quickly, and copying a step wrongly.

The common machine types

Most mains sets use a shift machine. The sorting keys are usually dictionary order for words (a to z, or z to a) and size for numbers. Some sets sort words by their number of letters, or numbers by the sum of their digits, so test the obvious key and then check it.

Finding the rule: a checklist

1. Compare the input with Step 1. Which elements moved? Where did they go?
2. Guess the sorting key: the smallest number, the largest, or the word first in the dictionary?
3. Check the guess on Step 2. The second element to move must be the next one by the same key.
4. Check that the elements that did not move kept their original order. In most shift machines they do, and it is how you copy a step correctly.
5. Look at the last step. If some elements are already in place, the machine finishes early.

Worked machine 1: word–number pairs from the left

Input: mango 29 apple 47 grape 16 berry 52

• Step 1: apple 16 mango 29 47 grape berry 52
• Step 2: apple 16 berry 29 mango 47 grape 52
• Step 3: apple 16 berry 29 grape 47 mango 52

Finding the rule. In Step 1, "apple", the first word in dictionary order, has moved to the left end, and 16, the smallest number, sits right after it. In Step 2 "berry" and 29 follow. So in each step, the next word in dictionary order moves to the left side, just after the elements already arranged, followed by the smallest remaining number. Everything else keeps its order.

After Step 3 only "mango 52" is left, and it is already in place. The arrangement is complete in three steps, not four.

Questions

1. How many steps are needed? Three.
2. In Step 2, which element is fifth from the left? apple, 16, berry, 29, mango.
3. In Step 1, which element is between 47 and berry? grape.
4. Which step reads "apple 16 berry 29 mango 47 grape 52"? Step 2.

Worked machine 2: numbers to one end, words to the other

Input: 46 term 18 claim 83 agent 27 policy 65 bonus

• Step 1: 83 46 18 claim agent 27 policy 65 bonus term
• Step 2: 83 65 46 18 claim agent 27 bonus policy term
• Step 3: 83 65 46 18 agent 27 bonus claim policy term
• Step 4: 83 65 46 27 18 agent bonus claim policy term

Finding the rule. In Step 1, 83, the largest number, moves to the left end, and "term", the last word in dictionary order, moves to the right end. In Step 2, 65 moves just after 83, and "policy" moves just before "term". So in each step, the largest remaining number joins the numbers at the left, and the last remaining word in dictionary order joins the words at the right.

Look at Step 3 carefully. The next number by the rule is 46, and it is already third from the left, so it does not appear to move. Only "claim" visibly moves. Machines often hide a step like this, and candidates who expect two visible moves decide the rule is wrong.

After Step 4 the numbers read 83 65 46 27 18 and the words read agent bonus claim policy term. Five numbers and five words, but only four steps, because 18 and "agent" end up in place without moving.

Questions

1. How many steps does the machine need? Four.
2. In Step 2, which element is fourth from the right? term, policy, bonus, 27.
3. In Step 3, how many elements are between 18 and "claim"? agent, 27, bonus: three.
4. Which step reads "83 46 18 claim agent 27 policy 65 bonus term"? Step 1.
5. In the last step, which element is fifth from the left? 18.

Working forward from a given step

Some questions give you a step for a new input, not the input itself: "Step 2 of an input is… What is Step 4?" Because each step depends only on the one before it, you can apply the rule from the step you are given. Identify how many elements are already arranged, then continue.

You cannot usually work backwards. Many different inputs produce the same Step 1, because the machine does not record where the moved elements started. If a question asks for the input from a later step, "cannot be determined" is often the right answer. Check the options for it.

A time plan for a set

Writing all the steps feels slow, but it turns every question into a lookup, and you check each step against the one above it as you go.

Practice set

Use the rule of worked machine 2 for all questions.

Step 1 of a new input: 92 57 claim 34 agent 61 fund bonus 12 term

1. What is Step 2?
2. What is Step 3?
3. How many steps are needed to complete the arrangement, counting Step 1?
4. In the last step, which element is third to the right of 12?
5. What was the input?

Answers

1. 92 61 57 claim 34 agent bonus 12 fund term. 61 is the largest remaining number and moves just after 92. "fund" is the last remaining word in dictionary order and moves just before "term".
2. 92 61 57 34 agent bonus 12 claim fund term. 57 is already in place. "claim" moves just before "fund".
3. Five. Step 4: 92 61 57 34 agent 12 bonus claim fund term (34 is already in place, and "bonus" moves). Step 5: 92 61 57 34 12 agent bonus claim fund term.
4. claim. The last step reads 92 61 57 34 12 agent bonus claim fund term. Counting right from 12: agent (1st), bonus (2nd), claim (3rd).
5. Cannot be determined. Step 1 tells you where 92 and "term" ended up, not where they started.

What to do next

• Solve two input–output sets this week, writing every step in aligned columns before you answer anything.
• Add input–output to the mains practice in reasoning for the LIC AAO mains.
• Practise data sufficiency in reasoning next, since it builds the same habit of checking what the data really fixes.