How to Solve Coded Inequalities Problems
Decode symbol-based inequality statements, chain relations correctly, and spot either-or and indeterminate cases with worked examples.
Expected Interview Answer
Coded inequalities replace the symbols >, <, =, ≥, ≤ with letters or other symbols in a coding key, and you solve them by first decoding every symbol back to its real meaning, then chaining the statements algebraically before checking whether the given conclusions follow.
The first step is always to build a symbol-to-meaning table from the legend given in the question, since the same letter can mean different things across different question sets. Once decoded, a statement like A % B $ C @ D becomes an ordinary chain such as A > B = C ≥ D, and you combine adjacent relations the same way you would in plain algebra, remembering that a chain only yields a direct conclusion between two ends if every link in between is compatible in direction. Two special traps decide most answers: an 'either-or' case arises when neither conclusion alone is definitely true but their combination covers all possibilities, and a chain breaks if it contains a mix of > and < with no equality bridging them, making the relationship between the extreme terms indeterminate. Always redraw the chain in real symbols before evaluating any conclusion; trying to reason directly in coded symbols is the most common source of errors.
- A single decode-then-chain method handles every coded inequality set
- Recognizing indeterminate chains avoids false-confident wrong answers
- Spotting either-or cases correctly is worth disproportionate marks
AI Mentor Explanation
Imagine a scoreboard where the commentary team uses code words instead of run-rate symbols: 'flying' means a higher score, 'tied' means equal, 'chasing' means lower. Before comparing three teams’ totals you must first translate every code word back into greater-than, equal-to, or less-than, then chain the translated relations exactly as you would with plain numbers on a scoreboard. If team A is 'flying' over B and B is 'chasing' C, you cannot conclude anything definite about A versus C without knowing the exact direction of both links, which mirrors why coded inequality chains only combine cleanly when their directions agree.
Step-by-Step Explanation
Step 1
Decode the symbol legend
Translate every coded symbol (%, $, @, ©, *, etc.) into its real meaning (>, <, =, ≥, ≤) using the key given in the question.
Step 2
Rewrite the full statement
Replace every symbol in the given statement with its decoded meaning to form an ordinary inequality chain.
Step 3
Chain adjacent relations
Combine consecutive relations algebraically (e.g., A > B = C gives A > C); stop if directions conflict without an equality bridge.
Step 4
Evaluate each conclusion
Check each conclusion against the chained relation; test for either-or cases when neither conclusion alone is guaranteed but together they cover all possibilities.
What Interviewer Expects
- Correctly building and applying the symbol-decoding table before reasoning
- Accurate chaining of decoded relations without skipping links
- Recognizing when a chain is indeterminate due to conflicting directions
- Correctly identifying either-or conclusion cases
Common Mistakes
- Reasoning directly in coded symbols instead of decoding first
- Chaining relations across a direction conflict without an equality bridge
- Missing valid either-or conclusions by evaluating each option in isolation
- Misreading the legend and swapping the meaning of two symbols
Best Answer (HR Friendly)
“I always start by building a small translation table from the coding key, since the same symbol can mean different things in different question sets. Once every symbol in the statement is decoded into a normal greater-than, less-than, or equal-to chain, I combine adjacent relations the way I would in plain algebra. If the chain has a clean direction throughout, I can conclude a relationship between the first and last term; if the directions conflict without an equality link, I mark the conclusion as indeterminate. I also specifically check for either-or cases, since two individually uncertain conclusions can together be definitely true.”
Follow-up Questions
- How do you determine whether two conclusions form a valid either-or pair?
- What happens to the chain when a ≥ or ≤ symbol is involved instead of a strict inequality?
- How would you handle a coding key where two different symbols decode to the same meaning?
- Can you always combine three decoded relations into one, and when does that fail?
MCQ Practice
1. If '@' means '>', '#' means '=', and '&' means '<', and the statement is A @ B # C, which conclusion follows?
A @ B # C decodes to A > B = C, so A > C follows directly by substitution.
2. Given the statement P & Q @ R (where '&' means '<' and '@' means '>'), what can be concluded about P and R?
P < Q and Q > R gives conflicting directions with no equality bridge, so the relationship between P and R is indeterminate.
3. If the decoded chain is A > B > C, which pair of conclusions forms a valid either-or?
When the chain gives A > C definitely, an either-or of "A > C or A = C" is technically covered by the stronger true conclusion, but the classic either-or pattern applies when neither strict inequality nor equality alone is guaranteed — here it illustrates that the exhaustive pair (> or =) always holds true when the direct relation is not itself decisively one specific strict case without ambiguity in the underlying chain.
Flash Cards
First step in any coded inequality problem? — Decode every symbol into its real meaning using the given legend before reasoning.
When does a chain give a definite conclusion? — When all links in the chain point in a consistent, combinable direction (or are bridged by equality).
What causes an indeterminate chain? — A mix of > and < directions in the chain with no equality link bridging them.
What is an either-or conclusion? — A case where neither of two conclusions is individually certain, but together they exhaust all possible outcomes.