Inductive Reasoning: Pattern Identification, Information Ordering, and Sequence Worked Examples

Inductive Reasoning on the CAT

Inductive reasoning tests whether you can identify patterns and extend them. Where deductive reasoning asks what must be true, inductive reasoning asks what most likely comes next given a pattern. The CAT presents number sequences, letter patterns, and information-ordering puzzles. The skill is spotting the rule that generates the pattern, then applying it once more.

Number Sequences

Number sequences on the CAT fall into a few common types. The strategy:

1. Compute the difference between consecutive terms.
2. If differences are constant, it is arithmetic.
3. If ratios are constant, it is geometric.
4. If differences themselves form a pattern, look for a second-level difference or alternating pattern.

Worked example — second-level arithmetic: Find the next term: 3, 7, 12, 18, 25, ?

Step 1: First differences — 7−3=4, 12−7=5, 18−12=6, 25−18=7. The differences increase by 1 each time (4, 5, 6, 7). Step 2: The next difference should be 8. Step 3: Next term = 25 + 8 = 33.

Worked example — geometric: Find the next term: 3, 6, 12, 24, ?

Step 1: Ratio between terms — 6 ÷ 3 = 2, 12 ÷ 6 = 2, 24 ÷ 12 = 2. Constant ratio of 2. Step 2: Next term = 24 × 2 = 48.

Worked example — alternating / interleaved: Find the next term: 4, 9, 6, 11, 8, 13, 10, ?

Step 1: One rule does not fit the whole sequence. Split into odd-position terms (1st, 3rd, 5th, 7th): 4, 6, 8, 10 — increasing by 2. Even-position terms (2nd, 4th, 6th): 9, 11, 13 — increasing by 2. Step 2: The 8th term is in the even-position sequence. Step 3: Next even term = 13 + 2 = 15.

Worked example — mixed operation: Find the next term: 2, 5, 11, 23, 47, ?

Step 1: Examine the jumps — 5 = 2×2+1, 11 = 5×2+1, 23 = 11×2+1, 47 = 23×2+1. Step 2: Rule: multiply by 2, then add 1. Step 3: Next term = 47 × 2 + 1 = 95.

Letter and Symbol Patterns

Some CAT items use letters or symbols. Treat letters by their alphabet position (A=1, B=2, …, Z=26).

Worked example: Find the next term: A, C, E, G, ?

Step 1: Convert — A=1, C=3, E=5, G=7. Step 2: Pattern — odd numbers, +2 each time. Step 3: Next = 7 + 2 = 9 = I.

Worked example — descending letters: Find the next term: Z, W, T, Q, ?

Step 1: Convert — Z=26, W=23, T=20, Q=17. Step 2: Differences — 26−23=3, 23−20=3, 20−17=3. Decreasing by 3. Step 3: Next = 17 − 3 = 14 = N.

Pattern-Spotting Tips

• Compute differences first — most CAT sequences are arithmetic or second-level arithmetic.
• Try ratios if differences vary wildly — geometric or mixed (multiply then add) patterns.
• Split interleaved sequences — if one rule does not fit the whole sequence, alternate two rules.
• Check the answer choices — only one choice will fit the rule you found. If two fit, your rule is too loose.

Information Ordering

Information-ordering items present a set of constraints (often rank or schedule) and ask you to determine a valid arrangement. The strategy:

1. List the items.
2. Translate each constraint into a "before/after" or "must be adjacent" rule.
3. Chain the rules into a single order.
4. Check the answer choices against the chain.

Worked example — rank order from constraints: Five candidates — B, C, D, E, F — finished a fitness test. Constraints:

• C finished before B.
• D finished immediately before E.
• F finished before D but after B.

Determine a valid finish order.

Step 1: Translate constraints:

• C < B (C before B)
• D immediately before E → pair (D, E)
• B < F < D

Step 2: Chain them — C < B < F < D < E.

Step 3: Verify each constraint:

• C before B? Yes.
• D immediately before E? Yes.
• F before D and after B? Yes.

Answer: C, B, F, D, E.

Worked example — shift schedule: Four officers — K, L, M, N — are assigned to four consecutive shifts (1, 2, 3, 4). Constraints:

• K cannot work shift 1.
• L must work immediately before M.
• N must work an earlier shift than K.

Determine the assignment.

Step 1: L immediately before M → (L, M) pair occupies two consecutive slots. Step 2: N before K. Step 3: K cannot be shift 1, so K is at least shift 2.

Try (L, M) in slots 1-2:

• Remaining slots 3, 4 for N, K. N before K → N=3, K=4. K ≠ 1 satisfied.
• Check: K=4, L=1, M=2, N=3. N(3) < K(4). All constraints satisfied.
• One valid arrangement: L, M, N, K (shifts 1, 2, 3, 4).

Try (L, M) in slots 2-3:

• Remaining slots 1, 4 for N, K. N before K → N=1, K=4. K ≠ 1 satisfied.
• Arrangement: N, L, M, K (shifts 1, 2, 3, 4). Also valid.

Try (L, M) in slots 3-4:

• Remaining slots 1, 2 for N, K. N before K → N=1, K=2. K ≠ 1 satisfied.
• Arrangement: N, K, L, M. Also valid.

When multiple arrangements satisfy the constraints, the CAT typically asks "which of the following is a valid arrangement?" — pick any answer that satisfies all constraints. If asked "which must be true," look for the constraint common to every valid arrangement (here, L immediately before M is true in all three; N before K is true in all three; K ≠ 1 is true in all three).

Worked example — eligibility ranking: Four applicants — P, Q, R, S — are ranked by interview score. Constraints:

• P scored higher than Q.
• R scored lower than S but higher than P.
• S did not score the highest.

Step 1: Translate:

• Q < P
• P < R < S
• S is not #1

Step 2: Chain so far — Q < P < R < S, but S is not the highest. The only person who could be above S is the one not yet placed above P — but everyone is in the chain. Wait: the chain Q < P < R < S makes S the highest, which violates the third constraint. Re-read: "S did not score the highest" means someone scored higher than S. The four are P, Q, R, S. The chain places S on top, so the constraint forces a contradiction unless we mis-ordered. Recheck: R lower than S means R < S, and R higher than P means P < R. So P < R < S, and Q < P. That gives Q < P < R < S — S is top. The constraint "S did not score the highest" is then unsatisfiable, which means our reading is wrong: re-read "R scored lower than S but higher than P" as P < R < S, and "S did not score the highest" requires someone above S. The only remaining applicant is Q, so Q > S. Combined: P < R < S < Q. But we also have P > Q from "P scored higher than Q." Contradiction again.

The resolution: the constraints as stated are inconsistent, which is itself a CAT trap — sometimes a constraint set has no valid arrangement, and the answer is "no valid arrangement exists." More commonly, the CAT keeps constraints consistent. A cleaner version drops the "S did not score highest" constraint; then the order is Q < P < R < S and S ranks first.

The takeaway: if your chain produces a contradiction, either you mis-translated a constraint or the answer is that no valid arrangement exists.

Ordering Tips

• Draw a chain — write each constraint as X < Y and chain them.
• Treat adjacency as a block — "immediately before" means the pair moves together.
• Eliminate answer choices that violate any constraint — faster than building the full order.
• If asked "which must be true," find the constraint that holds in every valid arrangement; if only one arrangement is valid, every constraint "must be true."
• If the chain contradicts itself, re-translate the constraints; if re-translation still contradicts, the answer may be that no valid arrangement exists.