Numerical reasoning
How to approach a number series
Before you hunt for the missing number, look at how the terms change. Practise four checks below: square numbers, a fixed multiplier, alternating operations and two interleaved sequences. Each original worked example checks every transition and explains the other options.
Read the whole question first
Notice where the gap is, how many terms you have and whether the question states a rule. A missing term in the middle must fit the transitions on both sides. Keep the answer options in view, but avoid building a rule just to reach your favourite option.
Try a small set of checks
Start with simple relationships and write down what you find. If one check does not explain every visible transition, move on instead of forcing it.
- Subtract neighbouring terms. Equal differences suggest repeated addition or subtraction. If the differences change regularly, inspect that smaller sequence too.
- Check multiplication or division when the size changes quickly. Verify the same relationship at each step, including any added or subtracted constant.
- If neighbouring terms seem unrelated, separate odd and even positions. Test each subsequence independently, then check which one contains the gap.
Changing differences: square numbers
Start by subtracting neighbouring terms. If the differences change regularly, continue their pattern and check the original numbers too.
A fixed multiplier
When the numbers grow quickly, divide each term by the one before it. A constant ratio can explain the sequence even when the differences keep changing.
Two operations taking turns
A sequence can alternate between addition and multiplication. Write the operation above each gap and check the whole cycle before choosing the next step.
Two sequences woven together
When one repeating operation cycle does not explain the terms, label their positions. Read positions 1, 3 and 5 together, then positions 2, 4 and 6. Each group may have its own rule.
Check the rule, not just the result
A finite list of numbers can fit more than one mathematical rule. In a test, use any stated constraints and favour a simple, consistent interpretation that explains all the given terms. If two options still seem possible, reread the question rather than assuming the first pattern you noticed must be right.
After checking an answer, note what you missed: an arithmetic slip, a skipped transition or a different type of pattern. Try a similar question and deliberately repeat the check you forgot. In a timed test, follow its navigation rules before deciding to leave a question and return later.
Put it into practice
Explore more questions and step-by-step explanations in Cognik.
