Understanding numerical reasoning in the ADF aptitude test
Numerical reasoning asks you to identify relationships between quantities and use them to reach an answer. In this JOA lesson, you will work through missing-value matrices, number sequences and several worded numerical problems. The aim is to understand why a method works so you can apply it to a fresh example, rather than memorising an answer from the video.
Read the question before starting a calculation. Identify what is known, what is missing and which quantity the answer must represent. A correct calculation can still answer the wrong question if you overlook a unit, a difference or the direction of a comparison.
Missing-value matrices and number sequences
For a missing-value matrix, compare the completed rows and columns first. Look for a relationship that explains more than one set of numbers. Addition, subtraction, multiplication or division may provide a useful starting point, but do not commit to a rule until you have checked it against the available information. Apply the same relationship to the incomplete part of the matrix.
For number sequences, write or mentally compare the changes between neighbouring terms. In an illustrative sequence such as 2, 5, 8, 11, each term increases by three. Other examples may involve changing differences or alternating operations. The useful habit is to test your proposed rule against the whole sequence, rather than choosing it because it explains only the first two numbers.
Worded problems: sum and difference
Translate a worded numerical problem into a simple relationship. If two quantities have a total of 30 and differ by 6, the larger is (30 + 6) ÷ 2 = 18 and the smaller is (30 − 6) ÷ 2 = 12. Check both conditions: 18 + 12 = 30, and 18 − 12 = 6.
This check matters because a plausible-looking number is not enough. When following the video's worked examples, identify which sentence supplies the total and which supplies the difference. Use the method only when those conditions actually match the question.
Squared differences and lowest common multiples
A difference of squares can be written as a² − b² = (a − b)(a + b). For consecutive numbers, the first bracket is one, so the answer equals their sum. For example, 27² − 26² = 1 × 53 = 53. This is squaring, not taking a square root. Recognising the relationship can avoid calculating both large squares separately.
For a lowest common multiple problem, look for the smallest positive number divisible by each of the given values. The lowest common multiple of 4 and 6 is 12. This can help with questions about repeating events that coincide, provided the events start together and the wording supports that interpretation.
Review your numerical reasoning practice
Try the questions in the video before watching their solutions. After each attempt, distinguish a calculation error from a method error or a missed instruction. Rework the question slowly if necessary, then try a fresh example. When you add timed practice, keep checking units and reasonableness rather than rushing every calculation.
Continue to verbal reasoning after this lesson, or use the free JOA quiz below to try a mix of numerical, verbal and abstract questions. Service Prep practice materials are independent examples, not official ADF assessment questions.
Official format reference: ADF Careers JOA guide, checked 16 October 2026. Follow your assessment invitation for current instructions. The examples and teaching categories in this course are independent practice material.