In abstract reasoning practice, the first pattern you notice is a hypothesis. It becomes useful only if it explains all the supplied information. A rule that fits one pair of numbers may fail on the next pair.
PMA’s entrance-examination guidance includes verbal and numerical reasoning and pattern analysis within SPMA. These original exercises build those reasoning habits. They do not reproduce official questions or establish the exact format of a future examination.
Sequence one: examine the differences
Consider 4, 7, 12, 19, 28. Under the rule that the increases are consecutive odd numbers, what comes next?
The differences are 3, 5, 7, and 9. The next increase is 11, so the answer under that rule is 39.
Writing the differences makes the explanation visible. “It looks like 39” is not the same as demonstrating why. In an unrestricted sequence, many mathematical continuations are possible; practice questions need sufficient constraints or answer choices to identify the intended rule. Here, the rule is explicitly supplied for that reason.
Use the PMA entrance exam study guide to allocate time to the reasoning gaps revealed by these exercises.
Sequence two: separate alternating positions
Try 2, 10, 4, 20, 6, 30. If the odd positions increase by two and the even positions increase by ten, the next two terms are 8 and 40.
Looking only at adjacent differences makes this sequence seem irregular. Splitting it into two smaller sequences exposes the structure: 2, 4, 6 and 10, 20, 30.
On paper, mark the positions before calculating. If you think a pattern alternates, check at least two transitions within each group. A single matching pair is weak evidence.
A relationship question: preserve the operation
Suppose each pair follows the rule “double the first number, then add three.” The pair 5 and 13 fits because 2 × 5 + 3 = 13. What number pairs with 8? 19.
Now compare “add three, then double.” That different order gives 22. The same numbers and operations can produce different results when their order changes. Writing the operation as an expression prevents that ambiguity.
Review wrong rules, not just wrong answers
After a mistake, keep the rule you initially proposed and identify the first step where it failed. Was the difference changing? Did you combine alternating sequences? Did you reverse the order of two operations?
Use Philippine PMA entrance exam practice questions for another set of original problems. Choose a fresh example after correcting the method. Repeating the same sequence tests answer memory more than pattern discovery.
For a short study session, solve one item slowly, explain the rule aloud, and create a variation for someone else to solve. Check that your variation has enough information to support the intended answer. Designing a clear problem forces you to distinguish a consistent rule from a guess that merely happens to fit one number.