AJA Officer Academies Entrance Examination study materials
AJA Officer Academies Entrance Examination study resources

AJA Officer Academies Entrance Examination: Logical and Abstract Reasoning

AJA Officer Academies Entrance Examination · Work through your exam, one topic at a time.

All guide sections

Logical and Abstract Reasoning

The question families

Expect series (number, letter and figure), analogies, odd-figure-out, coding-decoding, syllogisms, seating and ordering puzzles, blood relations, direction sense, matrix completion, and assumption/conclusion items on short passages.

Concepts to master

  • Series: check differences, then ratios, then alternating patterns; for figures, track one feature at a time - number of sides, shading, rotation, position of a single mark.
  • Rotation versus reflection: a shape turned 90 or 180 degrees keeps its internal arrangement anticlockwise; a mirror flips it. Follow one asymmetric detail, never the whole outline.
  • Syllogisms: "all A are B" plus "some B are C" forces nothing about A and C. Negate "all A are B" as "some A are not B" - not as "no A is B".
  • Direction and seating: draw it. A sketch on paper beats mental rotation every time.

Traps that appear

  1. Reading "only if" as "if" - conditionals have a direction.
  2. Assuming a figure was rotated when it was mirrored.
  3. Importing real-world knowledge into a syllogism or assumption question.
  4. Reversing the order in ranking or seating puzzles.
  5. Choosing a conclusion that is plausible but goes beyond the stated premises.

Worked example

Premises: All clerks are employees. Some employees are graduates. Question: which conclusion follows? Test each option against both premises only. "Some clerks are graduates" does not follow - the graduates may all be employees who are not clerks. "All employees are clerks" reverses the first premise. The only safe conclusion is the weak one that restates the premises, for example that some graduates are employees. Rule of thumb: in logic, the safest answer is the least ambitious one that still adds information.