AFPSAT Logical Reasoning: Patterns, Syllogisms, Deductive Logic

AFPSAT Logical Reasoning: Patterns, Syllogisms, Deductive Logic

Logical reasoning is one of the pattern-heavy parts of AFPSAT prep, along with spatial reasoning. Background matters less here; practice matters more.

A note on scope: the AFP does not publish the AFPSAT's subtests, item counts or weights. Reviewer sources describe logical and abstract-reasoning items like the ones below. Use this as a practice map, not an official breakdown.

This post is the topic plan that the AFPSAT guide hands off to.

Item types to practice

• Number series
• Letter series
• Syllogisms
• Conditional (if-then) reasoning
• Classification (odd one out)
• Cause-and-effect statements

Number series

Start by computing the differences between consecutive terms. Common patterns:

• Arithmetic (constant difference): 3, 7, 11, 15, ___ (next: 19)
• Geometric (constant ratio): 2, 6, 18, 54, ___ (next: 162)
• Differences that grow: 1, 4, 10, 19, 31, ___ (differences 3, 6, 9, 12, so next: 46)
• Two patterns alternating
• Squares and cubes
• Fibonacci-like (each term is the sum of the two before)
• Multi-step rules (×2 then +1, and so on)

Check the differences first. With practice, most series give themselves away within a few seconds.

Letter series

Convert letters to alphabet positions (A=1, B=2 …), find the pattern in the numbers, then convert back.

Memorize A to N (N=14), then count on from N for the rest of the alphabet.

Syllogisms

Know the four statement types:

• "All A are B": universal affirmative
• "No A are B": universal negative
• "Some A are B": particular affirmative
• "Some A are not B": particular negative

Venn diagrams solve most syllogism items quickly. Draw the circles, shade what the premises rule out, and check whether the conclusion must be true.

Worked example: "All officers wear uniforms. Some uniforms are camouflage. Therefore, some officers wear camouflage."

Valid? No. The camouflage uniforms could all belong to people who aren't officers. The premises never connect officers to the camouflage group, so the conclusion doesn't have to be true. This "undistributed middle" is one of the most common traps.

Conditional reasoning

• "If P then Q" → the contrapositive "If not Q then not P" is valid
• The inverse "If not P then not Q" is invalid (a trap)
• The converse "If Q then P" is invalid (a trap)

Drill 30 or more of these until you spot valid and invalid forms on sight.

Classification

Find the most specific category that all but one option share. If two options seem to be the odd one out, you haven't found the right category yet.

Cause and effect

You're given two statements. Decide whether one causes the other, both come from a common cause, or they're unrelated.

Trap: correlation is not causation. Read every option before you choose.

A 4-week logical drilling plan

The volume targets are a suggested pace. Review every wrong answer the same day.

Practice with Super Tutor

Super Tutor's AFPSAT reviewer has an Analytical Ability chapter (analogies, inferences, reading, logical reasoning), with practice quizzes at three difficulty levels and an AI tutor that explains each answer step by step. Start free — 5-day trial, no card.

What to read next

The AFPSAT guide covers the full review. Other area plans: Verbal, Numerical, Spatial, General Information.