Logical Arrangement Practice Questions
Logical arrangement questions test systematic counting. You may need to count code patterns, outfit choices, handshakes, digit arrangements, or letter shuffles without missing cases or counting the same case twice.
The Rules Every Logical Arrangement Question Uses
These questions reward careful structure. Decide what each position or pairing represents, then count choices in the correct order.
🔢 Rule 1: Multiply independent choices
If a choice is made in stages, multiply the number of options at each stage.
Example: 4 letters, then 4 letters, then 4 numbers gives 4 × 4 × 4 = 64 codes.
🚫 Rule 2: Restrictions reduce choices
If letters or digits cannot repeat, or a fixed symbol must be used, reduce the choices before multiplying.
Example: Two different letters from 4 choices gives 4 × 3 = 12 ordered pairs.
🤝 Rule 3: Pairings are counted twice
For handshakes, matches, or pairs, A with B is the same as B with A, so divide by 2.
Example: 6 people give 6 × 5 ÷ 2 = 15 pairs.
🔤 Rule 4: Arrangements lose one choice each time
When arranging different letters or digits with no repeats, each position has one fewer choice than the last.
Example: CHAIR has 5 different letters, so 5 × 4 × 3 × 2 × 1 = 120 arrangements.
How to Solve Logical Arrangement Questions
One straightforward, one multi-step, and one classic mistake to avoid.
1. Product Rule Choices
Question: Sean has 5 different hats and 3 different scarves. Each outfit uses one hat and one scarf. If Sean must choose one particular scarf, how many outfits are possible?
Worked Method
Step 1: The scarf choice is fixed, so it contributes only 1 option.
Step 2: There are still 5 possible hats.
1 × 5 = 5 outfits.
Tip: A fixed choice does not disappear. It counts as 1 option, not 0.
2. Restricted Code Patterns
Question: A ticket code uses two letters chosen from I, L, O, S, then one number chosen from 1, 2, 3, 4. Repeated letters are allowed. How many codes have two different letters and end in an even number?
Worked Method
Step 1: There are 4 choices for the first letter.
Step 2: The second letter must be different, so only 3 choices remain.
Step 3: The even numbers are 2 and 4, so there are 2 number choices.
4 × 3 × 2 = 24 codes.
Tip: Repeats are allowed in the full code system, but this particular question adds the restriction "two different letters".
3. Pairings Are Not Ordered
Question: 6 debaters are paired with every other debater once. How many debates are there in total?
Worked Method
Step 1: Each of the 6 people could be paired with 5 others, giving 6 × 5 = 30 ordered pair listings.
Step 2: Each debate has been counted twice. For example, A with B and B with A are the same debate.
30 ÷ 2 = 15 debates.
Tip: Divide by 2 for pairings where order does not matter. Do not divide for codes, where AB and BA are different codes.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Logical Arrangement pack contains 90 questions across 3 printable test sets, with 200 sub-questions covering product rule counting, codes, handshakes, pairings, digit arrangements, anagrams, and restricted patterns.
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