Numerical Deduction Puzzles Practice Test Worksheets
Numerical deduction questions give three clues about a two-digit number. The safest method is to test each answer option against every clue, crossing out choices as soon as they fail.
For students who can do arithmetic, but lose marks when they have to infer hidden values from several clues at once.
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What Do Numerical Deduction Questions Look Like?
Numerical deduction questions challenge you to discover a secret number using a set of logical clues about parity, digits, sums, and ranges. Here is a worked example.
Check a Simple Set of Clues
Question: The number is less than 50, prime, and the difference between its digits is 4. What number is it?
Options: A 37 B 95 C 11 D 16 E 29
Worked Method
Step 1: 37 is less than 50.
Step 2: 37 is prime.
Step 3: Its digit difference is 7 - 3 = 4, so it passes all clues.
Answer: A
Rules to Help You Solve Numerical Deduction Questions
To solve numerical deduction puzzles like the example above, filter options clue by clue. Keep these three rules in mind:
🔍 Rule 1: Test every clue
An option is correct only if it passes all three clues.
Example: 37 passes less than 50, prime, and digit difference 4.
✂️ Rule 2: Eliminate fast
Once an option fails a clue, cross it out and move on.
Example: 95 fails "less than 50", so it cannot be correct.
🔁 Rule 3: Reverse digits carefully
Reverse a two-digit number by swapping its digits: 21 becomes 12. If the reversal is 9 less than the original, subtract the reversed number from the original to check that the answer is 9.
Example: 21 - 12 = 9.
➕ Rule 4: Check digit facts
Clues may ask about digit sums, digit differences, whether a number is odd or even, multiples, squares, or primes. For a digit sum, add the digits. For a digit difference, subtract the smaller digit from the larger digit.
Example: 85 has digit sum 13 and is a multiple of 5.
Two More Worked Examples
Here are two more examples showing how to work with digit reversal clues and test all conditions.
Use Reversal Clues
Question: The number has a 3-digit square, is not prime, and its reversal is 9 less than the original. What number is it?
Options: A 21 B 25 C 51 D 19 E 70
A "3-digit square" means that when the number is multiplied by itself, the answer has three digits. Check the listed options against all three clues.
Worked Method
Step 1: 21² = 441, which has 3 digits.
Step 2: 21 is not prime because 21 = 3 × 7.
Step 3: Reversing 21 gives 12, and 21 - 12 = 9.
Answer: A
Check All Three Clues
Question: The number is a multiple of 5, its digits add to 13, and its reversal is 27 less than the original. What number is it?
Options: A 10 B 52 C 94 D 85 E 95
Worked Method
Step 1: 85 is a multiple of 5.
Step 2: Its digit sum is 8 + 5 = 13.
Step 3: Reversing 85 gives 58, and 85 - 58 = 27.
Answer: D. The trap: 95 is a multiple of 5, but its digit sum is 14, so it fails.
