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Number Reasoning

Numerical Deduction Puzzles

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.

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⬇ Download a free 3-question sample (PDF)

The Rules Every Numerical Deduction Question Uses

Each option is a possible two-digit number. A correct answer must satisfy all three clues, not just one or two.

Clues: less than 50, prime, digit difference is 4 Option less than 50 prime digit gap is 4 37 yes yes 7 - 3 = 4 95 no stop already failed 11 yes prime 1 - 1 = 0

🔍 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

Some clues compare a number with its reversal, such as 21 becoming 12.

Example: 21 - 12 = 9.

➕ Rule 4: Check digit facts

Digit sum, digit difference, parity, multiples, squares, and primes are common clues.

Example: 85 has digit sum 13 and is a multiple of 5.

How to Solve Numerical Deduction Puzzles

Three useful moves: test each clue in order, stop when an option fails, and be precise with digit reversals.

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Easy

1. 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

Test each option until only one passes every clue 37 passes 95 > 50 11 gap 0 16 not prime 29 gap 7 37 passes all three checks 37 < 50, 37 is prime, and 7 - 3 = 4 Answer: A

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

Medium

2. 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

Check the square, then reverse the digits carefully 21 original 12 reversal 21 x 21 = 441 3-digit square 21 - 12 = 9 reversal is 9 less Answer: A

Worked Method

Step 1: 21² = 441, which has 3 digits.

Step 2: 21 is not prime because 21 = 3 x 7.

Step 3: Reversing 21 gives 12, and 21 - 12 = 9.

Answer: A

Classic Trap

3. Do Not Stop After Two 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

Do not stop after the first clue that looks right Option multiple of 5 digit sum 13 reverse is 27 less 85 yes 8 + 5 = 13 85 - 58 = 27 95 yes 9 + 5 = 14 already failed 95 is the trap: it matches one clue, not all three.

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.

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 PDF

Get the Full Practice Pack

The full Numerical Deduction pack contains 90 clue-based questions across 3 printable test sets, with answer keys included for checking and review.

Numerical Deduction practice papers showing printable clue-based number puzzles Key learning benefits for numerical deduction worksheets including logic and reasoning
📄 3 Test Sets - 30 questions per set
🔍 90 numerical deduction questions
✅ Answer keys included
🖨️ Instant download printable PDF
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