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?
Each question gives three separate clues and five answer choices, A to E. Use all three clues to work out the number. This is the first question from the free sample, with the same option-by-option elimination used in its answer key.
Eliminate Using Digit Clues
Its digits add up to 8.
The difference between its digits is 6.
It is less than 50.
What number is it?
Checking Options by Elimination
Check each option against clues 1, 2, and 3 in the order above. Eliminate it as soon as a clue fails.
A) 19: Fails clue 1. 1 + 9 = 10, not 8.
B) 47: Fails clue 1. 4 + 7 = 11, not 8.
C) 71: Fails clue 3. Its digits add to 8 and differ by 6, but 71 is not less than 50.
D) 17: Passes all clues. 1 + 7 = 8; 7 − 1 = 6; 17 is less than 50.
E) 53: Fails clue 2. Its digits add to 8, but 5 − 3 = 2, not 6.
Answer: D (17)
Tip: 71 passes the first two clues. Keep checking: the final clue eliminates it.
Rules to Help You Solve Numerical Deduction Questions
Check each answer choice against the clues in order, as the sample answer key does. Cross out a choice at its first failed clue, and confirm that the remaining choice passes all three. Keep these four rules in mind:
🔍 Rule 1: Test every clue
An option is correct only if it passes all three clues.
Example: 17 passes all three clues: 1 + 7 = 8, 7 − 1 = 6, and 17 is less than 50.
✂️ Rule 2: Eliminate fast
Once an option fails a clue, cross it out and move on.
Example: 19 fails clue 1 because 1 + 9 = 10, not 8. Cross it out without checking the other clues.
🔁 Rule 3: Reverse digits carefully
Reverse a two-digit number by swapping its digits: 75 becomes 57. For a reversal that is 18 less, subtract the reversed number from the original. For a reversal that is more, subtract the original from the reversed number.
Example: 75 − 57 = 18, so the reversal is 18 less than the original.
➕ 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: 17 has digit sum 1 + 7 = 8 and digit difference 7 − 1 = 6.
Two More Worked Examples
These are questions 2 and 3 from the free sample. Each solution checks all five options, eliminates choices at the first failed clue, and confirms every clue for the correct answer.
Eliminate Using Even Numbers and Multiples
It is an even number.
The difference between its digits is 1.
It is a multiple of 5.
What number is it?
Checking Options by Elimination
Check each option against clues 1, 2, and 3 in the order above. Eliminate it as soon as a clue fails.
A) 62: Fails clue 2. 62 is even, but 6 − 2 = 4, not 1.
B) 10: Passes all clues. 10 is even; 1 − 0 = 1; 10 = 5 × 2.
C) 65: Fails clue 1. 65 is odd, not even.
D) 76: Fails clue 3. 76 is even and 7 − 6 = 1, but 76 ÷ 5 leaves a remainder of 1.
E) 44: Fails clue 2. 44 is even, but 4 − 4 = 0, not 1.
Answer: B (10)
Tip: 76 passes the first two clues but is not a multiple of 5. One failed clue is enough to eliminate a choice.
Eliminate Using a Reversal Clue
It is a multiple of 3.
It is an odd number.
Its reversal is 18 less than the original.
What number is it?
Checking Options by Elimination
Check each option against clues 1, 2, and 3 in the order above. Eliminate it as soon as a clue fails.
A) 99: Fails clue 3. 99 is a multiple of 3 and is odd, but its reversal is 99: 99 − 99 = 0, not 18.
B) 35: Fails clue 1. 35 ÷ 3 leaves a remainder of 2.
C) 78: Fails clue 2. 78 is a multiple of 3, but it is even, not odd.
D) 75: Passes all clues. 75 = 3 × 25; 75 is odd; its reversal is 57 and 75 − 57 = 18.
E) 12: Fails clue 2. 12 is a multiple of 3, but it is even, not odd.
Answer: D (75)
Tip: “18 less” means original minus reversal equals 18. Keep the subtraction in that order.
