Remainder Riddle Questions Practice Test Worksheets
Remainder riddle questions ask which number leaves the same remainder when divided by two different divisors. The reliable method is to divide each option by both numbers and compare the two remainders.
For students who know division, but get stuck using remainders as clues to identify the hidden number.
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What Do Remainder Riddles Questions Look Like?
Remainder riddle questions ask you to identify an unknown number based on the remainders left when dividing by different numbers. Solving them requires testing multiples and eliminating options systematically. Here is a worked example.
Match a Non-Zero Remainder
Question: Which number has the same remainder when divided by 3 and 9?
Options: A. 12 B. 48 C. 17 D. 19
Worked Method
Step 1: Test 19 with 3: 19 = 3 × 6 + 1, so the remainder is 1.
Step 2: Test 19 with 9: 19 = 9 × 2 + 1, so the remainder is also 1.
Step 3: The remainders match.
Answer: D
Rules to Help You Solve Remainder Riddles Questions
To solve remainder riddles like the example above, test candidate numbers against each divisor in order. Follow these three rules:
➗ Rule 1: Divide by both numbers
Check each option against both divisors. To find a remainder, subtract the largest multiple of the divisor that does not exceed the number. The remainder must be non-negative and smaller than the divisor.
Example: 19 = 3 × 6 + 1, so dividing 19 by 3 leaves remainder 1.
🧮 Rule 2: Compare the remainders
The quotient does not need to match. Only the leftover amount matters.
Example: 19 = 3 × 6 + 1 and 19 = 9 × 2 + 1. The quotients are 6 and 2, but both remainders are 1.
✅ Rule 3: Zero can be a remainder
If a number divides exactly by both divisors, the remainder is 0 for both.
Example: 10 divided by 2 and 5 leaves remainder 0.
⚠️ Rule 4: Do not choose by divisibility alone
A number may be divisible by one divisor but still fail the other remainder check.
Example: 12 leaves remainder 0 when divided by 3, but remainder 3 when divided by 9. The remainders do not match.
Two More Worked Examples
Here are two more examples showing how to handle exact division clues and test every condition thoroughly.
Use Remainder Zero
Question: Which number has the same remainder when divided by 2 and 5?
Options: A. 29 B. 19 C. 23 D. 10
Worked Method
Step 1: 10 divided by 2 leaves no remainder.
Step 2: 10 divided by 5 also leaves no remainder.
Step 3: Both remainders are 0, so they match.
Answer: D
Do Not Stop After One Divisor
Question: Which number has the same remainder when divided by 6 and 7?
Options: A. 49 B. 25 C. 42 D. 33
Worked Method
Step 1: 42 divided by 6 leaves remainder 0.
Step 2: 42 divided by 7 also leaves remainder 0.
Step 3: Both remainders match, so 42 works.
Answer: C. The trap: 49 is divisible by 7, but 49 divided by 6 leaves remainder 1.
