Remainder Riddle Questions
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.
The Rules Every Remainder Riddle Question Uses
A correct option must give the same leftover amount after division by both numbers in the question.
➗ Rule 1: Divide by both numbers
Each answer option must be checked against both divisors in the question.
Example: For 19, check division by 3 and by 9.
🧮 Rule 2: Compare the remainders
The quotient does not need to match. Only the leftover amount matters.
Example: 19 = 18 + 1 for both 3 and 9.
✅ 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: 17 leaves remainder 2 with 3, but 8 with 9.
How to Solve Remainder Riddle Questions
Three useful moves: calculate both remainders, compare only the leftovers, and remember that 0 can be the matching remainder.
1. 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 = 18 + 1, so the remainder is 1.
Step 2: Test 19 with 9: 19 = 18 + 1, so the remainder is also 1.
Step 3: The remainders match.
Answer: D
2. 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
3. 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.
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The full Remainder Riddle pack contains 90 multiple-choice questions across 3 printable test sets, with answer keys included for quick checking.
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