Problem
Find a number from division clues
A whole number lies strictly between 30 and 49. Subtracting 3 leaves a multiple of 5. The number itself is a multiple of 8. Find it.
Reasoning · Grade 3-2 Conditions and Division
Your answer
Watch out Reading the number itself as a multiple of 5 lands on 40 — the condition sits on the number minus 3.
How to solve
Strategy Make a Systematic List — The range 31-48 is small and finite, so I can list the numbers that fit each clue separately, then keep only the number that appears on every list. The divisibility-by-8 clue gives the shortest list, so I start there and check the other two clues against it.
1STEP 1
List the multiples of 8 in range
The multiples of 8 in range are just 32, 40, 48.
8 × 4 = 32, 8 × 5 = 40, 8 × 6 = 48
Counting by 8s is a Grade 3 multiplication fact, and it shrinks the whole problem to just three numbers to check.
3.OA.C.7Make A Systematic List2STEP 2
Apply the 'minus 3 is a multiple of 5' clue
Less 3 they give 29, 37 and 45 — only 45 divides by 5.
32-3=29, 40-3=37, 48-3=45=5 × 9
A multiple of 5 always ends in 0 or 5, so I can spot it instantly without dividing.
3.NBT.A.2Eliminate PossibilitiesA multiple of 5 always ends in 0 or 5, so the clue can be checked at a glance without dividing.
Why?
Every ten is itself a multiple of 5, so everything above the ones place already divides cleanly and only the last digit matters.
🧱Divisibility tests come from place valueBecause 10, 100 and 1000 sit in a fixed relation to a divisor, only certain digits matter — the last two decide 4, the digit sum decides 3 and 9.
Why?
The candidates whose last digit fails are struck out at once, leaving a list short enough to finish by hand.
🧱Rule out the rest and the last one is forcedIf every possibility but one has been ruled out, the survivor must be the answer — no further checking is needed.
3STEP 3
Confirm the range clue
So the number is 48, and it sits in range.
30 ＜ 48 ＜ 49
Checking the final survivor against every clue guarantees the answer is the unique number, not just one that fits some clues.
3.OA.A.4Guess And CheckAnswer
48
48 ÷ 8 = 6, 48 − 3 = 45
48 is a whole number strictly between 30 and 49, 48 = 8 x 6 is divisible by 8, and 48 - 3 = 45 = 5 x 9 is divisible by 5. All three conditions hold and no other multiple of 8 in range works, so the answer is unique and correct.
Takeaway
Start with the clue that gives the shortest list (multiples of 8), then cross off anything that breaks the other rules - only one number is left!
- List the multiples of 8 in range
- Apply the 'minus 3 is a multiple of 5' clue
- Confirm the range clue