Problem
Find unknowns satisfying multiple conditions
A whole number lies strictly between 30 and 50. It is divisible by 7. The number two less than it is divisible by 5. Find the number.
Reasoning · Grade 3-1 Multiplication and Division
Your answer
Watch out It reads as if the number itself divides by 5, but the condition sits on the number two less.
How to solve
Strategy Make a Systematic List — The strongest condition (divisible by 7, between 30 and 50) gives only a few candidates, so I list those first, then eliminate the ones that fail the 'minus 2 is a multiple of 5' test. This keeps the candidate set tiny and finite.
1STEP 1
List multiples of 7 between 30 and 50
The multiples of 7 in range are 35, 42, 49.
7 × 5 = 35, 7 × 6 = 42, 7 × 7 = 49
Using the divisibility-by-7 rule first is smart because it leaves only three numbers to check instead of all 19 numbers from 31 to 49.
3.OA.A.2Make A Systematic List2STEP 2
Subtract 2 from each candidate
Two less gives 33, 40, 47.
35-2=33, 42-2=40, 49-2=47
Each candidate just needs one small subtraction to prepare it for the last test.
3.NBT.A.2Make A Systematic List3STEP 3
Keep only the one whose 'minus 2' is a multiple of 5
Only 40 divides by 5, so the number is 42.
40 = 5 × 8
Numbers divisible by 5 always end in 0 or 5, so I can spot the survivor at a glance and eliminate the other two.
3.OA.A.2Eliminate PossibilitiesA number is divisible by 5 exactly when it ends in 0 or 5, so the survivor can be spotted at a glance.
Why?
Every ten is itself a multiple of 5, so everything above the ones place already divides cleanly and only the last digit can spoil it.
🧱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 two candidates whose last digit fails are crossed out at once, leaving exactly one number standing.
🧱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.
Answer
42
Check 42 against all three rules: it is between 30 and 50, 42 = 7 x 6 so it is divisible by 7, and 42 - 2 = 40 = 5 x 8 so the 'minus 2' is divisible by 5. All three hold, and no other candidate (35 or 49) passes, so the answer is unique.
Takeaway
Start with the pickiest clue (divisible by 7) to get just a few candidates, then knock them out one by one - that is Grade 3 multiplication facts at work!
- List multiples of 7 between 30 and 50
- Subtract 2 from each candidate
- Keep only the one whose 'minus 2' is a multiple of 5