Competition · AMC preparation · step 4 of 4
AMC 8 · 2001 · #2
Grade 4 arithmeticnumber-theoryPick an answer.
AMC 8 2001 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Because the product is 24, the two numbers must be a factor pair of 24. There are only four positive whole-number factor pairs, so Tool #2 (Make a List) lets us write them all down in a few seconds. For each pair, Tool #6 (Guess and Check) does the rest: just add the two numbers and see whether the sum is 11. No algebra is needed — the short list does all the work.
List the factor pairs of 24
List every positive factor pair of 24, walking the divisors up from 1.
Grade 4 factor-pair work: list divisors in order so no pair is missed.
4.OA.B.4Make A Systematic ListTest each sum against 11
Add each pair; only 3 and 8 sums to 11.
Only one row meets both conditions, so that pair must be the answer.
The two mystery numbers can only be the pair 3 and 8.
▸ Why?
Since the two numbers multiply to 24, each one must go into 24 evenly, so the pair has to be one of the factor pairs of 24: (1, 24), (2, 12), (3, 8), or (4, 6).
▸ Why?
A whole number that multiplies with another to make 24 splits 24 into that many equal groups with nothing left over, which is exactly what it means to be a factor of 24.
▸ Why?
Adding the two numbers in each of those four pairs gives 25, 14, 11, and 10, and only 3 and 8 reach the required sum of 11.
▸ Why?
The sum of a pair is just its two numbers joined into one total, so adding them and comparing to 11 faithfully tests the sum condition.
Take the larger number
The question asks for the larger of the two, which is 8.
Once the right pair is found, picking the larger value is a final reading-the-question check.
4.OA.A.3Make A Systematic ListWhen a problem gives both the product and the sum of two whole numbers, list the factor pairs of the product first — there are usually only a handful — and pick the one whose sum matches. Here the factor pair (3, 8) adds to 11, so the larger number is 8, choice (D).
- List the factor pairs of 24
- Test each sum against 11
- Take the larger number
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