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 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 ListAdd each pair; only 3 and 8 sums to 11.
Only one row meets both conditions, so that pair must be the answer.
4.OA.A.3Guess And CheckThe 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).