Q: Which pair of numbers whose sum is 40 has the largest product?

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10 and 28

Any pair of prime numbers. 5 and 7 11 and 13

If you are looking for two prime numbers whose difference is 1, then the numbers have to be 1 & 3.

Any two odd numbers will have an odd product and an even sum.

10 and 120

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41 & 39 = 1599. (40 x 40 = 1600 but I assume you meant different numbers)

1 and 1

That's a factor pair.

10 and 28

They are: 2 and 140

17 & 18 (306)

They are 2 and 140 because their LCM is 140 and their product is 280

Any pair of prime numbers. 5 and 7 11 and 13

2 and 2

(2356,1)(1178,2)(589,4)(124,19)(76,31)(62,38)

No pair of real numbers can do that.The numbers are4.5 + j 18.43234.5 - j 18.4323

38 + 62 = 100 38 x 62 = 2,356