A, B, C, D are distinct positive integers such that AB = 60, CD = 60, and A - B = C + D. What is the value of A?

Guest May 17, 2020

#2**+2 **

In this problem because A **- **B = C **+ **D, A has to be pretty big. So we start trying some cases in which A is big. First we try A = 10, so B has to equal 6. 10 -6 = 4. No 2 positive integers that multiply to 60 add up to 4. Next, we try 15 if A is 15 then B is 4，15 - 4 = 11 the smallest factor sum is 6 and 10 which adds up to 16 so that isn't right. Finally, we try A = 20 B = 3, 20 - 3 = 17. 12*5 = 20 and they add to 17 so we have found the answer. A = 20.

Mathlord May 18, 2020