Hi everyone, this must be a stupid question. I am usually really bad at counting.

See this example, (x,y) are both positive integers, and the sum of x+y is less than or equal to 20, how many of those pairs in total?

I am bad at adding one or subtracting one when counting numbers, say, how many consecutive integer numbers are between 5 to 200, it should be 200-5+1 right? I guess that is why the above question complicates? I am doing like (1,19)…(19, 1), and then like forming a triangle in the first quartdrum, and then I don’t know how to count.

So in the above question you’ve correctly identified the extreme pairs, that is, (1, 19) and (19, 1). How many numbers are between 1 and 19, both inclusive? 1 + 19 - 1 = 19, which is the answer.

Not really…There are other pairs, say (2, 18), which is not a straight line between (19,1) and (1, 19).
I don’t exactly remember one of the choices, but certainly much bigger than 20. This question was found at GRE or GMAT forum.

BUT (1,1),(1,2)…(1,19) already have 19 pairs right. then, (2, 1), (2,2)…(2,18) are another 18 pairs, so on and so forth. How can there only be 19 pairs???