Added note: the problem hopefully says (or should say, if it doesn't) something like "What is one possible value of k?" We're told that X<Y, which again means that the average must land higher than the midpoint of 10 and 20 (the Y tests on which we got 20 points are pulling the average closer to them, since there are more of them), and we're told that K is a positive integer, but in reality it could be any of the positive integers within the acceptable range, i.e. 16, 17, 18, or 19. (If x and y were 2 and 3 respectively, K would be 16; if x and y were 3 and 7 respectively, K would be 17; if x and y were 1 and 4 respectively, K would be 18; and if x and y were 1 and 9 respectively, K would be 19. Furthermore, if x and y were anything in the *ratio* 2:3, K would be 16, and so on for all the possibilities.)
Ashley Newman-Owens
GMAT Instructor
Veritas Prep
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