Olympiad workbookIOQMBasics of Mathematics
Find the number of positive integers n such that n + n+1 < 11 .
Correct answer
29
Step-by-step solution
aligned & N + N +1 < 11 & ~N =1,2,3,4,5,6,7,8 .16 25 & ~N +1 + N =11 ...(1) & 1 ~N +1 - N =11 & ~N +1 - N = 1 11 ...(2) & 2 ~N +1 = 122 11 ~N +1 = 61 11 ~N +1= 3721 121 & ~N = 3600 121 =29.75 aligned So 29 values