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From the second statement K cannot be an even number as sum of K consecutive numbers will always be odd when K is even and odd number cannot be divided by even number. Substitute an odd number in place of K Sum of 5 consecutive numbers = 13 + 14+15+16+17 = 75 is divisible by 5 Sum of 7 consecutive numbers = 8+9+10+11+12+13+14 = 77 is divisible by 7 So statement 2 alone is sufficient to conclude K is odd and hence K^2 is odd.