Qa - correlation

For two variables x and y , it is known that the cov(x,y) = 80, the variance of x is 16 and the sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data is

a) 7            b) 8            c) 9                   d) 10

Thanks in advance.

we will try to solve the problem by exploiting the fact that correlations is always less than or equal to 1

correlation = 80/((standard deviation of x)*(stadard deviation of y))

standard deviation of x = squareroot(16) = 4 standard deviation of y = squareroot (250/N) = 5(10/N)^0.5

so we get 80/(4*5*(10/N)^0.5)  <1 implies 4 < (10/n)^0.5 implies 16 <10/N implies N<10/16 which is impossible. the figures do not make sense once again. even if they do we cannot find out N just with the help of covariance.

variance of y how much ??/

we don't know because we were given only covariance and variance of x we could calculate it if we had correlation

Thanks.