Can I(aX+bY,C) larger than max{I(X,C),I(Y,C)}

Question

X,Y are two random variables, and in the range of (0,1)

C is the class tags. C=1,2,3...10. p(C=1)=p(C=2)=p(C=3)....=p(C=10)

a,b are in the range of (0,1)

aX+bY is the linear combination of two random variables

I(aX+bY,C) means the mutual information between sum of aX and bY and the Class C.

Can I(aX+bY,C) larger than I(X,C) or I(Y,C)?

I(aX+bY,C)>max{I(X,C),I(Y,C)}?

Thanks!