Ranges of Inequalities

[baily106]

Hello,

I read this question in NOVA's math prep course. The explanation wasn't adequate. The question: If 5<X<10 and Y=X+5, what is the greatest possible integer value of X+Y?

The answer choices are:
A) 18
B) 20
C) 23
D) 24
E) 25

I picked C because, the highest integer value of X can be 9. If Y=X+5, then Y=14. Then X+Y=23. However, the answer is D. Could you please explain? My only thought is that maybe one can pick non-integer values for X, but X+Y has to be an integer as to why 24 is the answer, but am not sure.

Thanks.

[tommywallach]

Hey Baily,

X and Y don't have to be integers, only X + Y.

We have to pick something that ends in .5 (because if we add 5 to it, it will still end in .5, so it will be an integer sum). What's the biggest thing less than 10 that ends in .5?

X = 9.5

So...

Y = 14.5

-t