hard sufficiency

Let u = units digit, t = tens digit. Also, we know that t = 2u.

(1) gives us the additional relation of t (t + u) = 54. We have two equations and two unknowns, and so this can be solved. Do I want to solve it? No. But it can be.

(2) gives the additional relation ut/2 = 9, another happy equation, leaving us with two equations and two unknowns. Sufficient.

D.

(Subtle note: it might be worth checking that the two equations do not "row reduce", or rather, are not constant multiples of one another, as if they are, they are considered the same equation. Still, it's fairly obvious here that they are not.)

thank youuu

hey guys

i've found that in some DS questions it's much easier to list out the options rather than go through the formula

in this case if the tens digit is twice the units digit, there're only 4 options

21
42
63
84

according to (1), 63 works since 6 * (6+3) = 54; sufficient
according to (2), 6*3 / 2 = 9; sufficient

D

Not a bad idea, but remember, you must test all the other solutions as well to make sure they DON'T work in that case. If more than one satisfies the conditions, then the data is insufficient.