tmua.me Extreme Set C Paper 2 · Question 17

The positive real numbers $a,b,c,d$ satisfy

ab=1,\qquad bc=2,\qquad cd=6,\qquad da=3.

Consider the two conditions

Which of the following correctly describes when these conditions are sufficient to guarantee that all four numbers $a,b,c,d$ are rational?

AS alone is sufficient, but T alone is not.

BT alone is sufficient, but S alone is not.

CEach of S and T alone is sufficient.

DS and T together are sufficient, but neither alone is sufficient.

EEven S and T together are not sufficient.

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