Bunuel wrote:

If \(0 < st < 1\), then which of the following can be true?

(A) s < -1 and t > 0

(B) s < -1 and t < — 1

(C) s > - 1 and t < - 1

(D) s > 1 and t < —1

(E) s > 1 and t > 1

Given 0 < st < 1,

we have s*t > 0, so s & t both have the same sign

s*t < 1, so either s or t or both are between 0 & 1 or both are between -1 & 0

(A) s < -1 and t > 0 gives opposite signs to s & t, hence not possible. s = -2 , t = 1 , s*t = - 2 < 0

(B) s < -1 and t < — 1 both are less than -1, hence not possible. s = -2, t = -1.5, s*t = 3 > 1

(C) s > - 1 and t < - 1 both can be of same sign & s can be more than -1 but less than 0. Possible. s = -0.5, t = - 1.2, s*t = 0.6 < 1

(D) s > 1 and t < —1 gives opposite signs to s & t, hence not possible. s = 2, t = -2, s*t = -4 < 0

(E) s > 1 and t > 1 both are more than 1, hence not possible. s = 1.2, t = 1.2, s*t = 1.44 > 1

Answer C.

Thanks,

GyM