Bunuel wrote:
Three points T, U and V on the number line have coordinates t, u, and v respectively. Is T between points U and V?
(1) \(t^2<4<u^2<v^2\). Since all parts of the inequality are non-negative, we can safely take the square root from it: \(|t| < 2 < |u| < |v|\). It's possible that T is between U and V, for example, if t=0, u=-3 and v=4, as well as it's possible that it's not, for example, t=0, u=3 and v=4. Not sufficient.
(2) u<0<v. Clearly insufficient.
(1) Since from (2) u<0<v, then from (1) we get \(|t| < 2 < -u < v\). If break it: we'll get \(u<-2\) (from 2 < -u), \(-2<t<2\) (from |t| < 2), and \(2<v\). T is between U and V. Sufficient.
Answer: C.
Hope it's clear.
When you take the sq rt of 4 in this, shouldn't the result be +/- 2?