pnf619 wrote:

Please help to solve the following:-

Is s between r and t

a) |r-s| < |r-t|

b) |r-s| < |s-t|

Is s between r and t

a) |r-t| > |r-s|

b) |r-t| > |t-s|

Use the property of absolute value, \(|a - b|\) is the distance between \(a\) and \(b,\) and visualization on the number line.

Q1:

(1) t- - - - s - - r - - s - - - - t

\(s\) and \(t\) can be on either side of \(r.\)

Not sufficient.

(2) t - - r - - - s - - - r - - t

Now \(r\) and \(t\) can be on either side of \(s.\)

Not sufficient.

(1) and (2): Still not sufficient, as one can see from the above situation for (1).

Answer E

Q2:

(1) t - - - s - - r - - s - - - t

\(s\) and \(t\) can be on either side of \(r.\)

Not sufficient.

(2) r - - s - - - t - - - s - - r

Now \(r\) and \(s\) can be on either side of \(t.\)

Not sufficient.

(1) and (2): Sufficient, because in (1) now \(s\) must be between \(r\) and \(t.\)

Answer C

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