Question

If $p,q,r,s,t$ are numbers such that $p+q<r+s$ ; $q+r<s+t$ ; $r+s<t+p$ ; $s+t<p+q$, then the largest and the smallest numbers are respectively

• A. $p$ and $q$
• B. $r$ and $t$
• C. $r$ and $p$
• D. $q$ and $p$

Answer 1

The correct option is A $p$ and $q$

Let $p+q<r+s$ .... (i)

$q+r<s+t$ .... (ii)

$r+s<t+p$ .... (iii)

$s+t<p+q$ .... (iv)
From equation (i) and (iii); $q<t$

From equation (ii) and (iv); $r<p$

From equation (i) and (iv); $t<r$

Thus $q<t<r<p$

From (i) $p+q<r+s$, also $r<p\Rightarrow q<s$

From (iv) $s+t<p+q\Rightarrow s<p$

Hence, largest and smallest numbers are $p$ and $q$ respectively.