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Given that \(0\lt p\lt q\lt r\lt s\) and \(p, q, r, s\) are integers, which of the following is the smallest?( )
A. \(\frac {p+q}{r+s}\)
B. \(\frac {p+s}{q+r}\)
C. \(\frac {q+s}{p+r}\)
D. \(\frac {r+s}{p+q}\)
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Question

Given that \(0\lt p\lt q\lt r\lt s\) and \(p, q, r, s\) are integers, which of the following is the smallest?( )
A. \(\frac {p+q}{r+s}\)
B. \(\frac {p+s}{q+r}\)
C. \(\frac {q+s}{p+r}\)
D. \(\frac {r+s}{p+q}\)

Answer

A
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Solution

A fraction is relatively smaller if the difference between numerator and denominator is high.
\(0\lt p\lt q\lt r\lt s\)
\(\implies p,q\) are the smallest and \(r,s\) are the greatest among \(p,q,r,s\)
\(\implies \) Difference between \(p+q\) and \(r+s\) is higher than any other combination, such that \(p+q\) is very small in comparison with \(r+s\).
Thus, \(\frac {p+q}{r+s}\) is the smallest.
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