Consider the following set of inequalities: pq, sr, qt, sp, and rq...

Question

Consider the following set of inequalities: p>q, s>r, q>t, s>p, and r>q. Between which two quantities is no relationship established?

GMAT Panda · Accepted Answer

Answer A: No relationship is established between p and r. We first make note of all the given inequalities. p>q s>r q>t s>p r>q We then connect the inequalities in a chain to compare s and t. Using the chain rule, if s>p and p>q and q>t, then s>t We then connect the inequalities in a chain to compare p and t. Using the chain rule, if p>q and q>t, then p>t We then connect the inequalities in a chain to compare r and t. Using the chain rule, if r>q and q>t, then r>t We then connect the inequalities in a chain to compare s and q. Using the chain rule, if s>p and p>q, then s>q We compare p and r: both are greater than q but they are not directly related. p>q r>q Neither p>r nor r>p can be concluded

Explanation	Calculations	Help
$We first make note of all the given inequalities.$	$p > q s > r q > t s > p r > q$
$We then connect the inequalities in a chain to compare s and t.$	$Using the chain rule, if s > p and p > q and q > t, then s > t$
$We then connect the inequalities in a chain to compare p and t.$	$Using the chain rule, if p > q and q > t, then p > t$
$We then connect the inequalities in a chain to compare r and t.$	$Using the chain rule, if r > q and q > t, then r > t$
$We then connect the inequalities in a chain to compare s and q.$	$Using the chain rule, if s > p and p > q, then s > q$
$We compare p and r: both are greater than q but they are not directly related.$	$p > q r > q Neither p > r nor r > p can be concluded$

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