GMAT Practice Question: Consider the following set of inequalities: p>q, s>r, q>t, s>p, and r>q...
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?
- p and r
- s and t
- s and q
- p and t
- r and t
Topics: inequalities
Solution
Step 1
We first make note of all the given inequalities.
p>q s>r q>t s>p r>q
Step 2
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
Step 3
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
Step 4
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
Step 5
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
Step 6
We compare p and r: both are greater than q but they are not directly related.
p>q r>q \text{Neither }p>r\text{ nor }r>p\text{ can be concluded}
Answer
\text{Answer A: No relationship is established between }p\text{ and }r.
