OGQR 2020: Question No. 81
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?
| Source | OGQR 2020 |
| Type | Problem Solving |
| Topic | Algebra |
| Sub-Topic | Inequality |
| Difficulty | Medium |
Solution
Given
In this question, we are given a set of inequalities, as follows
- p > q
- s > r
- q > t
- s > p
- r > q
To Find
We need to determine
- There is no relationship between which two quantities.
Approach & Working
Combining the relations s > p, p > q and q > t, we can write
- Relation 1: s > p > q > t
Also, combining the relations s > r, r > q, and q > t, we can write
- Relation 2: s > r > q > t
Now, checking the options one at a time:
- Between p and r: no direct relation exist
- Between s and t: from either relation we can say s > t
- Between s and q: from either relation we can say s > q
- Between p and t: from relation 1 we can say p > t
- Between r and t: from relation 2 we can say r > t
Hence, the correct answer is option A.
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