## 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__

__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__

__To Find__

We need to determine

- There is no relationship between which two quantities.

__Approach & Working__

__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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