Consider the following set of inequalities: p q, s r, q t, s p

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?

A. p and r
B. s and t
C. s and q
D. p and t
E. r and t

PS09502.01
Quantitative Review 2020 NEW QUESTION

IanStewart · Accepted Answer

Just by 'chaining' together the inequalities, we can arrive either at:

s > p > q > t

or at:

s > r > q > t

but we have no way to compare p and r.

EgmatQuantExpert · Answer

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.

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-Algebra-e1533292163516.png

Archit3110 · Answer

negate each option A/B/C/D/E as we go step by step
given
p>q 
s>r
q>t
s>p
r>q
seeeing all the relations we can say only p and r relation is missing
IMO A

LeoN88 · Answer

The diagram.

ScottTargetTestPrep · Answer

Let’s add together any inequalities with like terms:

Since p > q and s > p, we have s > q (so choice C is not correct).

Since p > q and q > t, we have p > t (so choice D is not correct).

Since r > q and q > t, we have r > t (so choice E is not correct).

Since s > q (from analysis above) and q > t, we have s > t (so choice B is not correct).

Thus, we see that p and r do not have a relationship.

Answer: A

Basshead · Answer

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 > q  ,   s > r  ,   q > t  , s > p, and   r > q   =

p > q > t

s > r > q

From the inequalities we can determine s > r and s > p, however we don't know if r > p or p > r.

Answer is A.

Ritwickhota · Answer

Hi, Did not understand the logic. I arrived at S>P>R>Q>T by combining all the inequalities and did not think to choose only select ones. Please can someone explain what I am missing here?

Kinshook · Answer

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

s > p > q > t 
s > r > q

IMO A

Anonymous · Answer

Guys, I'd like you to help me clear out a point.
Since p<s and r<s then we can say that there is a relationship between p,r (for instance if p=8 and r=9 then p<r or for p=8 and r=7 p>r).
The reason we choose A is because the direction of the inequality depends on the value of the variables p,r whereas in the other choices is fix?

Bunuel · Answer

From p > q, s > r, q > t, s > p, and r > q we can get that:

s > p > q > t

and:

s > r > q > t

As you can see we know that:

s > t;
s > q;
p  > t;
r  > t.

However, we cannot say whether  p > r, p < r, or  p = r.

Anonymous · Answer

That's exactly where i am confused. According to the highlighted inequalities we can say that r,p aren't equal since firstly in both inequalities there isn't the '=' and also we would have the same inequality twice. But by selecting values we can say if one of them is greater or smaller than the other. The only problem is that the result changes (as in the example above).

However, since s is greater than both r,p it follows that these two (r,p) as being smaller than s, the one will be smaller/greater than the other (let's say s=20 thus r,p<20 so it could be r=7 and p=13 and in this case it is p>r or r=19 and p=5 so it is r>p. in both cases it is still true that s>r and s>p).

Bunuel · Answer

Not sure I follow what you mean there. However, here are examples that should help:

Given: 
 s > p > q > t 
and:
s > r > q > t

Case 1: p > r 
 10 > 9 > 1 > 0
and:
10 > 2 > 1 > 0

Case 2: p < r 
 10 > 2 > 1 > 0 
and:
10 > 9 > 1 > 0

Case 3: p = r 
 10 > 9 > 1 > 0 
and:
10 > 9 > 1 > 0

BelronMajes · Answer

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Consider the following set of inequalities: p > q, s > r, q > t, s > p

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