If p, q, x, y and z are different positive integers, which of the five

(1) p + x < q
We can conclude that both p<q and x<q, since all are positive integers. Also, we can infer that q will be the median if y & z are found to be > than q; Since we do not have any info on y & z, this statement is insufficient.

(2) y<z;
No info about other integers; Insufficient.

Combining both statements, we still cannot find a median value since there is more than 1 possible median value.

Therefore, insufficient.

Ans is (E)

Solution:

Question Stem Analysis:

We need to determine the median of p, q, x, y, and z given that they are different positive integers.

Statement One Alone:

Since both p and x are positive, we see that q is greater than both p and x. If q is less than both y and z, then q will be the median. However, if it’s not, then the median will be one of the quantities other than q. Statement one alone is not sufficient.

Statement Two Alone:

Since we don’t know anything about p, q, and x, statement two alone is not sufficient.

Statements One and Two Together:

Even with the two statements together, we still do not have sufficient information to determine the median. For example, if p + x < q < y < z, then q is the median. However, if y < z < q, then the median will be one of the quantities other than q.

Answer: E

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