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

Question

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

(1) p + x < q
(2) y < z

Bunuel · Answer

SOLUTION:

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

(1) p + x < q
(2) y < z

Notice that we don't know relative positioning of  p, x, and q  to  y and z , thus we cannot find which is the median.

Answer: E.

kinjiGC · Answer

Statement 1)
If we arrange in increasing order, it can be either p x q or x p q. As we don't know about y and z values, we cannot arrange them and hence we cannot determine the median of the data points.
Hence Not sufficient.

Statement 2)
y< z. Here we don't know other values and hence not sufficient.

Combining the two statements.
we can arrive at the following four combinations when the positive integers are arranged in increasing order.
p x q y z
x p q y z
y z x p q
y z p x q
So as the middle term changes, not sufficient.

Hence Option E)

nutshell · Answer

(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)

ScottTargetTestPrep · Answer

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

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards