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

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If p, q, x, y, and z are different positive integers, which  [#permalink]

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Data Sufficiency
Question: 34
Category: Arithmetic Statistics
Page: 155
Difficulty: 600


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Re: If p, q, x, y, and z are different positive integers, which  [#permalink]

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New post 13 Jan 2014, 00:56
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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.
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Re: If p, q, x, y, and z are different positive integers, which  [#permalink]

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New post 14 Jan 2014, 11:05
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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



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)
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Re: If p, q, x, y, and z are different positive integers, which  [#permalink]

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New post 15 Jan 2014, 02:27
1
(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)
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Re: If p, q, x, y, and z are different positive integers, which  [#permalink]

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New post 17 Jan 2014, 03:25
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If p, q, x, y, and z are different positive integers, which  [#permalink]

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New post 10 Sep 2015, 23:58
there is no information about their relative positions
hence all the statements are inconclusive
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Re: If p, q, x, y, and z are different positive integers, which  [#permalink]

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Re: If p, q, x, y, and z are different positive integers, which &nbs [#permalink] 30 Mar 2018, 06:34
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