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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   45% (medium)

Question Stats: 63% (00:49) correct 37% (00:45) wrong based on 38 sessions

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If set $$S =\{2, 5, 1, x, 7\}$$, what is $$x$$ ?

(1) The range of set $$S$$ is 8

(2) The median of set $$S$$ is 2

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Math Expert V
Joined: 02 Sep 2009
Posts: 58430

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Official Solution:

Statement (1) by itself is insufficient. S1 allows $$x$$ to be either -1 or 9 (the range is either $$7 - (-1) = 8$$ or $$9 - 1 = 8$$).

Statement (2) by itself is insufficient. S2 allows $$x$$ to be any number smaller than 2.

Statements (1) and (2) combined are sufficient. S1 and S2 exclude $$x = 9$$ as a solution and we are left with $$x = -1$$.

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Intern  Joined: 24 Feb 2015
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GMAT 1: 570 Q37 V31 Show Tags

Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. S1 allows $$x$$ to be either -1 or 9 (the range is either $$7 - (-1) = 8$$ or $$9 - 1 = 8$$).

Statement (2) by itself is insufficient. S2 allows $$x$$ to be any number smaller than 2.

Statements (1) and (2) combined are sufficient. S1 and S2 exclude $$x = 9$$ as a solution and we are left with $$x = -1$$.

Hi!

Does the second condition mean that x is smaller than 2 but also equal?

If not, Why Not ?

ALe
Math Expert V
Joined: 02 Sep 2009
Posts: 58430

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BCCLSN wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. S1 allows $$x$$ to be either -1 or 9 (the range is either $$7 - (-1) = 8$$ or $$9 - 1 = 8$$).

Statement (2) by itself is insufficient. S2 allows $$x$$ to be any number smaller than 2.

Statements (1) and (2) combined are sufficient. S1 and S2 exclude $$x = 9$$ as a solution and we are left with $$x = -1$$.

Hi!

Does the second condition mean that x is smaller than 2 but also equal?

If not, Why Not ?

ALe

Yes, from the second statement, x can be 2 too.
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Intern  Joined: 24 Feb 2015
Posts: 13
GMAT 1: 570 Q37 V31 Show Tags

perfect ! thank you
Math Expert V
Joined: 02 Sep 2009
Posts: 58430

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JourneyToTheTop wrote:
The question must make clear that x is an integer, not any real number.

Hope the solution below explains why is that not necessary.

If set $$S =\{2, 5, 1, x, 7\}$$, what is $$x$$ ?

(1) The range of set $$S$$ is 8. If we consider the range of $$S =\{2, 5, 1, x, 7\}$$, without x, then it's largest - smallest = 7 - 1 = 6. Since, the range of S is 8, then x must be either the largest or the smallest element. If x is the largest, then x - 1 = 8 --> x = 9 and if x is the smallest, then 7 - x = 8 --> x = -1. Not sufficient.

(2) The median of set $$S$$ is 2. The median of a set with odd number of elements is the middle term, when arranged in ascending/descending order. Since 2 is the median, then it's the middle term: S = {x, 1, 2, 5, 7}. So, x must be less than or equal to 2. Not sufficient.

(1)+(2) From (1) x = 9 or x = -1 and from (2) x <=2, hence x = -1. Sufficient.

_________________ M18-11   [#permalink] 04 Jan 2018, 20:26
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