GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Jul 2018, 19:13

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# M18-11

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47019

### Show Tags

16 Sep 2014, 01:03
00:00

Difficulty:

55% (hard)

Question Stats:

64% (00:48) correct 36% (00:45) wrong based on 36 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 47019

### Show Tags

16 Sep 2014, 01:03
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 $$x = -1$$.

_________________
Intern
Joined: 24 Feb 2015
Posts: 13
GMAT 1: 570 Q37 V31

### Show Tags

18 Jun 2015, 07:52
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
Joined: 02 Sep 2009
Posts: 47019

### Show Tags

18 Jun 2015, 07:57
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.
_________________
Intern
Joined: 24 Feb 2015
Posts: 13
GMAT 1: 570 Q37 V31

### Show Tags

18 Jun 2015, 08:01
perfect ! thank you
Math Expert
Joined: 02 Sep 2009
Posts: 47019

### Show Tags

04 Jan 2018, 20:26
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
Display posts from previous: Sort by

# M18-11

Moderators: chetan2u, Bunuel

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.