Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 15:14 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # M13-22

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56304

### Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 68% (01:04) correct 32% (01:01) wrong based on 84 sessions

### HideShow timer Statistics If $$X$$ is a positive integer, which of the following cannot be a median of set $$S = (X, 9, 2, 5)$$?

A. 3.0
B. 3.5
C. 4.0
D. 5.0
E. 6.5

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56304

### Show Tags

Official Solution:

If $$X$$ is a positive integer, which of the following cannot be a median of set $$S = (X, 9, 2, 5)$$?

A. 3.0
B. 3.5
C. 4.0
D. 5.0
E. 6.5

$$X = 1$$ or $$2$$; the median is $$\frac{(2 + 5)}{2} = 3.5$$

$$X = 3$$; the median is $$\frac{(3 + 5)}{2} = 4.0$$

$$X = 5$$; the median is $$\frac{(5 + 5)}{2} = 5.0$$

$$X = 8$$; the median is $$\frac{(5 + 8)}{2} = 6.5$$

$$X \gt 8$$; the median is $$\frac{(5 + 9)}{2} = 7$$

The median cannot equal 3.0.

_________________
Intern  B
Joined: 19 Jul 2010
Posts: 5

### Show Tags

1
Another way to approach this by figuring out the range in which the median can lie i.e. in what conditions would you have the smallest and largest median.

[X 2 5 9 ] - when you know that X is the smallest - the median is 2+5=7/2=3.5
[2 5 9 X] - when you know that X is largest - the median will be 9+5=14/2= 7

Therefore, the median say y will be 3.5<y<7

Only A i.e. 3 is outside the range.
IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1363
Location: India
WE: Engineering (Other)

### Show Tags

Hi Bunuel niks18 pikolo2510 Abhishek009 chetan2u VeritasPrepKarishma

I could not understand the logic of cherry picking numbers.
Why are 4,5, and 6 for e.g. not considered?

As per definition of median, it is the middle no in a set of numbers
arranged in an increasing / decreasing fashion.

Only restriction for X is $$X\geq{0}$$
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Math Expert V
Joined: 02 Aug 2009
Posts: 7764

### Show Tags

Hi Bunuel niks18 pikolo2510 Abhishek009 chetan2u VeritasPrepKarishma

I could not understand the logic of cherry picking numbers.
Why are 4,5, and 6 for e.g. not considered?

As per definition of median, it is the middle no in a set of numbers
arranged in an increasing / decreasing fashion.

Only restriction for X is $$X\geq{0}$$

Hi..

Since you are looking for the median that is the central value, the minimum value will be when x<2, 2 because that is the least number comedian will be(2+5)/2=3.5
So the min value is 3.5...3 therefore cannot be the answer..
A
_________________
BSchool Forum Moderator P
Joined: 05 Jul 2017
Posts: 512
Location: India
GMAT 1: 700 Q49 V36 GPA: 4

### Show Tags

Hi Bunuel niks18 pikolo2510 Abhishek009 chetan2u VeritasPrepKarishma

I could not understand the logic of cherry picking numbers.
Why are 4,5, and 6 for e.g. not considered?

As per definition of median, it is the middle no in a set of numbers
arranged in an increasing / decreasing fashion.

Only restriction for X is $$X\geq{0}$$

As numbers keep increasing the median kept on increasing. There won't be a case when median decreases as you increase the value of X. Think aabout it . if X=3, then median=4. But when X=7, then median=6.

Now the lowest possible median is 2+5/2 = 3.5
All other possible values will be more than 3.5 as explained above. A quick glance at the options and we can see answer should be A

So there is no need to check for 4,5,6 or every possible value of X
_________________
IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1363
Location: India
WE: Engineering (Other)

### Show Tags

Thanks pikolo2510 and chetan2u for your two cents.

Any reason for not selecting 1 in spite of it satisfying condition in question stem?
May I know why does X has to be either minimum or maximum value for the
elements in the set though I have no restriction in choosing X less than 2 ie 1
and greater than 9, ie 10.
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!! Re: M13-22   [#permalink] 09 Jul 2018, 17:17
Display posts from previous: Sort by

# M13-22

Moderators: chetan2u, Bunuel  