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

 It is currently 16 Jul 2018, 23:11

### 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

# Is z equal to the median of the three positive integers, x, y, and z?

Author Message
TAGS:

### Hide Tags

Director
Joined: 03 Sep 2006
Posts: 839
Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

Updated on: 28 Nov 2017, 01:19
3
2
00:00

Difficulty:

25% (medium)

Question Stats:

77% (00:46) correct 23% (00:55) wrong based on 311 sessions

### HideShow timer Statistics

Is z equal to the median of the three positive integers, x, y, and z?

(1) x < y + z
(2) y = z

Attachment:

DS6.PNG [ 5.06 KiB | Viewed 5138 times ]

Originally posted by LM on 10 May 2010, 09:33.
Last edited by Bunuel on 28 Nov 2017, 01:19, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 47030
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

10 May 2010, 14:18
1
1
Is z equal to the median of the three positive integers, x, y, and z?

Median of the three numbers is the middle term, hence z would be the median in two cases: $$x\leq{z}\leq{y}$$ or $$x\geq{z}\geq{y}$$.

(1) x < y + z --> clearly insufficient. If x=1, y=10, z=0, then answer would be NO but x=1, y=10, z=2, then answer would be YES.

(2) y = z --> either the three numbers are z, z, x (in ascending order) --> media=z or the three numbers are x, z, z (in ascending order) --> median=z. Sufficient.

_________________
Director
Joined: 03 Sep 2006
Posts: 839
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

10 May 2010, 21:03
Bunuel wrote:
Is z equal to the median of the three positive integers, x,y, and z?

Median of the three numbers is the middle term, hence z would be the median in two cases: $$x\leq{z}\leq{y}$$ or $$x\geq{z}\geq{y}$$.

(1) x<y+z --> clearly insufficient. If x=1, y=10, z=0, then answer would be NO but x=1, y=10, z=2, then answer would be YES.

(2) y=z --> either the three numbers are z, z, x (in ascending order) --> media=z or the three numbers are x, z, z (in ascending order) --> median=z. Sufficient.

I just could not think that Z=0 is also possible.
IN this question will it be fair enough to assume that X=Y=Z is also one possibility because it does not say that they each is unique and different!
Math Expert
Joined: 02 Sep 2009
Posts: 47030
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

11 May 2010, 03:35
1
LM wrote:
Bunuel wrote:
Is z equal to the median of the three positive integers, x,y, and z?

Median of the three numbers is the middle term, hence z would be the median in two cases: $$x\leq{z}\leq{y}$$ or $$x\geq{z}\geq{y}$$.

(1) x<y+z --> clearly insufficient. If x=1, y=10, z=0, then answer would be NO but x=1, y=10, z=2, then answer would be YES.

(2) y=z --> either the three numbers are z, z, x (in ascending order) --> media=z or the three numbers are x, z, z (in ascending order) --> median=z. Sufficient.

I just could not think that Z=0 is also possible.
IN this question will it be fair enough to assume that X=Y=Z is also one possibility because it does not say that they each is unique and different!

z may or may not be zero. For (1) you can pick infinite examples x<y+z to hold true. Another example: x=5, y=10, z=3, then answer would be NO but x=6, y=10, z=8, then answer would be YES.

About x=y=z. For statement (2) x=y=z is possible --> three numbers would be z, z, z --> median still z.
_________________
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 384
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

22 Aug 2010, 21:37
kwhitejr wrote:
Is z equal to the median of the three positive integers x, y, and z?

(1) x < y + z
(2) y = z

Statement 1:

If we pick numbers we find that z may or may not be the median.

Hence insufficient.

Statement 2:

y = z then irrespective of x, z would be the median since there are only three integers.

Hence sufficient.

_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 288
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

19 Oct 2010, 10:44
Median of the three numbers is the middle term, hence z would be the median in two cases: $$x\leq{z}\leq{y}$$ or $$x\geq{z}\geq{y}$$.
[/quote]

Great. Remembering that line would help alot in solving such questions.
_________________

I'm the Dumbest of All !!

Manager
Joined: 25 Aug 2010
Posts: 68
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

20 Oct 2010, 06:45
If I go with the values for y and Z in (2) .. I would get the ans as (B) only...
lets say y=z=5

then Place the values in one order either desc or asc
X,5,5 ..so median is : 5

or 5,5,X again median is : 5

or 5,X,5 again ,median would be 5 and even X = 5 since X is a positive interger and X is btwn 5 and 5 ...so it should be equal to 5 only ...

From (2) only i can get the ans .... So B wins
Manager
Joined: 03 Mar 2011
Posts: 88
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

24 Apr 2011, 00:57
3
If we place these numbers in the increasing order, then the median will be the second number.

(a) x<y+z
Assume that x=y=z. Then x<y+z. However since all three numbers are equal, then z is equal to the median
Now assume, that y<x, but x<z. Then obviously, x<y+z, but the median is x.

So (i) is not sufficient.
If y=z, then numbers in increasing order are either x y z or y z x. However, since y=z, the median in both cases is equal to z. So (ii) is sufficient.

_________________

If my post is useful for you not be ashamed to KUDO me!
Let kudo each other!

Retired Moderator
Joined: 16 Nov 2010
Posts: 1468
Location: United States (IN)
Concentration: Strategy, Technology
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

24 Apr 2011, 19:41
(1)

x = 1, y = 2, z = 3

but median is y

z = 2, x = 1, y = 3
then z is median

(1) is insufficient

(2)

x = 2, y = 1, z = 1

z is the median when we arrange the numbers as 1,1,2

x = 1, y = 1 z = 1

z is median

x = 1, y = 2, z = 2

z is median when we arrange numbers as 1,2,2

(2) is sufficient

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1134
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

19 May 2011, 23:26
a 1,2,3 for x,y,z plays around with the median. not sufficient.

b x,z,z means z is definitely the median.
B
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Senior Manager
Joined: 15 Aug 2013
Posts: 271
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

11 Nov 2014, 15:05
LM wrote:
Bunuel wrote:
Is z equal to the median of the three positive integers, x,y, and z?

Median of the three numbers is the middle term, hence z would be the median in two cases: $$x\leq{z}\leq{y}$$ or $$x\geq{z}\geq{y}$$.

(1) x<y+z --> clearly insufficient. If x=1, y=10, z=0, then answer would be NO but x=1, y=10, z=2, then answer would be YES.

(2) y=z --> either the three numbers are z, z, x (in ascending order) --> media=z or the three numbers are x, z, z (in ascending order) --> median=z. Sufficient.

I just could not think that Z=0 is also possible.
IN this question will it be fair enough to assume that X=Y=Z is also one possibility because it does not say that they each is unique and different!

Is the median the middle term true even if the integers are not consecutive? Meaning, if it's 1 4 4 -- is the median still 4?
Math Expert
Joined: 02 Sep 2009
Posts: 47030
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

12 Nov 2014, 04:57
russ9 wrote:
LM wrote:
Bunuel wrote:
Is z equal to the median of the three positive integers, x,y, and z?

Median of the three numbers is the middle term, hence z would be the median in two cases: $$x\leq{z}\leq{y}$$ or $$x\geq{z}\geq{y}$$.

(1) x<y+z --> clearly insufficient. If x=1, y=10, z=0, then answer would be NO but x=1, y=10, z=2, then answer would be YES.

(2) y=z --> either the three numbers are z, z, x (in ascending order) --> media=z or the three numbers are x, z, z (in ascending order) --> median=z. Sufficient.

I just could not think that Z=0 is also possible.
IN this question will it be fair enough to assume that X=Y=Z is also one possibility because it does not say that they each is unique and different!

Is the median the middle term true even if the integers are not consecutive? Meaning, if it's 1 4 4 -- is the median still 4?

If a set has odd number of terms the median of the set is the middle number when arranged in ascending or descending order. So, the median of {1, 4, 4} is 4.

If a set has even number of terms the median of the set is the average of the two middle terms when arranged in ascending or descending order. For example, the median of {1, 1, 4, 4} is (1 + 4)/2 = 2.5.

Hope it's clear.
_________________
Senior Manager
Joined: 15 Aug 2013
Posts: 271
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

12 Nov 2014, 10:28
Bunuel wrote:
russ9 wrote:
LM wrote:

I just could not think that Z=0 is also possible.
IN this question will it be fair enough to assume that X=Y=Z is also one possibility because it does not say that they each is unique and different!

Is the median the middle term true even if the integers are not consecutive? Meaning, if it's 1 4 4 -- is the median still 4?

If a set has odd number of terms the median of the set is the middle number when arranged in ascending or descending order. So, the median of {1, 4, 4} is 4.

If a set has even number of terms the median of the set is the average of the two middle terms when arranged in ascending or descending order. For example, the median of {1, 1, 4, 4} is (1 + 4)/2 = 2.5.

Hope it's clear.

Thanks. Makes sense. I thought that rule only applied to consecutive terms, but thanks for clarifying!
Senior Manager
Joined: 09 Mar 2017
Posts: 445
Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

28 Nov 2017, 01:18
Bunuel
Are we assuming that x, y and z are not jumbled so as any integer can take any place? Is that why x can not be in the middle and only two possible order can be x,y,z or z,y,x ?

Thanks
_________________

------------------------------
"Trust the timing of your life"
Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq

Math Expert
Joined: 02 Sep 2009
Posts: 47030
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

28 Nov 2017, 01:22
TaN1213 wrote:
Bunuel
Are we assuming that x, y and z are not jumbled so as any integer can take any place? Is that why x can not be in the middle and only two possible order can be x,y,z or z,y,x ?

Thanks

We don't know the order of the variables. Therefore, x, y, and z could have 6 possible orderings.
_________________
Intern
Joined: 06 Oct 2016
Posts: 6
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

23 Jun 2018, 02:33
Bunuel wrote:
LM wrote:
Bunuel wrote:
Is z equal to the median of the three positive integers, x,y, and z?

Median of the three numbers is the middle term, hence z would be the median in two cases: $$x\leq{z}\leq{y}$$ or $$x\geq{z}\geq{y}$$.

(1) x<y+z --> clearly insufficient. If x=1, y=10, z=0, then answer would be NO but x=1, y=10, z=2, then answer would be YES.

(2) y=z --> either the three numbers are z, z, x (in ascending order) --> media=z or the three numbers are x, z, z (in ascending order) --> median=z. Sufficient.

I just could not think that Z=0 is also possible.
IN this question will it be fair enough to assume that X=Y=Z is also one possibility because it does not say that they each is unique and different!

z may or may not be zero. For (1) you can pick infinite examples x<y+z to hold true. Another example: x=5, y=10, z=3, then answer would be NO but x=6, y=10, z=8, then answer would be YES.

About x=y=z. For statement (2) x=y=z is possible --> three numbers would be z, z, z --> median still z.

if x=y=z, couldn't three numbers be (x,x,x), (y, y, y), or (z,z,z)? Hence x could be viewed as median as well.
Math Expert
Joined: 02 Sep 2009
Posts: 47030
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

23 Jun 2018, 06:54
Andy24 wrote:
Bunuel wrote:
LM wrote:

I just could not think that Z=0 is also possible.
IN this question will it be fair enough to assume that X=Y=Z is also one possibility because it does not say that they each is unique and different!

z may or may not be zero. For (1) you can pick infinite examples x<y+z to hold true. Another example: x=5, y=10, z=3, then answer would be NO but x=6, y=10, z=8, then answer would be YES.

About x=y=z. For statement (2) x=y=z is possible --> three numbers would be z, z, z --> median still z.

if x=y=z, couldn't three numbers be (x,x,x), (y, y, y), or (z,z,z)? Hence x could be viewed as median as well.

Yes, but if x = z, then x is the median is the same as z is the median.
_________________
SVP
Joined: 26 Mar 2013
Posts: 1719
Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

### Show Tags

24 Jun 2018, 12:18
Bunuel wrote:
Is z equal to the median of the three positive integers, x, y, and z?

Median of the three numbers is the middle term, hence z would be the median in two cases: $$x\leq{z}\leq{y}$$ or $$x\geq{z}\geq{y}$$.

(1) x < y + z --> clearly insufficient. If x=1, y=10, z=0, then answer would be NO but x=1, y=10, z=2, then answer would be YES.

(2) y = z --> either the three numbers are z, z, x (in ascending order) --> media=z or the three numbers are x, z, z (in ascending order) --> median=z. Sufficient.

Bunuel

In the highlighted part z can't be 0. The question stem says positive number. It should be another positive integer.

Thanks
Re: Is z equal to the median of the three positive integers, x, y, and z?   [#permalink] 24 Jun 2018, 12:18
Display posts from previous: Sort by

# 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®.