Is the median of three numbers x, y, z equal to y?

Question

(1) x < y

(2) x = z

TheUltimateWinner · Answer

Bunuel 
The topic name should be changed with "Is the median of three numbers x,y, z equal to y?  Rules# 3

Please Read the  rules for posting question  Before Posting New Question

Bunuel · Answer

________________________
Renamed the topic. Thank you.

Kinshook · Answer

Asked: Is the median of three numbers x, y, z equal to y?

(1) x < y
No information is provided for z
NOT SUFFICIENT

(2) x = z
No information is provided for y
NOT SUFFICIENT

(1) + (2)
(1) x < y
(2) x = z
{x=z}----y
y is not the median
SUFFICIENT

IMO C

TheNightKing · Answer

Start with S2:
x=z Well y can be anything.

Let's say x=z=10 and y =5 then series becomes 5,10,10. And median is now 10.

S1:

x<y 
Tells us nothing much.

Combined:

If x<y and x=z that makes series look like x z y or z x y in that order. But either way y is not the median.

Hence C.

Navneetsingh · Answer

Isn't B sufficient by stating that median can't be equal to Y?

TheNightKing · Answer

Elaborate a more please?

S2 says x=z. And nothing about y. So let's say x=y=z. Now median is y.

Also read my explanation with an example just above your post. Let me know if you still have a doubt.

Eternal · Answer

Statement 2) says x=z 
There is no information about y, and y can be anything.

If y = x= z in that case y can be the median.

If y>x. or y<x then the results will differ.

So 2) is not sufficient.

FaisalBahar · Answer

The median of three numbers is the middle value and so in the given case median is y. Y can take any value but it is y as media. (Statement 1 Sufficient as median is always y irrespective of any value of y). Here it is not asked what is the value of y.
Similarly for statement 2 x and z are equal or not equal median is always y. 
Where am I wrong? Please explain.

BelalHossain046 · Answer

Statement 1: x < y
YES. Y can take any value. But, Y IS NOT ALWAYS MEDIAN.
Let, x=2,  y=3 ,  Z=4    
Let, x=2,  y=3 ,  Z=1    
Let, x=2,  y=5 ,  Z=1

Statement 1: x = z
YES. Y can take any value. But, Y IS NOT ALWAYS MEDIAN.
Let, x=3,  y=3 , Z=3   
Let, x=5,  y=3 , Z=5   
Let, x=3,  y=5 , Z=3

Combining BOTH:
Since X and Z are equal and Y is greater than Y. So Y is also greater than Z. Thus Y is the greatest value.
So, if we arrange the dataset in increasing order, it will become {x,z,y} or {z,x,y}. So, Y is the greatest value. So, Y CAN NOT the median of the dataset. 
C is the answer.

BelalHossain046 · Answer

In the case of MEDIAN, VALUE doesn't matter. ONLY POSITION matters.

Jashan25 · Answer

Correct me if I am wrong!!!

Statement 2 says ....

X = Z. then the three numbers can be .... X X Y.
Now, If Y is greater than or smaller than X the median of three numbers should be X only.

For example, Case Y>X, X = 2, Y = 3.
Series - 2 2 3 
Median - 2

Case Y<X, X=2,Y = 1
Series - 1 2 2
Median again 2

So, Statement 2 alone should be sufficient in my opinion!!!

thyagi · Answer

That's the trap... What if X=y=z..

You are assuming that there are only two possibilities, either y>X or y<X. The question never states that all the numbers are distinct..

Posted from my mobile device

actionlaudari · Answer

Exactly, when there are two same numbers then the mid number will always be other than y

whatsinthename1 · Answer

1- In numeric order, we know x would always come in front of y but what about z? if z is the first number in the order x becomes the median and if z is in between x and y it becomes the median and if z is larger than y, y becomes the median.  y is not always the median.     IS

2- x=z. If x=y=z then all the three numbers can be the median. If y is not equal to z then either x or z is the median and not y.  y is not always the median. IS  
 
1+2 - since we know x<y, x=z≠y,  we know y is not the median and it's either x or z. Sufficient.

C

Is the median of three numbers x, y, z equal to y?

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GMAT Data Sufficiency (DS) Questions

Is the median of three numbers x, y, z equal to y?

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