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

Question

Is z equal to the median of the three positive integers, x, y, and z? (1) x < y + z (2) y = z DS6.PNG

Bunuel · Accepted Answer

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=2, y=10, z=1, 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.

Answer: B.

LM · Answer

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!

Bunuel · Answer

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.

ezhilkumarank · Answer

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.

Answer: B

shrive555 · Answer

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} .

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

vitamingmat · Answer

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

bagrettin · Answer

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.

The answer is B

subhashghosh · Answer

(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

Answer - B

amit2k9 · Answer

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

russ9 · Answer

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?

Bunuel · Answer

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.

russ9 · Answer

Thanks. Makes sense. I thought that rule only applied to consecutive terms, but thanks for clarifying!

TaN1213 · Answer

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

Bunuel · Answer

We don't know the order of the variables. Therefore, x, y, and z could have 6 possible orderings.

Andy24 · Answer

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.

Bunuel · Answer

Yes, but if x = z, then x is the median is the same as z is the median.

dortinator1234923 · Answer

Thanks for the explanation. One question though; why can't x be the middle number/median? It doesn't specify anywhere that it has to be the order xyz or zyx (in the case of statement 2: xzz or zzx)
Couldn't the order be zxz?  Bunuel

Thank you in advance!

Bunuel · Answer

The median is a middle number when arranged in ascending or descending order. When you arrange x, z, and z, in ascending order you get z, z, x or x, z, z. How can you have z, x, z?

dortinator1234923 · Answer

Thank you for your quick response. Was not aware of the fact that ascending/descending order was necessary, get it now.

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

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

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