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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.

Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

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10 May 2010, 20:03

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.

Answer: B.

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 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.

Answer: B.

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.
_________________

Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

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23 Apr 2011, 23:57

3

This post received KUDOS

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
_________________

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

Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

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11 Nov 2014, 14:05

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.

Answer: B.

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?

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.

Answer: B.

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.

Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

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12 Nov 2014, 09:28

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!

Re: Is z equal to the median of the three positive integers, x, y, and z? [#permalink]

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28 Nov 2017, 00:18

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

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.
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