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# If x, y, and z are three integers such that 0 x y z, is the range of x

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If x, y, and z are three integers such that 0 x y z, is the range of x  [#permalink]

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10 Apr 2018, 05:54
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Difficulty:

45% (medium)

Question Stats:

67% (01:18) correct 33% (01:15) wrong based on 36 sessions

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If x, y, and z are three integers such that 0 < x < y < z, is the range of x, y, and z equal to 2?

(1) The mean (arithmetic average) of x, y, and z is 2.
(2) The median of x, y, and z is 2.

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Intern
Joined: 02 Feb 2016
Posts: 34
Location: United States
GMAT 1: 710 Q49 V38
GPA: 3.5
Re: If x, y, and z are three integers such that 0 x y z, is the range of x  [#permalink]

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10 Apr 2018, 06:10
1. Mean = 2, (x+y+z)/3 = 2
So, the sum of all three values = 6

Since 0 < x < y < z, and all numbers are integers, x = 1, y = 2, z =3 is the only solution. Range = 3-1 = 2. Sufficient

2. Median = 2
Now, the numbers can be 1, 2, n, where n >= 3. If n = 3, range will be 2, else, range will be greater than 2. NOT sufficient.

A
Manager
Joined: 05 Feb 2016
Posts: 157
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Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: If x, y, and z are three integers such that 0 x y z, is the range of x  [#permalink]

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10 Apr 2018, 07:50
Bunuel wrote:
If x, y, and z are three integers such that 0 < x < y < z, is the range of x, y, and z equal to 2?

(1) The mean (arithmetic average) of x, y, and z is 2.
(2) The median of x, y, and z is 2.

1. Mean = 2 and 0 < x < y < z, and all numbers are integers, x = 1, y = 2, z =3 is the only solution. Range = 3-1 = 2. Sufficient

2. Median = 2
Now, the numbers can be 1, 2, n, where n can be any value, range is not fixed . NOT sufficient.

A
Re: If x, y, and z are three integers such that 0 x y z, is the range of x   [#permalink] 10 Apr 2018, 07:50
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# If x, y, and z are three integers such that 0 x y z, is the range of x

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