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

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Source: — Data Sufficiency |
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Re: Is z equal to the median of the three positive integers, x, y, and z?

by deloitte247 » Wed May 06, 2020 11:22 pm

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A

B

C

D

E

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Median = Element in the middle ( for an odd frequency) z will be the median $$if\ x\ge z\ge y\ or\ if\ x\le z\le y$$
Statement 1 => x < y + z
If x = 4, y = 6, and z = 5
4 < 6 + 5 => this is true for this statement and median = z = 5
But if x = 4, y = 6, and z = 3
4 < 6 + 3 => this is also true for this statement but median is now x = 4.
The information provided is not enough to arrive at a definite answer, so we cannot decide if z is equal to the median. Therefore, statement 1 is NOT SUFFICIENT

Statement 2 => y = z
If x = 4, y = 3 then z = 3
x, y, z => 4, 5, 5. The median = 5 = y = z
Since y and z are equal, irrespective of the value of x, the median will always = z
Statement 2 is SUFFICIENT

Answer = B
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