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Median of positive integers

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by gmattesttaker2 » Wed Feb 19, 2014 3:51 pm
Hello,

For the following:

What is the median of positive integers x, y, and z if their average is 120.

(1) x = 100
(2) y = 120

OA: B

1) x = 100. In-suff.

2) y = 100. Now what if the order of the integers are y, x and z. In-this case 2 is in-sufficient.

I am thinking that the question is implicitly saying that x, y and z are in ascending/descending order. Is it correct to make such an assumption if nothing to the contrary is stated in the question?

Thanks,
Sri
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Source: — Data Sufficiency |
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by tomada » Wed Feb 19, 2014 6:21 pm
gmattesttaker2 wrote:Hello,

For the following:

What is the median of positive integers x, y, and z if their average is 120.

(1) x = 100
(2) y = 120

OA: B

1) x = 100. In-suff.

2) y = 100. Now what if the order of the integers are y, x and z. In-this case 2 is in-sufficient.

I am thinking that the question is implicitly saying that x, y and z are in ascending/descending order. Is it correct to make such an assumption if nothing to the contrary is stated in the question?

Thanks,
Sri
I don't think that it matters whether x,y,z are in increasing order. Once you're given that X=100, all you have to show is whether the second largest number can vary while maintaining the overall avg. of 120. Whether that 2nd largest number is set equal to Y or to Z (or even X) doesn't matter.

The same applies to the second statement. Knowing that Y=120, there are only two possibilities: (1) all three numbers are the same (120), and (2) either X is lower than 120 or Z is lower than 120, with the remaining variable > 120.
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by [email protected] » Thu Feb 20, 2014 9:53 pm
Hi Sri,

This question is perfect for TESTing Values:

The question tells us that X, Y and Z are positive integers and the average is 120. We're asked what the median is.

Since the average of the 3 numbers is 120, we know that Sum/3 = 120, so X+Y+Z = 360.

Fact 1: X = 100

This tells us that Y+Z = 260

We could have...
Y = 1, Z = 259 so the median would be 100
Y = 120, Z = 140 so the median would be 120
Fact 1 is INSUFFICIENT

Fact 2: Y = 120

This tells us that Y+Z = 240

We could have....
Y = 1, Z = 239 so the median would be 120
Y = 100, Z = 140 so the median would be 120
Y = 120, Z = 120 so the median would be 120

In every scenario, we end up with a median of 120
Fact 2 is SUFFICIENT

Final Answer:B

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