Number Properties Data Sufficiency

Here is an interesting data sufficiency question.

How many of the numbers x, y, and z are positive if each of these numbers is less than 10?
1. x + y + z = 20
2. x + y = 14

Correct Answer : Choice A. Statement 1 alone is sufficient; Statement 2 is not sufficient.

Explanatory Answer:

Statement 1 : x + y + z = 20.
From the question stem we know that each number is less than 10.
So, x < 10, y < 10 and z < 10.
Therefore, the maximum sum of any two of these numbers, say x + y < 20.

However, from statement 1, x + y + z = 20.
Unless z is also positive x + y + z cannot be 20.
Hence, we can conclude that all 3 numbers x, y and z are positive.

Statement 2: x + y = 14
As each of x and y are less than 10, both x and y have to be positive for the sum to be 14.
However, from statement 2 we do not know whether z is positive.
Hence, data is insufficient.

Choice A is the correct answer.

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