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.

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

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.

Labels: GMAT Data Sufficiency, GMAT DS, GMAT Number Properties, GMAT Number Theory