# Practice GMAT Data Sufficiency Question

If n is a positive integer, is n + 2 > z?
1. z2 > n
2. z – n < 0
 A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
1. Evaluate Statement (1) alone.
1. The smallest possible value of n is 1 since n is a positive integer and the smallest positive integer is 1
2. You know that z2 > 1, which is the smallest possible value of n. Possible values of z include any number whose absolute value is greater than 1. This does not provide enough information to answer the question definitively. Consider the following examples.
If z = -10 and n = 1, two values that are permissible since (-10)2 > 1, then the answer to the original question is yes since 1 + 2 > -10.
However, if z = 10 and n = 1, two values that are permissible since (10)2 > 1, then the answer to the original question is no since 1 + 2 is not greater than 10.
Statement (1) is NOT SUFFICIENT.
2. Evaluate Statement (2) alone.
1. Statement (2) can be re-arranged:
z - n < 0
z < n
Stated Differently: n > z
Since n is greater than z, n+2 will definitely be greater than z because n is a positive integer and it will only become larger.
In other words, let z = (a number less than n). You can be sure that n + 2 will definitely be greater than (a number less than n).
Statement (2) is SUFFICIENT.
3. Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.