Practice GMAT Data Sufficiency Question

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If n is a positive integer, is n + 2 > z?
  1. z2 > n
  2. z – n < 0
Correct Answer: B
  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.

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