Practice GMAT Data Sufficiency Question
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If n is a positive integer, is n + 2 > z?
- z2 > n
- z – n < 0
Correct Answer: B
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Evaluate Statement (1) alone.
- The smallest possible value of n is 1 since n is a positive integer and the smallest positive integer is 1
- 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.
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Evaluate Statement (2) alone.
- 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.
- Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.
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