Question: If z is an integer smaller than integer n but greater than zero, is z a factor of n?

(1) n is divisible by all the positive integers less than or equal to 9.
(2) z is not a multiple of a prime number.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“If z is an integer smaller than integer n but greater than zero” is a topic of the GMAT Quantitative reasoning section of GMAT. The questions of GMAT Data Sufficiency consist of a problem statement and two factual statements. This specific GMAT data sufficiency question reckons the candidate’s abilities in analysing quantitative problems. It enhances the candidates’ skills in solving problems logically with mathematical calculations. The difficult part of these questions lies in their clever wording which candidates generally overlook. The GMAT Quant section comprises 31 questions, among which, GMAT data sufficiency contains 15 questions, two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

The problem statement suggests that

Given:

• z is an integer greater than zero i.e. z > 0
• z is less than an integer n, i.e. z<n

The question asks to find out whether z is a factor of n.

1. The statement suggests that n is divisible by all positive integers less than 9 or equal to 9.
   Therefore, if the value of z is 1 and n=9! , then the answer would be yes. It is important to note that the value of n could be less than 9!
   However, if z= 11 and n=9! , then the answer would be no. Therefore, the statement is not sufficient since we cannot derive whether z is a factor of n or not.
2. The statement states that z is not a multiple of a prime number. Therefore, we can say, z=1 (since 1 is the only positive integer which is not a multiple of any prime number)
   Even 1 is considered a factor of every integer that includes n too.
   Hence the statement alone is sufficient since we get the value of z which is also a factor of n.

Correct Answer: (B)

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