The function \(f(n) =\) the number of factors of \(n.\) If \(p\) and \(q\) are positive integers and \(f(pq) = 4,\) what

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The function \(f(n) =\) the number of factors of \(n.\) If \(p\) and \(q\) are positive integers and \(f(pq) = 4,\) what is the value of \(p?\)

(1) \(p + q\) is an odd integer.

(2) \(q\) is less than \(p.\)

Answer: E

Source: Manhattan GMAT

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M7MBA wrote:
Thu Jul 22, 2021 7:38 am
The function \(f(n) =\) the number of factors of \(n.\) If \(p\) and \(q\) are positive integers and \(f(pq) = 4,\) what is the value of \(p?\)

(1) \(p + q\) is an odd integer.

(2) \(q\) is less than \(p.\)

Answer: E

Source: Manhattan GMAT
Target question: What is the value of p?

Given: f(n) = the number of factors of n. If p and q are positive integers and f(pq) = 4

Statement 1: p + q is an odd integer
Here are two sets of values for p and q that satisfy statement 1:
Case a: p = 2 and q = 3. Notice that the product, 6, has 4 factors: 1, 2, 3 and 6. In this case, p = 2
Case b: p = 7 and q = 2. Notice that the product, 14, has 4 factors: 1, 2, 7 and 14. In this case, p = 7
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: q is less than p
Here are two sets of values for p and q that satisfy statement 2:
Case a: p = 3 and q = 2. Notice that the product, 6, has 4 factors: 1, 2, 3 and 6. In this case, p = 3
Case b: p = 7 and q = 2. Notice that the product, 14, has 4 factors: 1, 2, 7 and 14. In this case, p = 7
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of p and q that satisfy BOTH statements. Here are two:
Case a: p = 3 and q = 2. Notice that the product, 6, has 4 factors: 1, 2, 3 and 6. In this case, p = 3
Case b: p = 7 and q = 2. Notice that the product, 14, has 4 factors: 1, 2, 7 and 14. In this case, p = 7
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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