selvae wrote:
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
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 = 2Case b: p = 7 and q = 2. Notice that the product, 14, has 4 factors: 1, 2, 7 and 14. In this case,
p = 7Since 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 = 3Case b: p = 7 and q = 2. Notice that the product, 14, has 4 factors: 1, 2, 7 and 14. In this case,
p = 7Since 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 = 3Case b: p = 7 and q = 2. Notice that the product, 14, has 4 factors: 1, 2, 7 and 14. In this case,
p = 7Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent