The function f(x) can be defined for all positive integers x as "the n

Question

The function f(x) can be defined for all positive integers x as "the number of unique factors of x", squared. From the table below, select a pairing of x and f(x).

Sajjad1994 · Accepted Answer

Official Explanation

9 has exactly three factors (1, 3, and 9), and three-squared is 9, so f(9) = 9. None of the other options for x has a corresponding f(x) available as an option.

Ans: 9 for Both

kntombat · Answer

Hey  Sajjad1994 , can you share the Official Explanation for this question, according to me the answer can be 10 and 9 or 9 and 9.

Waiting to hear from you.

Hacchuu · Answer

The answer cannot be 10 & 9. Here's why:

Factors of 10: 1, 2, 5, 10
f(10) = 4^2 = 16, which is not present in the options.

CorporateAsset · Answer

Memory Formula for Number of Positive Factors
Prime Factorization
Write the number as a product of primes:
N = p1 × q2 × r3 × ...

Add 1 to Each Exponent
For each prime factor exponent, add 1:

(a+1),(b+1),(c+1),...

Multiply the Results
Multiply all those together:
(a+1)(b+1)(c+1)... = Total Positive Factors

xyzKunal · Answer

As f(x) is square of an integer, 9 is the only square here. so f(x) is 9.
Now, as 3 is the number of factor, x should be (prime number)^2. which again gives us 9 as only viable option.

The function f(x) can be defined for all positive integers x as "the n

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GMAT Two-part Analysis (TPA) Questions

The function f(x) can be defined for all positive integers x as "the n

Prep Toolkit

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