The function f(n) is defined as the product o… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

The function f(n) is defined as the product of all integers from 1 to n, inclusive, and the function g(n) is defined as the product of all odd integers from 1 to n, inclusive, where n is a positive integer. If p is a prime factor of $\frac{f(150)}{g(150)} + 1$ , then which of the following must be true

Correct answer marked below

p < 10

10 < p < 25

25 < p < 50

50 < p < 75

p > 75

Correct

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Explanation

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Official Explanation

Official

Let

k = \frac{f(150)}{g(150)}

\frac{f(150)}{g(150)}

= product of all integers from 1 to 150 / product of all odd integers from 1 to 150 = product of all even integers from 1 to 150.

So

k = 2 \times 4 \times 6 \times \dots \times 150

.

Factor out 2 from each term:

k = 2^{75}(1 \times 2 \times 3 \times \dots \times 75)

.

Now consider

k + 1

. Since

k

and

k + 1

are consecutive integers, they are coprime (share no common factors greater than 1).…

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.