f(x)=(4x+1)(4x–3) for all positive integers x… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Functions

$f(x)=(4x+1)(4x–3)$ for all positive integers x. Which of the following cannot be a factor of f(x)?
I. 7
II. 16
III. 25

Answer Choices

Correct answer marked below

I only

II only

Correct

I and II only

I and III only

I, II, and III

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Explanation

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Official Explanation

Official

As it can often be hard to understand the rules underlying divisibility, we'll try a few numbers to see the pattern. This is an Alternative approach.

Starting with x = 1, we get

5 \times 1

. Not divisible by 7, 16, or 25.

x = 2:

9 \times 5

. Not divisible by 7, 16, or 25.

x = 3:

13 \times 9

. Not divisible by 7, 16, or 25.

x = 4:

17 \times 13

. Not divisible by 7, 16, or 25.

x = 5:

21 \times 17

. Divisible by 7!

x = 6:

25 \times 21

. Divisible by 25!…

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What this question tests

What it tests

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

Common trap

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

f(x)=(4x+1)(4x–3)f(x)=(4x+1)(4x–3)f(x)=(4x+1)(4x–3) for all positive integers x. Which of the following cannot be a factor of f(x)?I. 7II. 16III. 25