If \(rs \neq 0,\) is \(\dfrac{1}{r} + \dfrac{1}{s} = 4 ?\)

[M7MBA]

If \(rs \neq 0,\) is \(\dfrac{1}{r} + \dfrac{1}{s} = 4 ?\)

(1) \(r + s = 4rs\)
(2) \(r = s\)

[spoiler]OA=A[/spoiler]

Source: Official Guide

[Brent@GMATPrepNow]

If \(rs \neq 0,\) is \(\dfrac{1}{r} + \dfrac{1}{s} = 4 ?\)

(1) \(r + s = 4rs\)
(2) \(r = s\)

[spoiler]OA=A[/spoiler]

Source: Official Guide

Target question: Is 1/r + 1/s = 4?

This one is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Let's add 1/r + 1/s to create ONE rational expression.
Find common denominator: s/rs + r/rs
Add numerators: (s+r)/rs
So, 1/r + 1/s = (s+r)/rs

So, rather than ask "Does 1/r + 1/s = 4?" we can ask "Does (s+r)/rs = 4?"

Even better, we can cross multiply the equation to get...
REPHRASED target question: Does s+r = 4sr?"

Statement 1: r + s = 4rs
This is exactly what our REPHRASED target questions asks.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: r = s
Knowing that r=s does not help us determine whether s+r = 4sr
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent