Data Sufficiency

If rs ≠ 0, is 1/r + 1/s = 4?

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

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

prernamalhotra wrote:Can't figure the error in my calculation

If rs not equal to 0, is 1/r + 1/s = 4?

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

From the question is (r+s) = 4rs

1) r+s = 4 rs - Sufficient

2) r=s
1/r+1/r = 4
2/r = 4
r =1/2, s=1/2
r+s = 1 -- sufficient

However that is not the answer.

Thank you,
Prerna

The problem with your solution is highlighted above in green.
We are trying to determine WHETHER OR NOT 1/r + 1/s = 4
However, you are ASSUMING that 1/r + 1/s = 4, when you replace s with r to get: 1/r + 1/r = 4

Here's how we need to look at it...
Target question: Does 1/r + 1/s = 4?

Statement 2: r = s
There are several values of r and s that satisfy this condition. Here are two:
Case a: r = 1/2 and s = 1/2, in which case 1/r + 1/s EQUALS 4
Case b: r = 1 and s = 1, in which case 1/r + 1/s does NOT EQUAL 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent

Hi Prerna,

Brent has properly explained the logic error in how you handled Fact 2, so I won't rehash it here. Instead, I want to re-iterate a point about how DS questions are written, so that you can avoid this error in the future:

The main prompt will always contain the QUESTION that you're attempting to answer. The issue behind all DS questions is "consistently" - does the answer "stay the same" or does the answer "change"? Sometimes the main prompt will include some information for you to work with, sometimes it won't. The two Facts underneath the prompt are INFORMATION. You use the information to attempt to answer the question, but the question itself is NOT information.

By taking lots of notes and organizing your work, you should be able to avoid this error in the future. Unfortunately, it's an issue that costs many Test Takers points on the actual GMAT. As such, you have to be diligent about your work so that you avoid this problem.

GMAT assassins aren't born, they're made,
Rich

Rich and Brent are right - you have mistaken your question for something you already know. This is a common error on DS questions.

To avoid this problem, I always have my students keep a strict organizational system with DS: keep your question on one side (with the question mark attached, so you know it's a question), and all given information, including statements, on the other side.



You can simplify and rephrase your question on the left side, and rework statements on the right side:



This should keep you from falling into this kind of trap again.