Question: Fraction with a and b

Comment on Fraction with a and b

I did not rephrase the

cabilesv2020 - December 26, 2019

I did not rephrase the question as presented in the video. I went to evaluate the Statements right away.

Statement 1: I used b=3 and a=1 to satisfy the result of 2/3. Since these are the only values that would satisfy the result of 2/3, I concluded that it can definitely answer the target question (sufficient).

Statement 2: I used the same values for b=3 and a=1, which satisfies 3a=b, and concluded it's also sufficient.

Is this approach all right? Thanks.

Your answer is correct, but

gmat-admin - December 26, 2019

Your answer is correct, but your approach might get you in trouble in the future.

You're saying that b = 3 and a = 1 is the only solution to the equation (b - a)/b = 2/3.
This is not true. In fact, there are infinitely many solutions. Here are just a few:
a = 1 and b = 3
a = 2 and b = 6
a = 5 and b = 15
a = -3 and b = -9
etc.

That said, if you test each of these possible solutions, you will find that we get the SAME answer to the target question each time.
The answer each time is that (a - b)/a = -2
Since we will always get an answer of -2 for our target question, statement 1 is sufficient.

That the same logic applies to statement 2

Cheers,
Brent

I understand Statement 2 is

sjiang24 - September 12, 2021

I understand Statement 2 is sufficient by letting a = b/3, and plug into the formula get -2.

However, I don't get statement 2, since there are two variables anyways, so that must be insufficient...

That's a common mistake

gmat-admin - September 13, 2021

That's a common mistake (discussed here: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1107)

If the target question asks you to find the specific value of an INDIVIDUAL variable, then having one equation with two variables will not be sufficient.
However, for this question, we aren't asked to find that the specific value of an individual variable; we're asked to find the value of the rational expression (a - b)/a.

Consider this example:
Target question: What is the value of x/y?
Statement 1: x = 2y
Take this equation and divide both sides by y to get: x/y = 2.
Sufficient!

So, even though statement 1 provides an equation with two variables, we're still able to answer the target question with certainty.

Does that help?

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