Explanation

Plug in any two unequal values for a and b, and Quantity A will always be equal to –1. This is because a negative sign can be factored out of the top or bottom of the fraction to show that the top and bottom are the same, except for their signs:

\(\frac{a-b}{b-b}=\frac{a-b}{-(a-b)}=-1\)

@ScottTargetTestPrep @Sandy

A quick help, please!

I was trying a different approach, but I does not work, why?

I did the following:

Quant A
a-b/b-a

Quant B
1 is the same as b-a/b-a

so, I need to compare a-b (Quant A) with b-a (Quant B)

Just I pick some numbers, but the answer is D:

Option 1: a=2, b=-3

QA: a-b = -1
QB: b-a = -3-2 = -5
so QA>QB

Option 1: a=-2, b=3

QA: a-b = 1
QB: b-a = 3+2 =5
so QB>QA

Why?

You got here:
QUANTITY A: (a-b)/(b-a)
QUANTITY B: (b-a)/(b-a)

From here, you basically multiplied both quantities by (b-a) to get:
QUANTITY A: (a-b)
QUANTITY B: (b-a)

This is where the problem lies.
We don't know whether (b-a) is POSITIVE or NEGATIVE.

As such, we cannot multiply both quantities by (b-a)

For more on this, watch the following:

Hi @GreenlightTestPrep Brent, thank you by your message!

It's a little confuse for me that I have just the option provided by Sandy/MGRE. Just I imagine myself doing the test and no be sure that I could use picking numbers or another strategy..


How do you do this exercise using picking numbers without a err as I had?
I tried two options, just because I was conscious that I do not know whether the values of a and b are positive or negative, integers of fractions.


Thank you

It's totally fine to test values. HOWEVER, you cannot first simplify the quantities as you did the first time.

We start with:
QUANTITY A: (a-b)/(b-a)
QUANTITY B: 1

Case 1
If a = 2, and b = -3, we get:
QUANTITY A: (2 - -3)/(-3 - 2) = 5/-5 = -1
QUANTITY B: 1
Quantity B is greater


Case 2
If a = -2, and b = 3, we get:
QUANTITY A: (-2 - 3)/(3 - -2) = -5/5 = -1
QUANTITY B: 1
Quantity B is greater


Case 3
If a = 1, and b = 7, we get:
QUANTITY A: (1 - 7)/(7 - 1) = -7/7 = -1
QUANTITY B: 1
Quantity B is greater


Case 4
If a = 11, and b = 2, we get:
QUANTITY A: (11 - 2)/(2 - 11) = 9/-9 = -1
QUANTITY B: 1
Quantity B is greater

Etc...

Does that help?

Cheers,
Brent

Why not just factor a -1 out of the denominator or numerator to get -1 * 1? Worked for me and super fast!

Didnt understand the condition a negative or b negative

Exactly.
That's how @leanhdung and @sandy (above) answered the question.

I'm not too sure what you're asking. Can you elaborate?

Whatever the values of \(a\) and \(b\), \(b-a\) will always be the negation of \(a-b\), and vice versa.

So Quantity A will always be \(-1\) and Quantity B is given as \(1\).

Therefore Quantity B will always be greater than Quantity A.

The answer is Choice B