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regards

I am not sure mine was the best approach but it did work.

Just by looking at the denominators, we know d will not be equal 0 or 2 because if d = (0 or 2), the denominators would be 0 which is undefined.

What happens if d is a positive number?

if d = 1 then you end up with 2 = -1 which is false.
If d is greater than 2, then 2/d will ALWAYS be a positive number. The numerator (2-d) will ALWAYS be a negative number and the denominator (d-2) will ALWAYS be a positive number. Since a positive number divided by a negative number always equals a negative number, you know d cannot be a positive number since d/2 is positive and 2-d/d-2 is negative.

What if d is less than 0?

When d is a negative number, 2/d will ALWAYS be negative. The numerator (2 - d) will ALWAYS be a positive number. The denominator (d - 2) will ALWAYS be negative. A positive number divided by a negative number will always be negative.

We do not know what d will be, but at least we know it will be a negative number because that is the only way both sides of the equation will have the same sign. Since 0 is more than any negative number, we can conclude quantity b is bigger.

I hope i didn't make a mistake here. If I did, I apologize in advance.

Great question.
It was tricky one.
Answer is B.

After solving the equation, we'll get
either d = 2 or d = -2

But d cannot be equals to 2, because the equation will become undefined.

Thus d = -2

So, Quantity B is greater.
Choice B correct.

great question, thanks, I just unconscionably assumed that it's D, since the d yielded -+2.

tricky question. I thought we could not do cross multiplication due to being unsure whether denominator was going to be 0 or not. It turns out we need to assume it's not going to be 0.

(a-b)/(b-a) is always equal to -1, so it simplifies to 2/d = -1, which means d is negative. Answer B.

You can cross multiply as shown above or range fractions to get the answer straight..
\(\frac{2}{d}= \frac{2-d}{d-2}\)..
\(\frac{2}{d}= \frac{-(d-2)}{(d-2)}\)=-1..
So \(\frac{2}{d}=-1\)..
Only possibility is d=-2

Hence B

\(\frac{2-d}{d-2}\) will always equal -1.

Try some values for that: Regardless whether positive, negative or 0, it will equal -1 (as both signs are inversed)


So, \(\frac{2}{d}\) = -1
Therefore, d=-2 and -2<0, hence answer B

why would not the answer be D?

D) The relationship cannot be determined from the information given.

To show that the answer is D, you must identify two values of d that yield conflicting comparisons (e.g., in one case Quantity A is greater, and in the other case Quantity B is greater)

\(\frac{2}{d} = \frac{2-d}{d-2}\)

\(\frac{2}{d} = \frac{2-d}{-(2-d)}\)

\(\frac{2}{d} = -\frac{2-d}{2-d} = -1\)

\(2 = -d\)

\(d = -2\)

Hence, answer is B

Hi Brent GreenlightTestPrep, question do not state d is positive/negative. Do we not need to concern about this before cross multiplication in this case? Thanks

The LHS and the RHS must be equal and d must be different from zero.

In this scenario you can cross multiply regardless