# Question: Fraction Within a Fraction

## Comment on Fraction Within a Fraction

### Instead, could you begin by

Instead, could you begin by multiplying both sides by the denominator in Quantity A. Then subtract 5 from both sides to get 0 for Quantity A and 5/K as Quantity B? Since we know K>0 quantity B must always be greater than 0.

Thats how I came to my solution.

### That's a perfectly valid

That's a perfectly valid solution. In fact, it's exactly the same as the first solution in the video :-)

### Hi, is it possible to assume

Hi, is it possible to assume is that the dominator of quantity A multiplied by the numerator of quantity B should be equal to the dominator of Quantity B multiplied by the numerator of quantity A, then we can deduce from the result (-4) and the given information about K is that the dominator of quantity A is greater then 5 which means the result of whole fraction is less than 1?

### Your strategy is based on a

Your strategy is based on a strategy use for equations.

That is, you are starting with the assumption that the two quantities are equal, but the goal of QC question is to determine the relationship between the quantities.

Cheers,
Brent

### => 5/5+5/k => 5/5K+5/k=> 5k

=> 5/(5 + 5/k) = 5/(5k + 5/k) = 5k/(5k+5) = k/(k+1)
=> plug k=1, 2, and 10,100... in k/k+1 will be less than 1.
=> B is solution
Is this correct approach Brent?

### The only problem with that

The only problem with that approach is that, even though you tested three values of k, we still can't be 100% certain that Quantity B will ALWAYS be greater.

For more on this, start watching the following video at 2:48 - https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...