goforgmat wrote:

kolodits wrote:

We need the ratio: b/(f+7).

1. We have b/f = 6x/7x. Since we need 6x/(7x+7) and we don't know what is x, this is clearly insufficient.

2. According to this statement: b/(f+7)=(b-4)/f. After some manipulation somehow I got: b/(f+7)= 4/7. So apperantly this is sufficient. I'm really not sure it's correct.

Anyway, the answer is B.

Sent from my Redmi 4 using

GMAT Club Forum mobile apphow did you get the ratio b/(f+7)= 4/7 ?

Can you explain?

Sorry about that. It's a little bit difficult to show all the maths using the cell app.

According to statement 2: \(\frac{b}{(f+7)}\) = \(\frac{(b-4)}{f}\)

multiply by the denominator:\(b*f = (b-4)*(f+7)\)

\(b*f = b*f +7b - 4f -28\)

\(0 = 7b - 4f -28\)

\(7b = 4f + 28\)

\(\frac{7b}{(4f + 28)} = 1\)

Finally we have to divide by 7 and multiply by 4 to get:\(\frac{b}{(f+7)} = \frac{4}{7}\)

This is what we were looking for.

If we want to verify this (actually no match time for this during the exam) we can choose values which satisfy this ratio.

let's say b = 8 , f = 7 --> \(\frac{b}{(f+7)} = \frac{8}{(7+7)}= \frac{8}{14} = \frac{4}{7}\)

In addition:\(\frac{(b-4)}{f} = \frac{(8-4)}{7} = \frac{4}{7}\)

This works for values: b = 16, f = 21, since f+7 = 28, b-4 = 12, which fulfill the ratio we have found.

Hope this is clear.