If 25/(x/5) = (1/25)/125 then x = ?

I would bet that the trap answer is B. We cannot cancel diagonally ACROSS an equals sign when dealing with equivalent fractions or equivalent fractional expressions.*

I. Cross multiply
We can cross multiply complex fractions. \(\frac{a}{b}=\frac{c}{d}:(a*d)=(b*c)\)
Treat the two simple fractions as \(b\) and \(c\)

\(\frac{25}{(\frac{x}{5})} = \frac{(\frac{1}{25})}{125}\)

\((\frac{x}{5}*\frac{1}{25})=(25*125)\)
Clear LHS denominator: (Both sides) * (5*25)
\(x=(25*125*5*25)=(5^2*5^3*5^1*5^2)=\)
\(5^{(2+3+1+2)}=5^8\)

Answer D

II. Simplify first
Simplify the complex fractions, then cross multiply

\(\frac{25}{(\frac{x}{5})} = \frac{(\frac{1}{25})}{125}\)
LHS:\(\frac{25}{(\frac{x}{5})}=(25*\frac{5}{x})=\frac{25*5}{x}\)

RHS: \(\frac{(\frac{1}{25})}{125}=(\frac{1}{25}*\frac{1}{125})=\frac{1}{125*25}\)

Equate: \(\frac{25*5}{x}=\frac{1}{125*25}\)
Do not cancel diagonally, i.e. LHS numerator and RHS.

Cross multiplication IS allowed, thus
\(x=(25*5*25*125)=(5^2*5^1*5^2*5^3)=5^8\)

Answer D

*For an informative post on what can and cannot be cancelled, see the GMAT Club blog, mikemcgarry , GMAT Quant, Rates and Ratios, here

If we multiply the left side of the equation by 5/5 and the right side of the equation by 25/25, we have:

125/x = 1/(25 * 125)

Cross-multiplying, we obtain:

x = 125 * 25 * 125 = 5^3 * 5^2 * 5^3 = 5^8

Answer: D