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If 25/(x/5) = (1/25)/125 then x = ?
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22 Jul 2018, 23:33
22 Jul 2018, 23:33
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If \(\frac{25}{(\frac{x}{5})} = \frac{(\frac{1}{25})}{125}\) then x = ?
(A) 5^(-2)
(B) 5^2
(C) 5^3
(D) 5^8
(E) 5^11
(A) 5^(-2)
(B) 5^2
(C) 5^3
(D) 5^8
(E) 5^11
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Re: If 25/(x/5) = (1/25)/125 then x = ?
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22 Jul 2018, 23:47
22 Jul 2018, 23:47
2
Kudos
Bunuel wrote:
If \(\frac{25}{(\frac{x}{5})} = \frac{(\frac{1}{25})}{125}\) then x = ?
(A) 5^(-2)
(B) 5^2
(C) 5^3
(D) 5^8
(E) 5^11
(A) 5^(-2)
(B) 5^2
(C) 5^3
(D) 5^8
(E) 5^11
OA: D
\(\frac{{5^2}}{{x*5^{-1}}}= \frac{{5^{-2}}}{{5^3}}\)
\(x = \frac{{{5^2}*{5^3}}}{{5^{-1}*5^{-2}}}\)
\(x = \frac{{5^5}}{{5^{-3}}}=5^5*5^3=5^8\)
Re: If 25/(x/5) = (1/25)/125 then x = ?
[#permalink]
24 Jul 2018, 12:06
24 Jul 2018, 12:06
Expert Reply
Bunuel wrote:
If \(\frac{25}{(\frac{x}{5})} = \frac{(\frac{1}{25})}{125}\) then x = ?
(A) 5^(-2)
(B) 5^2
(C) 5^3
(D) 5^8
(E) 5^11
(A) 5^(-2)
(B) 5^2
(C) 5^3
(D) 5^8
(E) 5^11
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
