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# Which of these fractions has the greatest value?

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Which of these fractions has the greatest value? [#permalink]  26 Jun 2012, 06:22
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Which of these fractions has the greatest value?

(A) $$\frac{1}{(3*5)}$$

(B) $$\frac{2}{(3^2*5)}$$

(C) $$\frac{4}{(5^2*3)}$$

(D) $$\frac{8}{(3^2*5^2)}$$

(E) $$\frac{135}{(3^2*5^3)}$$

Source: http://www.gmathacks.com
[Reveal] Spoiler: OA

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Re: Which of these fractions has the greatest value? [#permalink]  26 Jun 2012, 06:31
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Which of these fractions has the greatest value?

Transform fractions so that they have the common denominator of $$3^2*5^3$$

(A) $$\frac{1}{(3*5)}=\frac{3*5^2}{3^2*5^3}=\frac{75}{3^2*5^3}$$;

(B) $$\frac{2}{(3^2*5)}=\frac{2*5^2}{3^2*5^3}=\frac{50}{3^2*5^3}$$;

(C) $$\frac{4}{(3*5^2)}=\frac{4*(3*5)}{3^2*5^3}=\frac{60}{3^2*5^3}$$;

(D) $$\frac{8}{(3^2*5^2)}=\frac{8*5}{3^2*5^3}=\frac{40}{3^2*5^3}$$;

(E) $$\frac{135}{(3^2*5^3)}$$.

Since option E has the greatest numerator then this fraction has the greatest value.

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Re: Which of these fractions has the greatest value? [#permalink]  28 Jan 2014, 13:42
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Re: Which of these fractions has the greatest value? [#permalink]  04 Mar 2014, 03:17
LCM of the denominator = Denominator of E

After multiplying the factors, see that numerator of all A,B,C,D is less than E

Having denominators same, more the value of numerator, more big would be the result

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Re: Which of these fractions has the greatest value? [#permalink]  29 Aug 2014, 03:05
metallicafan wrote:
Which of these fractions has the greatest value?

(A) $$\frac{1}{(3*5)}$$

(B) $$\frac{2}{(3^2*5)}$$

(C) $$\frac{4}{(5^2*3)}$$

(D) $$\frac{8}{(3^2*5^2)}$$

(E) $$\frac{135}{(3^2*5^3)}$$

Source: http://www.gmathacks.com

You can quickly rule out that A > B > C > D. Now between A and E. Multiply 1/3*5 with 3*5² ---> 75/3²*5³. Hence E is greater.

E.
Re: Which of these fractions has the greatest value?   [#permalink] 29 Aug 2014, 03:05
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