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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]

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26 Jun 2012, 07:22
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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]

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26 Jun 2012, 07:31
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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]

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28 Jan 2014, 14:42
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Re: Which of these fractions has the greatest value? [#permalink]

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04 Mar 2014, 04:17
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]

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29 Aug 2014, 04:05
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.

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Re: Which of these fractions has the greatest value? [#permalink]

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26 Sep 2015, 07:30
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Re: Which of these fractions has the greatest value? [#permalink]

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30 Apr 2017, 15:42
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Re: Which of these fractions has the greatest value? [#permalink]

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06 May 2017, 17:26
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) $$\frac{135}{(3^2*5^3)}$$

Let’s compare each fraction by getting a common denominator of 3^2 x 5^3.

A)

[1/(3 x 5)][(3^1 x 5^2)/(3^1 x 5^2)] = (3^1 x 5^2)/(3^2 x 5^3)

B)

[2/(3^2 x 5)][5^2/5^2] = (2 x 5^2)/(3^2 x 5^3)

C)

[4/(5^2 x 3)][(5^1 x 3^1)/(5^1 x 3^1)] = (4 x 5^1 x 3^1)/(3^2 x 5^3)

D)

[8/(3^2 x 5^2)][5^1/5^1] = (8 x 5^1)/(3^2 x 5^3)

E)

135/(3^2 x 5^3)

We see that 135/(3^2 x 5^3) is the largest fraction.

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Re: Which of these fractions has the greatest value?   [#permalink] 06 May 2017, 17:26
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# Which of these fractions has the greatest value?

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