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Which of these fractions has the greatest value?

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metallicafan
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Which of these fractions has the greatest value? [#permalink] New post  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: https://www.gmathacks.com
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Bunuel
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Re: Which of these fractions has the greatest value? [#permalink] New post  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.

Answer: E.
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Re: Which of these fractions has the greatest value? [#permalink] New post  18 Jun 2018, 00:48
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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: https://www.gmathacks.com


When you multiply a positive number by a number less than 1, it becomes smaller. When you multiply it by a number greater than 1, it becomes larger.
e.g. 10*(1/2) = 5
10*(3/2) = 15

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

(B) \(\frac{2}{(3^2*5)} = \frac{1}{3*5}*\frac{2}{3}\) (less than option A)

(C) \(\frac{4}{(5^2*3)} = \frac{1}{3*5}*\frac{4}{5}\) (less than option A)

(D) \(\frac{8}{(3^2*5^2)} = \frac{1}{3*5}*\frac{8}{15}\) (less than option A)

(E) \(\frac{135}{(3^2*5^3)} = \frac{1}{3*5}*\frac{135}{75}\) (greater than option A)

Answer (E)
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Re: Which of these fractions has the greatest value? [#permalink] New post  16 Jun 2017, 22:03
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We can see that the HCF of Denominators of all the given fractions is 3*5 (every denominator has at least one 3 and one 5). If we take out 3*5 common from each denominator and compare the rest, here's what we are left with:

A) becomes 1

B) becomes 2/3 (less than 1)

C) becomes 4/5 (less than 1)

D) becomes 8/15 (less than 1)

E) becomes 135/75.. which is greater than 1

So obviously E is largest, hence E answer
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Re: Which of these fractions has the greatest value? [#permalink] New post  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
Answer = E
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Re: Which of these fractions has the greatest value? [#permalink] New post  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: https://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.
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Re: Which of these fractions has the greatest value? [#permalink] New post  06 May 2017, 17:26
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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.

Answer: E
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Re: Which of these fractions has the greatest value? [#permalink] New post  16 Jun 2017, 18:10
I did this a more visual way comparing each to A) 1/(3*5):

B) numerator doubles, but denominator triples: A wins
C) numerator quadruples, but denominator increases by factor of 5: A wins
D) numerator increases by factor of 8, but denominator increases by factor of 15: A wins
E) numerator increases by factor of 135, while denominator only increases by factor of 75: E wins

Answer E.
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