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Which of the following fractions has the greatest value

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Which of the following fractions has the greatest value  [#permalink]

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New post Updated on: 29 May 2017, 21:38
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A
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C
D
E

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Which of the following fractions has the greatest value?


(A) \(\frac{6}{(2^2)(5^2)}\)

(B) \(\frac{1}{(2^3)(5^2)}\)

(C) \(\frac{28}{(2^2)(5^3)}\)

(D) \(\frac{62}{(2^3)(5^3)}\)

(E) \(\frac{122}{(2^4)(5^3)}\)

Originally posted by jlgdr on 25 Sep 2013, 17:25.
Last edited by Bunuel on 29 May 2017, 21:38, edited 2 times in total.
Added the OA.
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Re: Which of the following fractions has the greatest value  [#permalink]

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New post 26 Sep 2013, 01:17
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jlgdr wrote:
Which of the following fractions has the greatest value?

(A) \(\frac{6}{(2^2)(5^2)}\)
(B) \(\frac{1}{(2^3)(5^2)}\)
(C) \(\frac{28}{(2^2)(5^3)}\)
(D) \(\frac{62}{(2^3)(5^3)}\)
(E) \(\frac{122}{(2^4)(5^3)}\)


The least common denominator is (2^4)(5^3).

(A) \(\frac{6}{(2^2)(5^2)}=\frac{6*2^2*5}{(2^4)(5^3)}=\frac{120}{(2^4)(5^3)}\)

(B) \(\frac{1}{(2^3)(5^2)}=\frac{2*5}{(2^4)(5^3)}=\frac{10}{(2^4)(5^3)}\)

(C) \(\frac{28}{(2^2)(5^3)}=\frac{28*2^2}{(2^4)(5^3)}=\frac{112}{(2^4)(5^3)}\)

(D) \(\frac{62}{(2^3)(5^3)}=\frac{62*2}{(2^4)(5^3)}=\frac{124}{(2^4)(5^3)}\)

(E) \(\frac{122}{(2^4)(5^3)}\)

Now, we only need to compare the numerators: 124 is the greatest.

Answer: D.
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Re: Which of the following fractions has the greatest value  [#permalink]

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New post 09 Feb 2015, 23:37
the highest numerator and lowest denominator wins:

A) 6/100

B) 1/200 (certainly less than A)

C) 28/500 (denominator 5 times more but numerator less than 5 times than A, so less than A)

D) 62/1000 (denominator 10 times more but numerator >10 times more than A, so more than A)

E) 122/2000 (denominator 2 times more but numerator <2 times more than D, so less than D)


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

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New post 22 Jun 2017, 09:31
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jlgdr wrote:
Which of the following fractions has the greatest value?


(A) \(\frac{6}{(2^2)(5^2)}\)

(B) \(\frac{1}{(2^3)(5^2)}\)

(C) \(\frac{28}{(2^2)(5^3)}\)

(D) \(\frac{62}{(2^3)(5^3)}\)

(E) \(\frac{122}{(2^4)(5^3)}\)


2*5= 10

Just looking at the denominator. Separate the 2*5 combinations.

(A) 2^2 * 5^2= 100
0.06

(B) 2^2 *5^2= 100
Now we left one 2 because there was no 5 for it. Divide 1 by 2.
0.005

(C) 2^2 *5^2= 100
Now we left one 5. So let's divide 28 by 5.
0.056

(D) 2^3 *5^3= 1000
0.062

(E) 2^3 *5^3= 1000
Same method.
0.061

Now it becomes easy to select the answer.
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Re: Which of the following fractions has the greatest value  [#permalink]

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New post 07 Apr 2018, 04:25
Bunuel wrote:
jlgdr wrote:
Which of the following fractions has the greatest value?

(A) \(\frac{6}{(2^2)(5^2)}\)
(B) \(\frac{1}{(2^3)(5^2)}\)
(C) \(\frac{28}{(2^2)(5^3)}\)
(D) \(\frac{62}{(2^3)(5^3)}\)
(E) \(\frac{122}{(2^4)(5^3)}\)


The least common denominator is (2^4)(5^3).

(A) \(\frac{6}{(2^2)(5^2)}=\frac{6*2^2*5}{(2^4)(5^3)}=\frac{120}{(2^4)(5^3)}\)

(B) \(\frac{1}{(2^3)(5^2)}=\frac{2*5}{(2^4)(5^3)}=\frac{10}{(2^4)(5^3)}\)

(C) \(\frac{28}{(2^2)(5^3)}=\frac{28*2^2}{(2^4)(5^3)}=\frac{112}{(2^4)(5^3)}\)

(D) \(\frac{62}{(2^3)(5^3)}=\frac{62*2}{(2^4)(5^3)}=\frac{124}{(2^4)(5^3)}\)

(E) \(\frac{122}{(2^4)(5^3)}\)

Now, we only need to compare the numerators: 124 is the greatest.

Answer: D.


H Bunuel hope you are enjoyong weekend :)

can you please explain how do additional numbers with exponents appear in numerator :)

\(\frac{6}{(2^2)(5^2)}=\frac{6*2^2*5}{(2^4)(5^3)}=\frac{120}{(2^4)(5^3)}\)

many thanks! :)
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Which of the following fractions has the greatest value  [#permalink]

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New post 07 Apr 2018, 05:31
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dave13 wrote:
Bunuel wrote:
jlgdr wrote:
Which of the following fractions has the greatest value?

(A) \(\frac{6}{(2^2)(5^2)}\)
(B) \(\frac{1}{(2^3)(5^2)}\)
(C) \(\frac{28}{(2^2)(5^3)}\)
(D) \(\frac{62}{(2^3)(5^3)}\)
(E) \(\frac{122}{(2^4)(5^3)}\)


The least common denominator is (2^4)(5^3).

(A) \(\frac{6}{(2^2)(5^2)}=\frac{6*2^2*5}{(2^4)(5^3)}=\frac{120}{(2^4)(5^3)}\)

(B) \(\frac{1}{(2^3)(5^2)}=\frac{2*5}{(2^4)(5^3)}=\frac{10}{(2^4)(5^3)}\)

(C) \(\frac{28}{(2^2)(5^3)}=\frac{28*2^2}{(2^4)(5^3)}=\frac{112}{(2^4)(5^3)}\)

(D) \(\frac{62}{(2^3)(5^3)}=\frac{62*2}{(2^4)(5^3)}=\frac{124}{(2^4)(5^3)}\)

(E) \(\frac{122}{(2^4)(5^3)}\)

Now, we only need to compare the numerators: 124 is the greatest.

Answer: D.


H Bunuel hope you are enjoyong weekend :)

can you please explain how do additional numbers with exponents appear in numerator :)

\(\frac{6}{(2^2)(5^2)}=\frac{6*2^2*5}{(2^4)(5^3)}=\frac{120}{(2^4)(5^3)}\)

many thanks! :)



Hey dave13

Whenever we have 2 fractions and have been asked to find which fraction has the greatest value.
One way of comparing fractions is by making their bases equal. In order to make the bases equal,
we can multiply and divide the fraction by a common number.

For example, \(\frac{4}{5}\) can also be written as \(\frac{4*3}{5*3} = \frac{12}{15}\)
As you see, we multiply and divide both the numerator and denominator by 3.

Hope this helps you!
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Which of the following fractions has the greatest value  [#permalink]

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New post 07 Apr 2018, 11:42
I multiplied each expression by 5^3.

I then multiplied each expression by 4.

B was clearly the smallest so I crossed it out.

A= 30
C= 28
D = 31
E = 30.5

Answer d
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Re: Which of the following fractions has the greatest value  [#permalink]

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Re: Which of the following fractions has the greatest value   [#permalink] 12 Apr 2019, 06:54
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