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Which of the following fractions has the greatest value

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jlgdr
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Which of the following fractions has the greatest value [#permalink] New post   Updated on: 29 May 2017, 21:38
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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) \(\frac{122}{(2^4)(5^3)}\)
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D

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] 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] New post   09 Feb 2015, 23:37
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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)


D
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Re: Which of the following fractions has the greatest value [#permalink] 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] 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] 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] 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] New post   02 Oct 2020, 09:07
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Hi Bunuel VeritasKarishma

I took 2^2 & 5^2 as common and was left with 6,1/2,28/5,31/5 & 61/10.

Compared these fractions - 6,0.5,5.6,6.2 & 6.1, and arrived at the correct answer.

Is my approach correct ?
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Which of the following fractions has the greatest value [#permalink] New post   05 Oct 2020, 02:14
deepajain90 wrote:
Hi Bunuel VeritasKarishma

I took 2^2 & 5^2 as common and was left with 6,1/2,28/5,31/5 & 61/10.

Compared these fractions - 6,0.5,5.6,6.2 & 6.1, and arrived at the correct answer.

Is my approach correct ?

deepajain90
There's nothing wrong in your approach.
As long as you stick with either numerator or denominator of either of the options it is good. You can take denominator as 100 or 1000 or 2000 or anything else and solve. Our target is to do as little math as possible. If done so the question can be solved in less than a minute also, though solving in less time should not be the target.
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Re: Which of the following fractions has the greatest value [#permalink] New post   06 Oct 2020, 04:29
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deepajain90 wrote:
Hi Bunuel VeritasKarishma

I took 2^2 & 5^2 as common and was left with 6,1/2,28/5,31/5 & 61/10.

Compared these fractions - 6,0.5,5.6,6.2 & 6.1, and arrived at the correct answer.

Is my approach correct ?


Yes, as long as what you are taking common is positive, it is fine. If all terms have negative sign, the relation reverses.
Also, eliminate options as you go along instead of calculating all.

6 greater than 1/2. Eliminate 1/2
6 is 30/5 so eliminate 28/5
31/5 is greater so eliminate 6.
31/5 is 62/10 so eliminate 61/10.
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Re: Which of the following fractions has the greatest value [#permalink] New post   31 Dec 2021, 03:51
Is there a shortcut for comparing fractions like this-
147/200 and 150/203?
3/4 and 5/9?
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Re: Which of the following fractions has the greatest value [#permalink] New post   01 Jan 2022, 04:56
ToboBoto wrote:
Is there a shortcut for comparing fractions like this-
147/200 and 150/203?
3/4 and 5/9?


Bunuel KarishmaB chetan2u
Is there any faster ways we can use for comparing the fractions?
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Re: Which of the following fractions has the greatest value [#permalink] New post   01 Jan 2022, 08:59
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Arvind123 wrote:
ToboBoto wrote:
Is there a shortcut for comparing fractions like this-
147/200 and 150/203?
3/4 and 5/9?


Bunuel KarishmaB chetan2u
Is there any faster ways we can use for comparing the fractions?



Hi

I’ll just pick the two fractions given.

\(\frac{147}{200}\) and \(\frac{150}{203}=\frac{147+3}{200+3}>\frac{147}{200}\).
You can check the fractions in my signature. May help you.

3/4 and 5/9 or such small fractions can be done by cross multiplying.
9*3 and 4*5
So 3/4 is greater.
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Re: Which of the following fractions has the greatest value [#permalink] New post   16 Dec 2022, 13:58
Multiply all answers by 100. Thus, we will receive 6, 1/2, 28/5, 62/10, and 122/20. The greatest value is 6.2. The answer is D.
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Re: Which of the following fractions has the greatest value [#permalink] New post   13 Mar 2024, 07:55
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Re: Which of the following fractions has the greatest value [#permalink]
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