Which of the following fractions has the greatest value

Question

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)}

Bunuel · Accepted Answer

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.

Temurkhon · Answer

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

Shiv2016 · Answer

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.

dave13 · Answer

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!

pushpitkc · Answer

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!

Funsho84 · Answer

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

deepajain90 · Answer

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 ?

unraveled · Answer

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.

KarishmaB · Answer

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.

TinaGMAT02 · Answer

Is there a shortcut for comparing fractions like this- 
147/200 and 150/203?
3/4 and 5/9?

Arvind123 · Answer

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

chetan2u · Answer

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.

Viorik · Answer

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.

ManishaPrepMinds · Answer

Step 1:
6 ÷ (2 × 5)2 = 6 ÷ 100 = 0.06
Step 2:
1 ÷ (2 × 5)2 × 2 = 0.5 ÷ 100 = 0.005
Step 3:
28 ÷ (2 × 5)2 × 5 = 28 ÷ 500 = 0.056
Alternatively, 28 ÷ (2 × 5)2 × 5 = 5.6 ÷ 100 = 0.056
Step 4:
62 ÷ (2 × 5)3 = 62 ÷ 1000 = 0.062
Step 5:
122 ÷ (2 × 5)3 × 2 = 122 ÷ 2000 = 0.061
Conclusion:
The greatest value is 0.062, which corresponds to Option D.

YolandaSami · Answer

Best approach - I solved this in 30 secs thanks to your method!!

Which of the following fractions has the greatest value

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Which of the following fractions has the greatest value

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