Which of these fractions has the greatest value?

Question

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

Bunuel · Accepted Answer

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.

PareshGmat · Answer

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

unceldolan · Answer

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.

ScottTargetTestPrep · Answer

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

A)

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

B)

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

C)

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

D)

= (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

fiel9882 · Answer

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.

amanvermagmat · Answer

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

KarishmaB · Answer

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)

bumpbot · Answer

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Which of these fractions has the greatest value?

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Which of these fractions has the greatest value?

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