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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 06 Jun 2014, 12:45
2
7
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:44) correct 25% (01:43) wrong based on 206 sessions

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Which of the following fractions has the greatest value?

(A) \(\frac{1}{(3^2)(5^2)}\)
(B) \(\frac{2}{(3^2)(5^2)}\)
(C) \(\frac{7}{(3^3)(5^2)}\)
(D)\(\frac{45}{(3^3)(5^3)}\)
(E) \(\frac{75}{(3^4)(5^5)}\)
Spoiler: OA

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

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New post 06 Jun 2014, 13:05
2
MensaNumber wrote:
Which of the following fractions has the greatest value?

(A) \(\frac{1}{(3^2)(5^2)}\)
(B) \(\frac{2}{(3^2)(5^2)}\)
(C) \(\frac{7}{(3^3)(5^2)}\)
(D)\(\frac{45}{(3^3)(5^3)}\)
(E) \(\frac{75}{(3^4)(5^5)}\)


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

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

(C) \(\frac{7}{(3^3)(5^2)}=\frac{\approx{2.3}}{(3^2)(5^2)}\)

(D) \(\frac{45}{(3^3)(5^3)}=\frac{3}{(3^2)(5^2)}\)

(E) \(\frac{75}{(3^4)(5^5)}=\frac{1}{(3^3)(5^3)}\)

D is the greatest.

Answer: D.

Similar question: which-of-the-following-fractions-has-the-greatest-value-160537.html
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Re: Which of the following fractions has the greatest value?  [#permalink]

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New post 06 Jun 2014, 13:07
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Should be D.
Multiply Numerator and Denominator of B by 3 , You will get 6/3^3*5^2 which is less than c.
SO A and B are ruled out.
Simplify D and you will get 1/3*5^2 for E you will get 7/3^3*5^2
So you can easily compare the last three and get to D.
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Re: Which of the following fractions has the greatest value?  [#permalink]

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New post 11 Nov 2016, 12:30
Here what we can do is we can make the denominators constant and compare the fractions w.r.t their numerators.
The fraction with highest numerator will the highest one.
Lets make the dominator common

Let 3^2*5^2 be p

A) 1/p
B)2/p
C)(7/3 )/p
D)3/p
E)[75/(9*125)]/p

Numerator of D is the highest hence D is the Greatest fraction.

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

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New post 29 Jun 2019, 18:00
Multiply all by 3^4 * 5^5 (denominator of answer E)

A) 3^2 * 5^3 = 9 * 5^3
B) 2 * 3^2 * 5^3 = 18 * 5^3
C) 7 * 3 * 5^3 = 21 * 5^3
D) 45 * 3 * 5^2 = 27 * 5^3
E) 3 * 5^2

D is the largest value.
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Re: Which of the following fractions has the greatest value?   [#permalink] 29 Jun 2019, 18:00
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