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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Which of the following fractions has the greatest value?
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22 Dec 2022, 07:08
22 Dec 2022, 07:08
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Expert Reply
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Question Stats:
25% (01:44) correct
75% (01:43) wrong based on 4 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) \(\frac{75}{(3^4)(5^5)}\)
(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) \(\frac{75}{(3^4)(5^5)}\)
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: Which of the following fractions has the greatest value?
[#permalink]
24 Dec 2022, 02:17
24 Dec 2022, 02:17
1
Expert Reply
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
(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
gmatclubot
Re: Which of the following fractions has the greatest value? [#permalink]
24 Dec 2022, 02:17
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